Plane strain problem in microstretch elastic solid
Rajneesh Kumar; Ranjit Singh; T K Chadha
2003-12-01
The eigenvalue approach is developed for the two-dimensional plane strain problem in a microstretch elastic medium. Applying Laplace and Fourier transforms, an inﬁnite space subjected to a concentrated force is studied. The integral transforms are inverted using a numerical technique to get displacement, force stress, couple stress and ﬁrst moment, which are also shown graphically. The results of micropolar elasticity are deduced as a special case from the present formulation.
Maximum-Entropy Meshfree Method for Compressible and Near-Incompressible Elasticity
Ortiz, A; Puso, M A; Sukumar, N
2009-09-04
Numerical integration errors and volumetric locking in the near-incompressible limit are two outstanding issues in Galerkin-based meshfree computations. In this paper, we present a modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision. Secondly, a locking-free small-strain elasticity formulation for meshfree methods is proposed, which draws on developments in assumed strain methods and nodal integration techniques. In this study, maximum-entropy basis functions are used; however, the generality of our approach permits the use of any meshfree approximation. Various benchmark problems in two-dimensional compressible and near-incompressible small strain elasticity are presented to demonstrate the accuracy and optimal convergence in the energy norm of the maximum-entropy meshfree formulation.
Euler-Lagrange Elasticity: elasticity without stress or strain
Hardy, Humphrey
2014-03-01
A Euler-Lagrange (E-L) approach to elasticity is proposed that produces differential equations of elasticity without the need to define stress or strain tensors. The positions of the points within the body are the independent parameters instead of strain. Force replaces stress. The advantage of this approach is that the E-L differential equations are the same for both infinitesimal and finite deformations. Material properties are expressed in terms of the energy of deformation. The energy is expressed as a function of the principal invariants of the deformation gradient tensor. This scalar invariant representation of the energy of deformation enters directly into the E-L differential equations so that there is no need to define fourth order tensor material properties. By experimentally measuring the force and displacement of materials the functional form of the energy of deformation can be determined. The E-L differential equations can be input directly into finite element, finite difference, or other numerical models. If desired, stress and stain can be calculated as dependent parameters.
Models for elastic shells with incompatible strains
2012-01-01
The three-dimensional shapes of thin lamina such as leaves, flowers, feathers, wings etc, are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric, given on the thin sheet as a function of location in the central plane and also across its thickness. The shape is then a consequence of elastic energy minimization on the frustrated geometrical object. Here we provide a rigorous derivation of the asymptotic theories f...
Rolling motion of an elastic cylinder induced by elastic strain gradients
Chen, Lei; Chen, Shaohua
2014-10-01
Recent experiment shows that an elastic strain gradient field can be utilized to transport spherical particles on a stretchable substrate by rolling, inspired by which a generalized plane-strain Johnson-Kendall-Roberts model is developed in this paper in order to verify possible rolling of an elastic cylinder adhering on an elastic substrate subject to a strain gradient. With the help of contact mechanics, closed form solutions of interface tractions, stress intensity factors, and corresponding energy release rates in the plane-strain contact model are obtained, based on which a possible rolling motion of an elastic cylinder induced by strain gradients is found and the criterion for the initiation of rolling is established. The theoretical prediction is consistent well with the existing experimental observation. The result should be helpful for understanding biological transport mechanisms through muscle contractions and the design of transport systems with strain gradient.
PLASTICITY AND NON-LINEAR ELASTIC STRAINS
conditions existing in plane waves in an extended medium to give the time rate of change of stress as a function of the time rate of change of strain, the stress invariants, the total strain and the plastic strain. (Author)
GLOBAL ATTRACTOR FOR THE NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES
戴正德; 杜先云
2001-01-01
In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and thefiniteness of the Hausdorff and the fractal dimensions of the attractors.
Modeling elastic anisotropy in strained heteroepitaxy
Krishna Dixit, Gopal; Ranganathan, Madhav
2017-09-01
Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the Ge0.25 Si0.75 on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to facets on the surface.
Modeling elastic anisotropy in strained heteroepitaxy.
Dixit, Gopal Krishna; Ranganathan, Madhav
2017-09-20
Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the [Formula: see text] [Formula: see text] on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to [Formula: see text] facets on the surface.
Evidence for residual elastic strain in deformed natural quartz
Kunz, Martin; Chen, Kai; Tamura,Nobumichi; Wenk, Hans-Rudolf
2009-01-30
Residual elastic strain in naturally deformed, quartz-containing rocks can be measured quantitatively in a petrographic thin section with high spatial resolution using Laue microdiffraction with white synchrotron x-rays. The measurements with a resolution of one micrometer allow the quantitative determination of the deviatoric strain tensor as a function of position within the crystal investigated. The observed equivalent strain values of 800-1200 microstrains represent a lower bound of the actual preserved residual strain in the rock, since the stress component perpendicular to the cut sample surface plane is released. The measured equivalent strain translates into an equivalent stress in the order of {approx} 50 MPa.
Maximum relative height of elastic interfaces in random media.
Rambeau, Joachim; Bustingorry, Sebastian; Kolton, Alejandro B; Schehr, Grégory
2011-10-01
The distribution of the maximal relative height (MRH) of self-affine one-dimensional elastic interfaces in a random potential is studied. We analyze the ground-state configuration at zero driving force, and the critical configuration exactly at the depinning threshold, both for the random-manifold and random-periodic universality classes. These configurations are sampled by exact numerical methods, and their MRH distributions are compared with those with the same roughness exponent and boundary conditions, but produced by independent Fourier modes with normally distributed amplitudes. Using Pickands' theorem we derive an exact analytical description for the right tail of the latter. After properly rescaling the MRH distributions we find that corrections from the Gaussian independent modes approximation are, in general, small, as previously found for the average width distribution of depinning configurations. In the large size limit all corrections are finite except for the ground state in the random-periodic class whose MRH distribution becomes, for periodic boundary conditions, indistinguishable from the Airy distribution. We find that the MRH distributions are, in general, sensitive to changes of boundary conditions.
The atomistic representation of first strain-gradient elastic tensors
Admal, Nikhil Chandra; Marian, Jaime; Po, Giacomo
2017-02-01
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical second-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products of relative atomic positions. Moreover, all expressions are local, in the sense that they depend only on the atomic neighborhood of a lattice site. Our results emanate from the condition of energetic equivalence between continuum and atomistic representations of a crystal, when the kinematics of the latter is governed by the Cauchy-Born rule. Using the derived expressions, we prove that the odd-order tensors vanish if the lattice basis admits central-symmetry. The analytical expressions are implemented as a KIM compliant algorithm to compute the strain gradient elastic tensors for various materials. Numerical results are presented to compare representative interatomic potentials used in the literature for cubic crystals, including simple lattices (fcc Al and Cu and bcc Fe and W) and multi-lattices (diamond-cubic Si). We observe that central potentials exhibit generalized Cauchy relations for the rank-six tensor of strain-gradient elastic moduli. In addition, this tensor is found to be indefinite for many potentials. We discuss the relationship between indefiniteness and material stability. Finally, the atomistic representations are specialized to central potentials in simple lattices. These expressions are used with analytical potentials to study the sensitivity of the elastic tensors to the choice of the cutoff radius.
Approaching the ideal elastic strain limit in silicon nanowires.
Zhang, Hongti; Tersoff, Jerry; Xu, Shang; Chen, Huixin; Zhang, Qiaobao; Zhang, Kaili; Yang, Yong; Lee, Chun-Sing; Tu, King-Ning; Li, Ju; Lu, Yang
2016-08-01
Achieving high elasticity for silicon (Si) nanowires, one of the most important and versatile building blocks in nanoelectronics, would enable their application in flexible electronics and bio-nano interfaces. We show that vapor-liquid-solid-grown single-crystalline Si nanowires with diameters of ~100 nm can be repeatedly stretched above 10% elastic strain at room temperature, approaching the theoretical elastic limit of silicon (17 to 20%). A few samples even reached ~16% tensile strain, with estimated fracture stress up to ~20 GPa. The deformations were fully reversible and hysteresis-free under loading-unloading tests with varied strain rates, and the failures still occurred in brittle fracture, with no visible sign of plasticity. The ability to achieve this "deep ultra-strength" for Si nanowires can be attributed mainly to their pristine, defect-scarce, nanosized single-crystalline structure and atomically smooth surfaces. This result indicates that semiconductor nanowires could have ultra-large elasticity with tunable band structures for promising "elastic strain engineering" applications.
Effect of large elastic strains on cavitation instability predictions for elastic-plastic solids
Tvergaard, Viggo
1999-01-01
For an infinite solid containing a void, the cavitation instability limit is defined as the remote stress-and strain state, at which the void grows without bound, driven by the elastic energy stored in the surrounding material. Such cavitation limits have been analysed by a number of authors...
Measuring the elastic strain of individual grains in polycrystalline materials
on some of the important aspects you have to take into account in order to determine the strain tensors of the individual grains to the desired accuracy of 10-4. The first thing is how to handle the peak overlaps that will inevitably occur, especially for textured and/or deformed materials. Secondly...... within FitAllB. In addition to the centre-of-mass grain positions, orientations and strain tensors, FitAllB also calculates the relative volumes of the grains based on the peak intensities, so using a tessellation routine a crude 3D map of the elastic strain in the polycrystal can be obtained....
Medical ultrasound: imaging of soft tissue strain and elasticity.
Wells, Peter N T; Liang, Hai-Dong
2011-11-07
After X-radiography, ultrasound is now the most common of all the medical imaging technologies. For millennia, manual palpation has been used to assist in diagnosis, but it is subjective and restricted to larger and more superficial structures. Following an introduction to the subject of elasticity, the elasticity of biological soft tissues is discussed and published data are presented. The basic physical principles of pulse-echo and Doppler ultrasonic techniques are explained. The history of ultrasonic imaging of soft tissue strain and elasticity is summarized, together with a brief critique of previously published reviews. The relevant techniques-low-frequency vibration, step, freehand and physiological displacement, and radiation force (displacement, impulse, shear wave and acoustic emission)-are described. Tissue-mimicking materials are indispensible for the assessment of these techniques and their characteristics are reported. Emerging clinical applications in breast disease, cardiology, dermatology, gastroenterology, gynaecology, minimally invasive surgery, musculoskeletal studies, radiotherapy, tissue engineering, urology and vascular disease are critically discussed. It is concluded that ultrasonic imaging of soft tissue strain and elasticity is now sufficiently well developed to have clinical utility. The potential for further research is examined and it is anticipated that the technology will become a powerful mainstream investigative tool.
Karimi, Alireza; Navidbakhsh, Mahdi; Alizadeh, Mansour; Razaghi, Reza
2014-10-01
There have been different stress-strain definitions to measure the elastic modulus of spongy materials, especially polyvinyl alcohol (PVA) sponge. However, there is no agreement as to which stress-strain definition should be implemented. This study was aimed to show how different results are given by the various definitions of stress-strain used, and to recommend a specific definition when testing spongy materials. A fabricated PVA sponge was subjected to a series of tensile tests in order to measure its mechanical properties. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were used to determine the elastic modulus. The results revealed that the Almansi-Hamel strain definition exhibited the highest non-linear stress-strain relation and, as a result, may overestimate the elastic modulus at different stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress). The Green-St. Venant strain definition failed to address the non-linear stress-strain relation using different definitions of stress and invoked an underestimation of the elastic modulus values. Engineering stress and strain definitions were only valid for small strains and displacements, which make them impractical when analyzing spongy materials. The results showed that the effect of varying the stress definition on the maximum stress measurements was significant but not when calculating the elastic modulus. It is important to consider which stress-strain definition is employed when characterizing the mechanical properties of spongy materials. Although the true stress-true strain definition exhibits a non-linear relation, we favor it in spongy materials mechanics as it gives more accurate measurements of the material's response using the instantaneous values.
Semi-analytical solution to plane strain loading of elastic layered coating on an elastic substrate
Thamarai Selvan Vasu; Tanmay K Bhandakkar
2015-10-01
The plane strain loading of a linear elastic layered coating halfspace is solved semi-analytically through a combination of Airy stress function and Fourier transforms and highly simplified and compact expressions for displacement and stresses in layer and substrate are presented in terms of pressure distribution in the loaded region. The results are applied to study the influence of layer thickness and mismatch in elastic modulus between layer and substrate on the stresses and displacement during loading of layered coating system. Lastly the effect of degree of smoothness of the pressure profile on the plane strain loading response of layered coating system is simulated through three different pressure profiles for a fixed total load and loading zone length.
Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticity
Lazar, Markus
2016-01-01
In isotropic strain gradient elasticity, we decompose the strain gradient tensor into its irreducible pieces under the n-dimensional orthogonal group O(n). Using the Young tableau method for traceless tensors, four irreducible pieces (n>2), which are canonical, are obtained. In three dimensions, the strain gradient tensor can be decomposed into four irreducible pieces with 7+5+3+3 independent components whereas in two dimensions, the strain gradient tensor can be decomposed into three irreducible pieces with 2+2+2 independent components. The knowledge of these irreducible pieces is extremely useful when setting up constitutive relations and strain energy.
Tunable thermoelectric transport in nanomeshes via elastic strain engineering
Piccione, Brian; Gianola, Daniel S., E-mail: gianola@seas.upenn.edu [Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)
2015-03-16
Recent experimental explorations of silicon nanomeshes have shown that the unique metastructures exhibit reduced thermal conductivity while preserving bulk electrical conductivity via feature sizes between relevant phonon and electron mean free paths, aiding in the continued promise that nanometer-scale engineering may further enhance thermoelectric behavior. Here, we introduce a strategy for tuning thermoelectric transport phenomena in semiconductor nanomeshes via heterogeneous elastic strain engineering, using silicon as a model material for demonstration of the concept. By combining analytical models for electron mobility in uniformly stressed silicon with finite element analysis of strained silicon nanomeshes in a lumped physical model, we show that the nonuniform and multiaxial strain fields defined by the nanomesh geometry give rise to spatially varying band shifts and warping, which in aggregate accelerate electron transport along directions of applied stress. This allows for global electrical conductivity and Seebeck enhancements beyond those of homogenous samples under equivalent far-field stresses, ultimately increasing thermoelectric power factor nearly 50% over unstrained samples. The proposed concept and structures—generic to a wide class of materials with large dynamic ranges of elastic strain in nanoscale volumes—may enable a new pathway for active and tunable control of transport properties relevant to waste heat scavenging and thermal management.
Controlling surface reactions with nanopatterned surface elastic strain.
Li, Zhisheng; Potapenko, Denis V; Osgood, Richard M
2015-01-27
The application of elastic lattice strain is a promising approach for tuning material properties, but the attainment of a systematic approach for introducing a high level of strain in materials so as to study its effects has been a major challenge. Here we create an array of intense locally varying strain fields on a TiO2 (110) surface by introducing highly pressurized argon nanoclusters at 6-20 monolayers under the surface. By combining scanning tunneling microscopy imaging and the continuum mechanics model, we show that strain causes the surface bridge-bonded oxygen vacancies (BBOv), which are typically present on this surface, to be absent from the strained area and generates defect-free regions. In addition, we find that the adsorption energy of hydrogen binding to oxygen (BBO) is significantly altered by local lattice strain. In particular, the adsorption energy of hydrogen on BBO rows is reduced by ∼ 35 meV when the local crystal lattice is compressed by ∼ 1.3%. Our results provide direct evidence of the influence of strain on atomic-scale surface chemical properties, and such effects may help guide future research in catalysis materials design.
Second strain gradient elasticity of nano-objects
Cordero, Nicolas M.; Forest, Samuel; Busso, Esteban P.
2016-12-01
Mindlin's second strain gradient continuum theory for isotropic linear elastic materials is used to model two different kinds of size-dependent surface effects observed in the mechanical behaviour of nano-objects. First, the existence of an initial higher order stress represented by Mindlin's cohesion parameter, b0, makes it possible to account for the relaxation behaviour of traction-free surfaces. Second, the higher order elastic moduli, ci, coupling the strain tensor and its second gradient are shown to significantly affect the apparent elastic properties of nano-beams and nano-films under uni-axial loading. These two effects are independent from each other and allow for separated identification of the corresponding material parameters. Analytical results are provided for the size-dependent apparent shear modulus of a nano-thin strip under shear. Finite element simulations are then performed to derive the dependence of the apparent Young modulus and Poisson ratio of nano-films with respect to their thickness, and to illustrate hole free surface relaxation in a periodic nano-porous material.
Retaining Large and Adjustable Elastic Strains of Kilogram-Scale Nb Nanowires.
Hao, Shijie; Cui, Lishan; Wang, Hua; Jiang, Daqiang; Liu, Yinong; Yan, Jiaqiang; Ren, Yang; Han, Xiaodong; Brown, Dennis E; Li, Ju
2016-02-10
Individual metallic nanowires can sustain ultralarge elastic strains of 4-7%. However, achieving and retaining elastic strains of such magnitude in kilogram-scale nanowires are challenging. Here, we find that under active load, ∼ 5.6% elastic strain can be achieved in Nb nanowires embedded in a metallic matrix deforming by detwinning. Moreover, large tensile (2.8%) and compressive (-2.4%) elastic strains can be retained in kilogram-scale Nb nanowires when the external load was fully removed, and adjustable in magnitude by processing control. It is then demonstrated that the retained tensile elastic strains of Nb nanowires can increase their superconducting transition temperature and critical magnetic field, in comparison with the unstrained original material. This study opens new avenues for retaining large and tunable elastic strains in great quantities of nanowires and elastic-strain-engineering at industrial scale.
Retaining Large and Adjustable Elastic Strains of Kilogram-Scale Nb Nanowires
Hao, Shijie; Cui, Lishan; Wang, Hua; Jiang, Daqiang; Liu, Yinong; Yan, Jiaqiang; Ren, Yang; Han, Xiaodong; Brown, Dennis E.; Li, Ju
2016-02-10
Individual metallic nanowires can sustain ultra-large elastic strains of 4-7%. However, achieving and retaining elastic strains of such magnitude in kilogram-scale nanowires are challenging. Here, we find that under active load, ~5.6% elastic strain can be achieved in Nb nanowires embedded in a metallic matrix deforming by detwinning. Moreover, large tensile (2.8%) and compressive (-2.4%) elastic strains can be retained in kilogram-scale Nb nanowires when the external load was fully removed, and adjustable in magnitude by processing control. It is then demonstrated that the retained tensile elastic strains of Nb nanowires can increase their superconducting transition temperature and critical magnetic field, in comparison with the unstrained original material. This study opens new avenues for retaining large and tunable elastic strains in great quantities of nanowires and elastic-strain-engineering at industrial scale.
Lai, Adrian; Schache, Anthony G; Lin, Yi-Chung; Pandy, Marcus G
2014-09-01
The human ankle plantar-flexors, the soleus and gastrocnemius, utilize tendon elastic strain energy to reduce muscle fiber work and optimize contractile conditions during running. However, studies to date have considered only slow to moderate running speeds up to 5 m s(-1). Little is known about how the human ankle plantar-flexors utilize tendon elastic strain energy as running speed is advanced towards maximum sprinting. We used data obtained from gait experiments in conjunction with musculoskeletal modeling and optimization techniques to calculate muscle-tendon unit (MTU) work, tendon elastic strain energy and muscle fiber work for the ankle plantar-flexors as participants ran at five discrete steady-state speeds ranging from jogging (~2 m s(-1)) to sprinting (≥8 m s(-1)). As running speed progressed from jogging to sprinting, the contribution of tendon elastic strain energy to the positive work generated by the MTU increased from 53% to 74% for the soleus and from 62% to 75% for the gastrocnemius. This increase was facilitated by greater muscle activation and the relatively isometric behavior of the soleus and gastrocnemius muscle fibers. Both of these characteristics enhanced tendon stretch and recoil, which contributed to the bulk of the change in MTU length. Our results suggest that as steady-state running speed is advanced towards maximum sprinting, the human ankle plantar-flexors continue to prioritize the storage and recovery of tendon elastic strain energy over muscle fiber work.
Three dimensional winds: A maximum cross-correlation application to elastic lidar data
Buttler, William Tillman [Univ. of Texas, Austin, TX (United States)
1996-05-01
Maximum cross-correlation techniques have been used with satellite data to estimate winds and sea surface velocities for several years. Los Alamos National Laboratory (LANL) is currently using a variation of the basic maximum cross-correlation technique, coupled with a deterministic application of a vector median filter, to measure transverse winds as a function of range and altitude from incoherent elastic backscatter lidar (light detection and ranging) data taken throughout large volumes within the atmospheric boundary layer. Hourly representations of three-dimensional wind fields, derived from elastic lidar data taken during an air-quality study performed in a region of complex terrain near Sunland Park, New Mexico, are presented and compared with results from an Environmental Protection Agency (EPA) approved laser doppler velocimeter. The wind fields showed persistent large scale eddies as well as general terrain-following winds in the Rio Grande valley.
Burial stress and elastic strain of carbonate rocks
Fabricius, Ida Lykke
2014-01-01
mechanisms. The principle is illustrated by comparing carbonate sediments and sedimentary rocks from the North Sea Basin and three oceanic settings: a relatively shallow water setting dominated by coarse carbonate packstones and grainstones and two deep water settings dominated by fine‐grained carbonate......Burial stress on a sediment or sedimentary rock is relevant for predicting compaction or failure caused by changes in, e.g., pore pressure in the subsurface. For this purpose, the stress is conventionally expressed in terms of its effect: “the effective stress” defined as the consequent elastic...... strain multiplied by the rock frame modulus. We cannot measure the strain directly in the subsurface, but from the data on bulk density and P‐wave velocity, we can estimate the rock frame modulus and Biot's coefficient and then calculate the “effective vertical stress” as the total vertical stress minus...
Dependence of the elastic strain coefficient of copper on the pre-treatment
Kuntze, Wilhelm
1950-01-01
The effect of various pre-treatments on the elastic strain coefficient (alpha) (defined as the reciprocal of the modulus of elasticity E) (Epsilon) and on the mechanical hysteresis of copper has been investigated. Variables comprising the pre-treatments were pre-straining by stretching in a tensile testing machine and by drawing through a die, aging at room and elevated temperatures and annealing. The variation of the elastic strain coefficient with test stress was also investigated.
Yang, Hui; Zhu, Xiaoxu; Bai, Wei; Zhao, Yongli; Zhang, Jie; Liu, Zhu; Zhou, Ziguan; Ou, Qinghai
2016-09-01
Virtualization is considered to be a promising solution to support various emerging applications. This paper illustrates the problem of virtual mapping from a new perspective, and mainly focuses on survivable mapping of virtual networks and the potential trade-off between spectral resource usage effectiveness and failure resilience level. We design an optimum shared protection mapping (OSPM) scheme in elastic optical networks. A differentiable maximum shared capacity of each frequency slot is defined to more efficiently shared protection resource. In order to satisfy various assessment standards, a metric called ambiguity similitude is defined for the first time to give insight on the optimizing difficulty. Simulation results are presented to compare the outcome of the novel OSPM algorithm with traditional dedicated link protection and maximum shared protection mapping. By synthetic analysis, OSPM outperforms the other two schemes in terms of striking a perfect balance among blocking probability, resources utilization, protective success rate, and spectrum redundancy.
Rajagopal, K. R.
2011-01-06
This paper is the first part of an extended program to develop a theory of fracture in the context of strain-limiting theories of elasticity. This program exploits a novel approach to modeling the mechanical response of elastic, that is non-dissipative, materials through implicit constitutive relations. The particular class of models studied here can also be viewed as arising from an explicit theory in which the displacement gradient is specified to be a nonlinear function of stress. This modeling construct generalizes the classical Cauchy and Green theories of elasticity which are included as special cases. It was conjectured that special forms of these implicit theories that limit strains to physically realistic maximum levels even for arbitrarily large stresses would be ideal for modeling fracture by offering a modeling paradigm that avoids the crack-tip strain singularities characteristic of classical fracture theories. The simplest fracture setting in which to explore this conjecture is anti-plane shear. It is demonstrated herein that for a specific choice of strain-limiting elasticity theory, crack-tip strains do indeed remain bounded. Moreover, the theory predicts a bounded stress field in the neighborhood of a crack-tip and a cusp-shaped opening displacement. The results confirm the conjecture that use of a strain limiting explicit theory in which the displacement gradient is given as a function of stress for modeling the bulk constitutive behavior obviates the necessity of introducing ad hoc modeling constructs such as crack-tip cohesive or process zones in order to correct the unphysical stress and strain singularities predicted by classical linear elastic fracture mechanics. © 2011 Springer Science+Business Media B.V.
An Elastic Plastic Contact Model with Strain Hardening for the LAMMPS Granular Package
Kuhr, Bryan [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Brake, Matthew Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Component Science and Mechanics; Lechman, Jeremy B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Nanoscale and Reactive Processes
2015-03-01
The following details the implementation of an analytical elastic plastic contact model with strain hardening for normal im pacts into the LAMMPS granular package. The model assumes that, upon impact, the co llision has a period of elastic loading followed by a period of mixed elastic plas tic loading, with contributions to each mechanism estimated by a hyperbolic seca nt weight function. This function is implemented in the LAMMPS source code as the pair style gran/ep/history. Preliminary tests, simulating the pouring of pure nickel spheres, showed the elastic/plastic model took 1.66x as long as similar runs using gran/hertz/history.
On the influence of strain rate in acousto-elasticity : experimental results for Berea sandstone
Riviere, J. V.; Candela, T.; Scuderi, M.; Marone, C.; Guyer, R. A.; Johnson, P. A.
2013-12-01
Elastic nonlinear effects are pervasive in the Earth, including during strong ground motion, tidal forcing and earthquake slip processes. We study elastic nonlinear effects in the laboratory with the goal of developing new methods to probe elastic changes in the Earth, and to characterize and understand their origins. Here we report on nonlinear, frequency dispersion effects by applying a method termed dynamic acousto-elasticity (DAE), analogous to quasi-static acousto-elasticity. DAE allows one to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. We perform DAE on samples of Berea sandstone subject to 0.5 MPa uniaxial and biaxial loading conditions with oscillating loads at frequencies from 0.001 to 10 Hz and amplitudes of a few 100 kPa. We compare results to DAE measurements made in the kHz range. We observe that the average decrease in modulus due to nonlinear material softening increases with frequency, suggesting a frequency and/or a strain rate dependence. Previous quasi-static measurements (Claytor et al., GRL 2009) show that stress-strain nonlinear hysteretic behavior disappears when the experiment is performed at a very low strain-rate, implying that a rate dependent nonlinear elastic model would be useful (Gusev et al., PRB 2004). Our results also suggest that when elastic nonlinear Earth processes are studied, stress forcing frequency is an important consideration, and may lead to unexpected behaviors.
Zile, M R; Izzi, G; Gaasch, W H
1991-02-01
We tested the hypothesis that maximum systolic elastance (Emax) fails to detect a decline in left ventricular (LV) contractile function when diastolic dysfunction is present. Canine hearts were studied in an isolated blood-perfused heart apparatus (isovolumic LV); contractile dysfunction was produced by 60 or 90 minutes of global ischemia, followed by 90 minutes of reperfusion. Nine normal hearts underwent 60 minutes of ischemia, and five underwent 90 minutes of ischemia. After the ischemia-reperfusion sequence, developed pressure, pressure-volume area, and myocardial ATP level were significantly less than those at baseline in all 14 hearts. In the group undergoing 60 minutes of ischemia, LV diastolic pressure did not increase, whereas Emax decreased from 5.2 +/- 2.5 to 2.9 +/- 1.4 mm Hg/ml (p less than 0.05). In the group undergoing 90 minutes of ischemia, diastolic pressure increased (from 10 +/- 2 to 37 +/- 20 mm Hg, p less than 0.05), and Emax did not change significantly (from 5.1 +/- 4.3 to 4.3 +/- 2.5 mm Hg/ml). A second series of experiments was performed in 13 hearts with pressure-overload hypertrophy (aortic-band model with echocardiography and catheterization studies before the ischemia-reperfusion protocol). Five had evidence for pump failure, whereas eight remained compensated. After 60 minutes of ischemia and 90 minutes of reperfusion, developed pressure, pressure-volume area, and myocardial ATP level were significantly less than those at baseline in all 13 hearts. In the group with compensated LV hypertrophy, LV diastolic pressure did not change, whereas Emax decreased from 6.9 +/- 3.0 to 3.1 +/- 2.3 mm Hg/ml (p less than 0.05).(ABSTRACT TRUNCATED AT 250 WORDS)
Spectral Modeling of Residual Stress and Stored Elastic Strain Energy in Thermal Barrier Coatings
Donegan, Sean; Rolett, Anthony
2013-12-31
Solutions to the thermoelastic problem are important for characterizing the response under temperature change of refractory systems. This work extends a spectral fast Fourier transform (FFT) technique to analyze the thermoelastic behavior of thermal barrier coatings (TBCs), with the intent of probing the local origins of failure in TBCs. The thermoelastic FFT (teFFT) approach allows for the characterization of local thermal residual stress and strain fields, which constitute the origins of failure in TBC systems. A technique based on statistical extreme value theory known as peaks-over-threshold (POT) is developed to quantify the extreme values ("hot spots") of stored elastic strain energy (i.e., elastic energy density, or EED). The resolution dependence of the teFFT method is assessed through a sensitivity study of the extreme values in EED. The sensitivity study is performed both for the local (point-by-point) eld distributions as well as the grain scale eld distributions. A convergence behavior to a particular distribution shape is demonstrated for the local elds. The grain scale fields are shown to exhibit a possible convergence to a maximum level of EED. To apply the teFFT method to TBC systems, 3D synthetic microstructures are created to approximate actual TBC microstructures. The morphology of the grains in each constituent layer as well as the texture is controlled. A variety of TBC materials, including industry standard materials and potential future materials, are analyzed using the teFFT. The resulting hot spots are quantified using the POT approach. A correlation between hot spots in EED and interface rumpling between constituent layers is demonstrated, particularly for the interface between the bond coat (BC) and the thermally grown oxide (TGO) layer.
Generalization of strain-gradient theory to finite elastic deformation for isotropic materials
Beheshti, Alireza
2017-03-01
This paper concerns finite deformation in the strain-gradient continuum. In order to take account of the geometric nonlinearity, the original strain-gradient theory which is based on the infinitesimal strain tensor is rewritten given the Green-Lagrange strain tensor. Following introducing the generalized isotropic Saint Venant-Kirchhoff material model for the strain-gradient elasticity, the boundary value problem is investigated in not only the material configuration but also the spatial configuration building upon the principle of virtual work for a three-dimensional solid. By presenting one example, the convergence of the strain-gradient and classical theories is studied.
Determination of Modulus of Elasticity and Shear Modulus by the Measurement of Relative Strains
Labašová, Eva
2016-12-01
This contribution is focused on determining the material properties (Young modulus and shear modulus) of the testing samples. The theoretical basis for determining material properties are the knowledge of linear elasticity and strength. The starting points are dependencies among the modulus of elasticity, shear modulus, normal stress and relative strain. The relative strains of the testing samples were obtained by measuring predefined load conditions using a strain-gauge bridge and the universal measurement system Quantum X MX 840. The integration of these tasks into the teaching process enhances practical and intellectual skills of students at secondary level technical universities.
W.R. Solonick
2003-04-01
Rapidly applied transient dynamic loads produce stresses and deflections in structures that typically exceed those from static loading conditions. Previous acceptance criteria for structures designed for rapidly applied transient dynamic loading limited stresses to those determined from elastic analysis. Different stress limits were established for different grades of structure depending upon the amount of permanent set considered acceptable. Structure allowed to sustain very limited permanent set is designed to stress limits not significantly greater than yield stress. Greater permanent set in structure under rapidly applied transient dynamic loading conditions is permitted by establishing stress limits that are significantly greater than yield stress but still provide adequate safety margin (with respect to failure). This paper presents a strain-based elastic-plastic (i.e., inelastic) analysis criterion developed as an alternative to the more conservative stress-based elastic analysis stress criterion for structures subjected to rapidly applied transient dynamic loading. The strain limits established are based on material ductility considerations only and are set as a fraction of the strain at ultimate stress obtained from an engineering stress/strain curve of the material. Strains limits are categorized by type as membrane or surface and by region as general, local , or concentrated. The application of the elastic-plastic criterion provides a more accurate, less conservative design/analysis basis for structures than that used in elastic stress-based analysis criteria, while still providing adequate safety margins.
Vattré, A.
2017-08-01
A parametric energy-based framework is developed to describe the elastic strain relaxation of interface dislocations. By means of the Stroh sextic formalism with a Fourier series technique, the proposed approach couples the classical anisotropic elasticity theory with surface/interface stress and elasticity properties in heterogeneous interface-dominated materials. For any semicoherent interface of interest, the strain energy landscape is computed using the persistent elastic fields produced by infinitely periodic hexagonal-shaped dislocation configurations with planar three-fold nodes. A finite element based procedure combined with the conjugate gradient and nudged elastic band methods is applied to determine the minimum-energy paths for which the pre-computed energy landscapes yield to elastically favorable dislocation reactions. Several applications on the Au/Cu heterosystems are given. The simple and limiting case of a single set of infinitely periodic dislocations is introduced to determine exact closed-form expressions for stresses. The second limiting case of the pure (010) Au/Cu heterophase interfaces containing two crossing sets of straight dislocations investigates the effects due to the non-classical boundary conditions on the stress distributions, including separate and appropriate constitutive relations at semicoherent interfaces and free surfaces. Using the quantized Frank-Bilby equation, it is shown that the elastic strain landscape exhibits intrinsic dislocation configurations for which the junction formation is energetically unfavorable. On the other hand, the mismatched (111) Au/Cu system gives rise to the existence of a minimum-energy path where the fully strain-relaxed equilibrium and non-regular intrinsic hexagonal-shaped dislocation rearrangement is accompanied by a significant removal of the short-range elastic energy.
Internal strain estimation for quantification of human heel pad elastic modulus: A phantom study
Holst, Karen; Liebgott, Hervé; Wilhjelm, Jens E.
2013-01-01
Shock absorption is the most important function of the human heel pad. However, changes in heel pad elasticity, as seen in e.g. long-distance runners, diabetes patients, and victims of Falanga torture are affecting this function, often in a painful manner. Assessment of heel pad elasticity......, and the three hard phantoms were 89kPa, 153kPa, and 168kPa, respectively. The combination of ultrasound images and force measurements provided an effective way of assessing the elastic properties of the heel pad due to the internal strain estimation....
Nonlinear elastic response in solid helium: critical velocity or strain?
Day, James; Syshchenko, Oleksandr; Beamish, John
2010-02-19
Torsional oscillator experiments show evidence of mass decoupling in solid 4He. This decoupling is amplitude dependent, suggesting a critical velocity for supersolidity. We observe similar behavior in the elastic shear modulus. By measuring the shear modulus over a wide frequency range, we can distinguish between an amplitude dependence which depends on velocity and one which depends on some other parameter such as displacement. In contrast with the torsional oscillator behavior, the modulus depends on the magnitude of stress, not velocity. We interpret our results in terms of the motion of dislocations which are weakly pinned by 3He impurities but which break away when large stresses are applied.
Zhang, Min-juan; Wang, Zhi-bin; Li, Xiao; Li, Jin-hua; Wang, Yan-chao
2015-05-01
In order to improve the accuracy and stability of the rebuilt spectrums, it is necessary that stability analysis and nicety measuring of the maximum optical path difference of interferograms in the photo-elastic modulator Fourier transform spectrometers(PEM-FTS). The maximum optical difference of interferograms is uncertain parameter, and it is relate to the resonant state, characteristic of frequency-thermal drift and driving voltage of PEM. Therefore, based on the principle of photo-elastic modulator Fourier transform interferometer, the model of the freguency-thermal drift is built, and the variety of the maximum optical path difference is analyzed; A measuring method of the maximum optical path difference is put forward, which is zero-crossing counting of laser's interference signal when the driving signal of PEM is as the standard. In the method the dual channel high-speed comparator and FPGA are used to transform sine wave to square wave, to realize zero-crossing trigger counting and errors compensation. On the condition that the 670. 8 nm laser is as the power source to produce the reference interferograms by the PEM interferometer, the 77. 471 µm maximum optical path difference could be measured by the zero-crossing counting the measuring errors is less than 0. 167 nm, the rebuilt spectral peak wavelength errors of the infrared blackbody is less than 2 nm. the result is content with PEM-FTS.
Elastic rods with incompatible strain: Macroscopic versus microscopic buckling
Lestringant, Claire; Audoly, Basile
2017-06-01
We consider the buckling of a long prismatic elastic solid under the combined effect of a pre-stress that is inhomogeneous in the cross-section, and of a prescribed displacement of its endpoints. A linear bifurcation analysis is carried out using different structural models (namely a double beam, a rectangular thin plate, and a hyper-elastic prismatic solid in 3-d): it yields the buckling mode and the wavenumber qc that are first encountered when the end-to-end displacement is progressively decreased with fixed pre-stress. For all three structural models, we find a transition from a long-wavelength (qc = 0) to a short-wavelength first buckling mode (qc ≠ 0) when the inhomogeneous pre-stress is increased past a critical value. A method for calculating the critical inhomogeneous pre-stress is proposed based on a small-wavenumber expansion of the buckling mode. Overall, our findings explain the formation of multiple perversions in elastomer strips, as well as the large variations in the number of perversions as a function of pre-stress and cross-sectional geometry, as reported by Liu et al. (2014).
Lim, C. W.; Zhang, G.; Reddy, J. N.
2015-05-01
In recent years there have been many papers that considered the effects of material length scales in the study of mechanics of solids at micro- and/or nano-scales. There are a number of approaches and, among them, one set of papers deals with Eringen's differential nonlocal model and another deals with the strain gradient theories. The modified couple stress theory, which also accounts for a material length scale, is a form of a strain gradient theory. The large body of literature that has come into existence in the last several years has created significant confusion among researchers about the length scales that these various theories contain. The present paper has the objective of establishing the fact that the length scales present in nonlocal elasticity and strain gradient theory describe two entirely different physical characteristics of materials and structures at nanoscale. By using two principle kernel functions, the paper further presents a theory with application examples which relates the classical nonlocal elasticity and strain gradient theory and it results in a higher-order nonlocal strain gradient theory. In this theory, a higher-order nonlocal strain gradient elasticity system which considers higher-order stress gradients and strain gradient nonlocality is proposed. It is based on the nonlocal effects of the strain field and first gradient strain field. This theory intends to generalize the classical nonlocal elasticity theory by introducing a higher-order strain tensor with nonlocality into the stored energy function. The theory is distinctive because the classical nonlocal stress theory does not include nonlocality of higher-order stresses while the common strain gradient theory only considers local higher-order strain gradients without nonlocal effects in a global sense. By establishing the constitutive relation within the thermodynamic framework, the governing equations of equilibrium and all boundary conditions are derived via the variational
Analytical phase-tracking-based strain estimation for ultrasound elasticity.
Yuan, Lili; Pedersen, Peder C
2015-01-01
A new strain estimator for quasi-static elastography is presented, based on tracking of the analytical signal phase as a function of the external force. Two implementations are introduced: zero-phase search with moving window (SMW) and zero-phase band tracking using connected component labeling (CCL). Low analytical signal amplitude caused by local destructive interference is associated with large error in the phase trajectories, and amplitude thresholding can thus be used to terminate the phase tracking along a particular path. Interpolation is then applied to estimate displacement in the eliminated path. The paper describes first a mathematical analysis based on 1-D multi-scatter modeling, followed by a statistical study of the displacement and strain error. Simulation and experiment with an inhomogeneous phantom indicate that SMW and CCL are capable of reliably estimating tissue displacement and strain over a larger range of deformation than standard timedomain cross-correlation (SCC). Results also show that SMW is roughly 40 times faster than SCC with comparable or even better accuracy. CCL is slower than SMW, but more noise robust. Simulation assessment at compression level 3% and 6% with SNR 20 dB demonstrates average strain error for SMW and CCL of 10%, whereas SCC achieves 18%.
Soutas-Little, Robert William
2010-01-01
According to the author, elasticity may be viewed in many ways. For some, it is a dusty, classical subject . . . to others it is the paradise of mathematics."" But, he concludes, the subject of elasticity is really ""an entity itself,"" a unified subject deserving comprehensive treatment. He gives elasticity that full treatment in this valuable and instructive text. In his preface, Soutas-Little offers a brief survey of the development of the theory of elasticity, the major mathematical formulation of which was developed in the 19th century after the first concept was proposed by Robert Hooke
Elastic strain energy behavior in the polymer nanocrystals
Alexander I. Slutsker
2016-06-01
Full Text Available In the paper, the changes in axial and contour lengths of skeletal interatomic bonds in the chain molecules of polyethylene nanocrystals have been measured using X-ray diffractometry and Raman spectrometry. In the course of the measurements the samples were subjected to stretching and heating (mechanical and thermal actions. The measured force and temperature dependences were analyzed and the calculated description of the polymer nanocrystal strain was inferred from them. In so doing the original results were obtained for the thermal action. The potential energy components related to both the skeletal bond stretching and the chain molecule bending were determined for the strained polymer crystal. The sharp distinction between the ratios of these components for the object under mechanical and thermal actions was found.
Converting strain maps into elasticity maps for materials with small contrast
Bellis, Cédric
2017-01-01
This study addresses the question of the quantitative reconstruction of heterogeneous distributions of isotropic elastic moduli from full strain field data. This parameter identification problem exposes the need for a local reconstruction procedure that is investigated here in the case of materials with small contrast. To begin with the integral formulation framework for the periodic linear elasticity problem, first- and second-order asymptotics are retained for the strain field solution and the effective elasticity tensor. Properties of the featured Green's tensor are investigated to characterize its decomposition into an isotropic term and an orthogonal part. The former is then shown to define a local contribution to the volume integral equations considered. Based on this property, then the combination of multiple strain field solutions corresponding to well-chosen applied macroscopic strains is shown to lead to a set of local and uncoupled identities relating, respectively, the bulk and shear moduli to the spherical and deviatoric components of the strain fields. Valid at the first-order in the weak contrast limit, such relations permit point-wise conversions of strain maps into elasticity maps. Furthermore, it is also shown that for macroscopically isotropic material configurations a single strain field solution is actually sufficient to reconstruct either the bulk or the shear modulus distribution. Those results are then revisited in the case of bounded media. Finally, some sets of analytical and numerical examples are provided for comparison and to illustrate the relevance of the obtained strain-modulus local equations for a parameter identification method based on full-field data.
Strain path's influence on the elastic behaviour of theTRIP 700 steel
MENDIGUREN, Joseba; CORTES, Fernando; GALDOS, Lander; Berveiller, Sophie
2013-01-01
This paper deals with the analysis of thestrain path's influence on the elastic behaviour of TRIP700 steel; it aims to validate the cyclic testing method to characterise inelastic behaviour of advanced high strength steels (AHSS). Different cyclic tests are done, where the strain path is changed from test to test. Large deformation strain gages are used to determine the inelastic behaviour of the specimens at macro-level. At a lower scale, stress measurements are carried out using the XRD tec...
Frequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone
Rivière, Jacques; Pimienta, Lucas; Scuderi, Marco; Candela, Thibault; Shokouhi, Parisa; Fortin, Jérôme; Schubnel, Alexandre; Marone, Chris; Johnson, Paul A.
2016-04-01
Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi-static (f→0) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2-3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1f appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. These findings can be used to improve theories relating the macroscopic elastic response to microstructural features.
Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels.
Nam, Sungmin; Hu, Kenneth H; Butte, Manish J; Chaudhuri, Ovijit
2016-05-17
The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell culture models of tissue. One of the most striking features of these gels is that they exhibit nonlinear elasticity, undergoing strain stiffening. However, these gels are also viscoelastic and exhibit stress relaxation, with the resistance of the gel to a deformation relaxing over time. Recent studies have suggested that cells sense and respond to both nonlinear elasticity and viscoelasticity of ECM, yet little is known about the connection between nonlinear elasticity and viscoelasticity. Here, we report that, as strain is increased, not only do biopolymer gels stiffen but they also exhibit faster stress relaxation, reducing the timescale over which elastic energy is dissipated. This effect is not universal to all biological gels and is mediated through weak cross-links. Mechanistically, computational modeling and atomic force microscopy (AFM) indicate that strain-enhanced stress relaxation of collagen gels arises from force-dependent unbinding of weak bonds between collagen fibers. The broader effect of strain-enhanced stress relaxation is to rapidly diminish strain stiffening over time. These results reveal the interplay between nonlinear elasticity and viscoelasticity in collagen gels, and highlight the complexity of the ECM mechanics that are likely sensed through cellular mechanotransduction.
Optimal Control Problems in Finite-Strain Elasticity by Inner Pressure and Fiber Tension
Andreas eGünnel
2016-04-01
Full Text Available Optimal control problems for finite-strain elasticity are considered.An inner pressure or an inner fiber tension are acting as driving forces.Such internal forces are typical, for instance, for the motion of heliotropic plants, and for muscle tissue.Non-standard objective functions relevant for elasticity problems are introduced.Optimality conditions are derived on a formal basis, and a limited-memory quasi-Newton algorithm for their solution is formulated in function space.Numerical experiments confirm the expected mesh-independent performance.
Franquet, Alexandre; Badel, Pierre; Riche, Rodolphe Le; 10.1080/10255842.2010.547192
2011-01-01
Assessing the vulnerability of atherosclerotic plaques requires an accurate knowledge of the mechanical properties of the plaque constituents. It is possible to measure displacements in vivo inside a plaque using magnetic resonance imaging. An important issue is to solve the inverse problem that consists in estimating the elastic properties inside the plaque from measured displacements. This study focuses on the identifiability of elastic parameters e.g. on the compromise between identification time and identification accuracy. An idealised plane strain. Finite Element (FE) model is used. The effects of the FE mesh, of the a priori assumptions about the constituents, of the measurement resolution and of the data noise are numerically investigated.
Kakeshita, Tomoyuki; Xiao, Fei; Fukuda, Takashi
2016-08-13
A Fe-31.2Pd (at.%) alloy exhibits a weak first-order martensitic transformation from a cubic structure to a tetragonal structure near 230 K. This transformation is associated with significant softening of elastic constant C'. Because of the softening, the alloy shows a large elastic strain of more than 6% in the [001] direction. In addition, the alloy has a critical point and shows a high elastocaloric effect in a wide temperature range for both the parent and the martensite phases.This article is part of the themed issue 'Taking the temperature of phase transitions in cool materials'.
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Mandsberg, Lotte Frigaard
2008-01-01
that best describes data is a model taking into account the full covariance structure. An inference study is made in order to determine whether the growth rate of the five bacteria strains is the same. After applying a likelihood-ratio test to models with a full covariance structure, it is concluded...... that the specific growth rate is the same for all bacteria strains. This study highlights the importance of carrying out an explorative examination of residuals in order to make a correct parametrization of a model including the covariance structure. The ML method is shown to be a strong tool as it enables......The specific growth rate for P. aeruginosa and four mutator strains mutT, mutY, mutM and mutY–mutM is estimated by a suggested Maximum Likelihood, ML, method which takes the autocorrelation of the observation into account. For each bacteria strain, six wells of optical density, OD, measurements...
Tanabe, Yuki; Kido, Teruhito; Kurata, Akira; Sawada, Shun; Suekuni, Hiroshi; Kido, Tomoyuki; Yokoi, Takahiro; Miyagawa, Masao; Mochizuki, Teruhito [Ehime University Graduate School of Medicine, Department of Radiology, Toon City, Ehime (Japan); Uetani, Teruyoshi; Inoue, Katsuji [Ehime University Graduate School of Medicine, Department of Cardiology, Pulmonology, Hypertension and Nephrology, Toon City, Ehime (Japan)
2017-04-15
To evaluate the feasibility of three-dimensional (3D) maximum principal strain (MP-strain) derived from cardiac computed tomography (CT) for detecting myocardial infarction (MI). Forty-three patients who underwent cardiac CT and magnetic resonance imaging (MRI) were retrospectively selected. Using the voxel tracking of motion coherence algorithm, the peak CT MP-strain was measured using the 16-segment model. With the trans-mural extent of late gadolinium enhancement (LGE) and the distance from MI, all segments were classified into four groups (infarcted, border, adjacent, and remote segments); infarcted and border segments were defined as MI with LGE positive. Diagnostic performance of MP-strain for detecting MI was compared with per cent systolic wall thickening (%SWT) assessed by MRI using receiver-operating characteristic curve analysis at a segment level. Of 672 segments excluding16 segments influenced by artefacts, 193 were diagnosed as MI. Sensitivity and specificity of peak MP-strain to identify MI were 81 % [95 % confidence interval (95 % CI): 74-88 %] and 86 % (81-92 %) compared with %SWT: 76 % (60-95 %) and 68 % (48-84 %), respectively. The area under the curve of peak MP-strain was superior to %SWT [0.90 (0.87-0.93) vs. 0.80 (0.76-0.83), p < 0.05]. CT MP-strain has a potential to provide incremental value to coronary CT angiography for detecting MI. (orig.)
Mangeri, John; Heinonen, Olle; Karpeyev, Dmitry; Nakhmanson, Serge
2015-07-01
Core-shell nanoparticle systems of Zn-ZnO and ZnO-TiO2 are studied computationally using finite-element methods. The inclusion of a surface free energy and the elastic mismatch of the core and shell create an imprinting effect within the shell structure that produces a wide variation of strains. Due to this diversity of strains, the sharp, direct, band-gap edges of the bulk semiconductor are observed to be broadened. We show that a variety of factors, such as particle size, core-to-shell volume ratio, applied hydrostatic pressure, shell microstructure, as well as the effect of elastic anisotropy, can influence the distribution of optical band-gap values throughout the particle.
Menzel, Andreas M
2016-01-01
One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)elastic substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we present a hydrodynamic description of (visco)elastic composite materials. For this purpose, additional strain variables reflect the state of the inclusions and their immediate environment. These additional strain variables in general are not set by a coarse-grained macroscopic displacement field. Apart from that, during our derivation, we also include the macroscopic variables of relative translations and relative rotat...
无
2007-01-01
An expansion theory of spherical cavities in strain-softening materials with different moduli of tension and compression was presented. For geomaterials, two controlling parameters were introduced to take into account the different moduli and strain-softening properties. By means of elastic theory with different moduli and stress-softening models, g. eneral solutions calculating Tresca and Mohr-Coulomb materials' stress and displacement fields of expansion of spherical cavity were derived. The effects caused by different elastic moduli in tensile and compression and strain-softening rates on stress and displacement fields and development of plastic zone of expansion of cavity were analyzed. The results show that the ultimate expansion pressure,stress and displacement fields and development of plastic zone vary with the different elastic moduli and strain-softening properties. If classical elastic theory is adopted and strain-softening properties are neglected, rather large errors may be the result.
A 3D Orthotropic Strain-Rate Dependent Elastic Damage Material Model.
English, Shawn Allen
2014-09-01
A three dimensional orthotropic elastic constitutive model with continuum damage and cohesive based fracture is implemented for a general polymer matrix composite lamina. The formulation assumes the possibility of distributed (continuum) damage followed b y localized damage. The current damage activation functions are simply partially interactive quadratic strain criteria . However, the code structure allows for changes in the functions without extraordinary effort. The material model formulation, implementation, characterization and use cases are presented.
A highly elastic, capacitive strain gauge based on percolating nanotube networks.
Cohen, Daniel J; Mitra, Debkishore; Peterson, Kevin; Maharbiz, Michel M
2012-04-11
We present a highly elastic strain gauge based on capacitive sensing of parallel, carbon nanotube-based percolation electrodes separated by a dielectric elastomer. The fabrication, relying on vacuum filtration of single-walled carbon nanotubes and hydrophobic patterning of silicone, is both rapid and inexpensive. We demonstrate reliable, linear performance over thousands of cycles at up to 100% strain with less than 3% variability and the highest reported gauge factor for a device of this class (0.99). We further demonstrate use of this sensor in a robotics context to transduce joint angles.
Elastic Strain Energy Storage and Neighboring Organ Assistance for Fluid Propulsion
Arun, C. P.
2003-11-01
Storage of elastic strain energy by non-muscular structures such as tendons and ligaments, is a common scheme employed by jumping animals. Also, since skeletal muscle is attached to bone, mechanical advantage is obtained, allowing a burst of power that is unobtainable by muscle contraction alone. This is important at launch since force may be applied for only the brief period when the legs are in contact with the ground. Liquid propelling structures such as the urinary bladder and the heart face the similar problem of being able to impart force to the content only as long as the wall is in a stretched state. Using data from videocystometry and cardiac catheterisation we show that the means employed to achieve liquid propulsion appears to involve a combination of isometric contraction (contraction against a closed sphincter or valve) with hyperelastic stretch of the wall, elastic strain energy storage by the wall, overshoot past the undistended state and neighboring organ assistance (NOA). Thus, the heart, a partially collapsible thick muscular shell without the benefit of NOA manages an ejection fraction of about 70%. Using all of the above means, the collapsible urinary bladder is able to nearly always empty. Elastic strain energy storage and NOA appear to be important strategies for liquid propulsion employed by hollow viscera.
Curiale, Ariel H; Vegas-Sánchez-Ferrero, Gonzalo; Bosch, Johan G; Aja-Fernández, Santiago
2015-08-01
The strain and strain-rate measures are commonly used for the analysis and assessment of regional myocardial function. In echocardiography (EC), the strain analysis became possible using Tissue Doppler Imaging (TDI). Unfortunately, this modality shows an important limitation: the angle between the myocardial movement and the ultrasound beam should be small to provide reliable measures. This constraint makes it difficult to provide strain measures of the entire myocardium. Alternative non-Doppler techniques such as Speckle Tracking (ST) can provide strain measures without angle constraints. However, the spatial resolution and the noisy appearance of speckle still make the strain estimation a challenging task in EC. Several maximum likelihood approaches have been proposed to statistically characterize the behavior of speckle, which results in a better performance of speckle tracking. However, those models do not consider common transformations to achieve the final B-mode image (e.g. interpolation). This paper proposes a new maximum likelihood approach for speckle tracking which effectively characterizes speckle of the final B-mode image. Its formulation provides a diffeomorphic scheme than can be efficiently optimized with a second-order method. The novelty of the method is threefold: First, the statistical characterization of speckle generalizes conventional speckle models (Rayleigh, Nakagami and Gamma) to a more versatile model for real data. Second, the formulation includes local correlation to increase the efficiency of frame-to-frame speckle tracking. Third, a probabilistic myocardial tissue characterization is used to automatically identify more reliable myocardial motions. The accuracy and agreement assessment was evaluated on a set of 16 synthetic image sequences for three different scenarios: normal, acute ischemia and acute dyssynchrony. The proposed method was compared to six speckle tracking methods. Results revealed that the proposed method is the most
Grain-resolved elastic strains in deformed copper measured by three-dimensional X-ray diffraction
Oddershede, Jette, E-mail: jeto@risoe.dtu.dk [Center for Fundamental Research: Metal Structures in Four Dimensions, Materials Research Division, Riso DTU, Frederiksborgvej 399, DK-4000 Roskilde (Denmark); Schmidt, Soren; Poulsen, Henning Friis; Margulies, Lawrence [Center for Fundamental Research: Metal Structures in Four Dimensions, Materials Research Division, Riso DTU, Frederiksborgvej 399, DK-4000 Roskilde (Denmark); Wright, Jonathan [European Synchrotron Research Facility, 38043 Grenoble (France); Moscicki, Marcin [Max-Planck-Institut fuer Eisenforschung GmbH, Max-Planck-Str. 1, 40237 Duesseldorf (Germany); Reimers, Walter [Technische Universitaet Berlin, Sekr. BH18, Ernst-Reuter-Platz 1, 10587 Berlin (Germany); Winther, Grethe [Center for Fundamental Research: Metal Structures in Four Dimensions, Materials Research Division, Riso DTU, Frederiksborgvej 399, DK-4000 Roskilde (Denmark)
2011-07-15
This X-ray diffraction study reports the grain-resolved elastic strains in about 1000 randomly oriented grains embedded in a polycrystalline copper sample. Diffraction data were collected in situ in the undeformed state and at a plastic strain of 1.5% while the sample was under tensile load. For each grain the centre-of-mass position was determined with an accuracy of 10 {mu}m, the volume with a relative error of 20%, the orientation to 0.05{sup o} and the axial strain to 10{sup -4}. The elastic strain along the tensile direction exhibited a grain orientation dependence with grains within 20 deg. of <100> carrying the largest strain. While the width of the strain distribution for all grains did not change upon plastic loading, the grain-resolved data show a significant widening of the distribution evaluated for small subsets of initially elastically similar grains. This widening appears independent of the grain orientation. - Research Highlights: {yields} X-ray diffraction study of {approx} 1000 Cu grains during in situ plastic deformation. {yields} Grain averaged positions, orientations, volumes and elastic strain tensors derived. {yields} Both lattice rotation and axial strain depend on the initial grain orientation. {yields} Grains within 20{sup o} of <100> carry the largest elastic strain along the tensile axis. {yields} The results enable evaluation and development of polycrystal plasticity models.
Development of Ti-Nb-Zr alloys with high elastic admissible strain for temporary orthopedic devices.
Ozan, Sertan; Lin, Jixing; Li, Yuncang; Ipek, Rasim; Wen, Cuie
2015-07-01
A new series of beta Ti-Nb-Zr (TNZ) alloys with considerable plastic deformation ability during compression test, high elastic admissible strain, and excellent cytocompatibility have been developed for removable bone tissue implant applications. TNZ alloys with nominal compositions of Ti-34Nb-25Zr, Ti-30Nb-32Zr, Ti-28Nb-35.4Zr and Ti-24.8Nb-40.7Zr (wt.% hereafter) were fabricated using the cold-crucible levitation technique, and the effects of alloying element content on their microstructures, mechanical properties (tensile strength, yield strength, compressive yield strength, Young's modulus, elastic energy, toughness, and micro-hardness), and cytocompatibilities were investigated and compared. Microstructural examinations revealed that the TNZ alloys consisted of β phase. The alloy samples displayed excellent ductility with no cracking, or fracturing during compression tests. Their tensile strength, Young's modulus, elongation at rupture, and elastic admissible strain were measured in the ranges of 704-839 MPa, 62-65 GPa, 9.9-14.8% and 1.08-1.31%, respectively. The tensile strength, Young's modulus and elongation at rupture of the Ti-34Nb-25Zr alloy were measured as 839 ± 31.8 MPa, 62 ± 3.6 GPa, and 14.8 ± 1.6%, respectively; this alloy exhibited the elastic admissible strain of approximately 1.31%. Cytocompatibility tests indicated that the cell viability ratios (CVR) of the alloys are greater than those of the control group; thus the TNZ alloys possess excellent cytocompatibility. Copyright © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Cervera, M.; Lafontaine, N.; Rossi, R.; Chiumenti, M.
2016-09-01
This paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales. A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields ( P1 P1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr-Coulomb and Drucker-Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.
Superelastic stress-strain behavior in ferrogels of different types of magneto-elastic coupling
Cremer, Peet; Menzel, Andreas M
2016-01-01
Colloidal magnetic particles embedded in an elastic polymer matrix constitute a smart material called ferrogel. It responds to an applied external magnetic field by changes in elastic properties, which can be exploited for various applications like dampers, vibration absorbers, or actuators. Under appropriate conditions, the stress-strain behavior of a ferrogel can display a fascinating feature: superelasticity, the capability to reversibly deform by a huge amount while barely altering the applied load. In a previous work, using numerical simulations, we investigated this behavior assuming that the magnetic moments carried by the embedded particles can freely reorient to minimize their magnetic interaction energy. Here, we extend the analysis to ferrogels where restoring torques by the surrounding matrix hinder rotations towards a magnetically favored configuration. For example, the particles can be chemically cross-linked into the polymer matrix and the magnetic moments can be fixed to the particle axes. We ...
Grain-resolved elastic strains in deformed copper measured by three-dimensional X-ray diffraction
Oddershede, Jette; Schmidt, Søren; Poulsen, Henning Friis
2011-01-01
. For each grain the centre-of-mass position was determined with an accuracy of 10 μm, the volume with a relative error of 20%, the orientation to 0.05° and the axial strain to 10− 4. The elastic strain along the tensile direction exhibited a grain orientation dependence with grains within 20° of carrying...
Dynamics of pre-strained bi-material elastic systems linearized three-dimensional approach
Akbarov, Surkay D
2015-01-01
This book deals with dynamics of pre-stressed or pre-strained bi-material elastic systems consisting of stack of pre-stressed layers, stack of pre-stressed layers and pre-stressed half space (or half plane), stack of pre-stressed layers as well as absolute rigid foundation, pre-stressed compound solid and hollow cylinders and pre-stressed sandwich hollow cylinders. The problems considered in the book relate to the dynamics of a moving and oscillating moving load, forced vibration caused by linearly located or point located time-harmonic forces acting to the foregoing systems. Moreover, a considerable part of the book relate to the problems regarding the near surface, torsional and axisymmetric longitudinal waves propagation and dispersion in the noted above bi-material elastic systems. The book carries out the investigations within the framework of the piecewise homogeneous body model with the use of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies.
Standard test method for linear-elastic plane-strain fracture toughness KIc of metallic materials
American Society for Testing and Materials. Philadelphia
2013-01-01
1.1 This test method covers the determination of fracture toughness (KIc) of metallic materials under predominantly linear-elastic, plane-strain conditions using fatigue precracked specimens having a thickness of 1.6 mm (0.063 in.) or greater subjected to slowly, or in special (elective) cases rapidly, increasing crack-displacement force. Details of test apparatus, specimen configuration, and experimental procedure are given in the Annexes. Note 1—Plane-strain fracture toughness tests of thinner materials that are sufficiently brittle (see 7.1) can be made using other types of specimens (1). There is no standard test method for such thin materials. 1.2 This test method is divided into two parts. The first part gives general recommendations and requirements for KIc testing. The second part consists of Annexes that give specific information on displacement gage and loading fixture design, special requirements for individual specimen configurations, and detailed procedures for fatigue precracking. Additional a...
On the Relationship between Stress and Elastic Strain for Porous and Fractured Rock
Liu, Hui-Hai; Rutqvist, Jonny; Berryman, James G.
2008-02-25
Modeling the mechanical deformations of porous and fractured rocks requires a stress-strain relationship. Experience with inherently heterogeneous earth materials suggests that different varieties of Hook's law should be applied within regions of the rock having significantly different stress-strain behavior, e.g., such as solid phase and various void geometries. We apply this idea by dividing a rock body conceptually into two distinct parts. The natural strain (volume change divided by rock volume at the current stress state), rather than the engineering strain (volume change divided by the unstressed rock volume), should be used in Hooke's law for accurate modeling of the elastic deformation of that part of the pore volume subject to a relatively large degree of relative deformation (i.e., cracks or fractures). This approach permits the derivation of constitutive relations between stress and a variety of mechanical and/or hydraulic rock properties. We show that the theoretical predictions of this method are generally consistent with empirical expressions (from field data) and also laboratory rock experimental data.
Skin-like pressure and strain sensors based on transparent elastic films of carbon nanotubes
Lipomi, Darren J.; Vosgueritchian, Michael; Tee, Benjamin C.-K.; Hellstrom, Sondra L.; Lee, Jennifer A.; Fox, Courtney H.; Bao, Zhenan
2011-12-01
Transparent, elastic conductors are essential components of electronic and optoelectronic devices that facilitate human interaction and biofeedback, such as interactive electronics, implantable medical devices and robotic systems with human-like sensing capabilities. The availability of conducting thin films with these properties could lead to the development of skin-like sensors that stretch reversibly, sense pressure (not just touch), bend into hairpin turns, integrate with collapsible, stretchable and mechanically robust displays and solar cells, and also wrap around non-planar and biological surfaces such as skin and organs, without wrinkling. We report transparent, conducting spray-deposited films of single-walled carbon nanotubes that can be rendered stretchable by applying strain along each axis, and then releasing this strain. This process produces spring-like structures in the nanotubes that accommodate strains of up to 150% and demonstrate conductivities as high as 2,200 S cm-1 in the stretched state. We also use the nanotube films as electrodes in arrays of transparent, stretchable capacitors, which behave as pressure and strain sensors.
Skin-like pressure and strain sensors based on transparent elastic films of carbon nanotubes.
Lipomi, Darren J; Vosgueritchian, Michael; Tee, Benjamin C-K; Hellstrom, Sondra L; Lee, Jennifer A; Fox, Courtney H; Bao, Zhenan
2011-10-23
Transparent, elastic conductors are essential components of electronic and optoelectronic devices that facilitate human interaction and biofeedback, such as interactive electronics, implantable medical devices and robotic systems with human-like sensing capabilities. The availability of conducting thin films with these properties could lead to the development of skin-like sensors that stretch reversibly, sense pressure (not just touch), bend into hairpin turns, integrate with collapsible, stretchable and mechanically robust displays and solar cells, and also wrap around non-planar and biological surfaces such as skin and organs, without wrinkling. We report transparent, conducting spray-deposited films of single-walled carbon nanotubes that can be rendered stretchable by applying strain along each axis, and then releasing this strain. This process produces spring-like structures in the nanotubes that accommodate strains of up to 150% and demonstrate conductivities as high as 2,200 S cm(-1) in the stretched state. We also use the nanotube films as electrodes in arrays of transparent, stretchable capacitors, which behave as pressure and strain sensors.
Psiachos, D., E-mail: dpsiachos@gmail.com [ICAMS, Ruhr-Universitaet Bochum, Bochum (Germany); Hammerschmidt, T., E-mail: thomas.hammerschmidt@icams.rub.de [ICAMS, Ruhr-Universitaet Bochum, Bochum (Germany); Drautz, R., E-mail: ralf.drautz@icams.rub.de [ICAMS, Ruhr-Universitaet Bochum, Bochum (Germany)
2011-06-15
The effect of hydrostatic strain and of interstitial hydrogen on the elastic properties of {alpha}-iron is investigated using ab initio density-functional theory calculations. We find that the cubic elastic constants and the polycrystalline elastic moduli to a good approximation decrease linearly with increasing hydrogen concentration. This net strength reduction can be partitioned into a strengthening electronic effect which is overcome by a softening volumetric effect. The calculated hydrogen-dependent elastic constants are used to determine the polycrystalline elastic moduli and anisotropic shear moduli. For the key slip planes in {alpha}-iron, [11-bar0] and [112-bar], we find a shear modulus reduction of approximately 1.6% per at.% H.
Semenova, I. V.; Belashov, A. V.; Garbuzov, F. E.; Samsonov, A. M.; Semenov, A. A.
2017-06-01
We demonstrate an alternative approach to determination of the third order elastic moduli of materials based on registration of nonlinear bulk strain waves in three basic structural waveguides (rod, plate and shell) and further calculation of the Murnaghan moduli from the recorded wave parameters via simple algebra. These elastic moduli are available in literature for a limited number of materials and are measured with considerable errors, that evidences a demand in novel approaches to their determination.
Ganau, Sergi, E-mail: sganau@tauli.cat [Women' s Imaging Department, UDIAT-Centre Diagnòstic, Institut Universitari Parc Taulí – UAB, Parc Taulí, 1, 08205 Sabadell, Barcelona (Spain); Andreu, Francisco Javier, E-mail: xandreu@tauli.cat [Pathology Department, UDIAT-Centre Diagnòstic, Institut Universitari Parc Taulí – UAB, Parc Taulí, 1, 08205 Sabadell, Barcelona (Spain); Escribano, Fernanda, E-mail: fescribano@tauli.cat [Women' s Imaging Department, UDIAT-Centre Diagnòstic, Institut Universitari Parc Taulí – UAB, Parc Taulí, 1, 08205 Sabadell, Barcelona (Spain); Martín, Amaya, E-mail: amartino@tauli.cat [Women' s Imaging Department, UDIAT-Centre Diagnòstic, Institut Universitari Parc Taulí – UAB, Parc Taulí, 1, 08205 Sabadell, Barcelona (Spain); Tortajada, Lidia, E-mail: ltortajada@tauli.cat [Women' s Imaging Department, UDIAT-Centre Diagnòstic, Institut Universitari Parc Taulí – UAB, Parc Taulí, 1, 08205 Sabadell, Barcelona (Spain); Villajos, Maite, E-mail: mvillajos@tauli.cat [Women' s Imaging Department, UDIAT-Centre Diagnòstic, Institut Universitari Parc Taulí – UAB, Parc Taulí, 1, 08205 Sabadell, Barcelona (Spain); and others
2015-04-15
Highlights: •Shear wave elastography provides a quantitative assessment of the hardness of breast lesions. •The hardness of breast lesions correlates with lesion size: larger lesions are harder than smaller ones. •Histologic type and grade do not correlate clearly with elastography parameters. •HER2, luminal B HER2+, and triple-negative tumors have lower maximum hardness and mean hardness than other tumor types. •Half the tumors classified as BI-RADS 3 were luminal A and half were HER2. -- Abstract: Purpose: To evaluate the correlations of maximum stiffness (Emax) and mean stiffness (Emean) of invasive carcinomas on shear-wave elastography (SWE) with St. Gallen consensus tumor phenotypes. Methods: We used an ultrasound system with SWE capabilities to prospectively study 190 women with 216 histologically confirmed invasive breast cancers. We obtained one elastogram for each lesion. We correlated Emax and Emean with tumor size, histologic type and grade, estrogen and progesterone receptors, HER2 expression, the Ki67 proliferation index, and the five St. Gallen molecular subtypes: luminal A, luminal B without HER2 overexpression (luminal B HER2−), luminal B with HER2 overexpression (luminal B HER2+), HER2, and triple negative. Results: Lesions larger than 20 mm had significantly higher Emax (148.04 kPa) and Emean (118.32 kPa) (P = 0.005) than smaller lesions. We found no statistically significant correlations between elasticity parameters and histologic type and grade or molecular subtypes, although tumors with HER2 overexpression regardless whether they expressed hormone receptors (luminal B HER2+ and HER2 phenotypes) and triple-negative tumors had lower Emax and Emean than the others. We assessed the B-mode ultrasound findings of the lesions with some of the Emax or Emean values less than or equal to 80 kPa; only four of these had ultrasound findings suggestive of a benign lesion (two with luminal A phenotype and two with HER2 phenotype). Conclusions: We
Paul, Shirshendu; Katiyar, Amit; Sarkar, Kausik; Chatterjee, Dhiman; Shi, William T; Forsberg, Flemming
2010-06-01
Two nonlinear interfacial elasticity models--interfacial elasticity decreasing linearly and exponentially with area fraction--are developed for the encapsulation of contrast microbubbles. The strain softening (decreasing elasticity) results from the decreasing association between the constitutive molecules of the encapsulation. The models are used to find the characteristic properties (surface tension, interfacial elasticity, interfacial viscosity and nonlinear elasticity parameters) for a commercial contrast agent. Properties are found using the ultrasound attenuation measured through a suspension of contrast agent. Dynamics of the resulting models are simulated, compared with other existing models and discussed. Imposing non-negativity on the effective surface tension (the encapsulation experiences no net compressive stress) shows "compression-only" behavior. The exponential and the quadratic (linearly varying elasticity) models result in similar behaviors. The validity of the models is investigated by comparing their predictions of the scattered nonlinear response for the contrast agent at higher excitations against experimental measurement. All models predict well the scattered fundamental response. The nonlinear strain softening included in the proposed elastic models of the encapsulation improves their ability to predict subharmonic response. They predict the threshold excitation for the initiation of subharmonic response and its subsequent saturation.
Tien-Wei Shyr
2011-01-01
Full Text Available To use e-textiles as a strain-resistance sensor they need to be both elastic and conductive. Three kinds of elastic-conductive webbings, including flat, tubular, and belt webbings, made of Lycra fiber and carbon coated polyamide fiber, were used in this study. The strain-resistance properties of the webbings were evaluated in stretch-recovery tests and measured within 30% strain. It was found that tensile hysteresis and contact resistance significantly influence the tensile elasticity and the resistance sensitivity of the webbings. The results showed that the webbing structure definitely contributes to the tensile hysteresis and contact resistance. The smaller the friction is among the yarns in the belt webbing, the smaller the tensile hysteresis loss. However the close proximity of the conductive yarns in flat and tubular webbings results in a lower contact resistance.
Im, Jooeun; Kim, Mihyun; Choi, Ki-Sun; Hwang, Tae-Kyung; Kwon, Il-Bum
2014-06-10
In this paper, new fiber Bragg grating (FBG) sensor probes are designed to intermittently detect the maximum tensile strain of composite materials, so as to evaluate the structural health status. This probe is fabricated by two thin Al films bonded to an FBG optical fiber and two supporting brackets, which are fixed on the surface of composite materials. The residual strain of the Al packaged FBG sensor probe is induced by the strain of composite materials. This residual strain can indicate the maximum strain of composite materials. Two types of sensor probes are prepared-one is an FBG with 18 μm thick Al films, and the other is an FBG with 36 μm thick Al films-to compare the thickness effect on the detection sensitivity. These sensor probes are bonded on the surfaces of carbon fiber reinforced plastics composite specimens. In order to determine the strain sensitivity between the residual strain of the FBG sensor probe and the maximum strain of the composite specimen, tensile tests are performed by universal testing machine, under the loading-unloading test condition. The strain sensitivities of the probes, which have the Al thicknesses of 18 and 36 μm, are determined as 0.13 and 0.23, respectively.
Aldakheel, Fadi
2017-05-01
The coupled thermo-mechanical strain gradient plasticity theory that accounts for microstructure-based size effects is outlined within this work. It extends the recent work of Miehe et al. (Comput Methods Appl Mech Eng 268:704-734, 2014) to account for thermal effects at finite strains. From the computational viewpoint, the finite element design of the coupled problem is not straightforward and requires additional strategies due to the difficulties near the elastic-plastic boundaries. To simplify the finite element formulation, we extend it toward the micromorphic approach to gradient thermo-plasticity model in the logarithmic strain space. The key point is the introduction of dual local-global field variables via a penalty method, where only the global fields are restricted by boundary conditions. Hence, the problem of restricting the gradient variable to the plastic domain is relaxed, which makes the formulation very attractive for finite element implementation as discussed in Forest (J Eng Mech 135:117-131, 2009) and Miehe et al. (Philos Trans R Soc A Math Phys Eng Sci 374:20150170, 2016).
Analysis and simulation of high strain compression of anisotropic open-cell elastic foams
无
2010-01-01
By elongating the regular Kelvin model in one direction and keeping unchanged in the other two directions,the anisotropic model was constructed.Then,the simplified periodic structural cell was obtained according to the periodicity and symmetry of the model in the whole space.Using the half-strut element and elastic deflection theory to analyze the mechanical behavior as were adopted in the previous studies,this paper obtained the theoretical expressions for the compressive stress and strain as well as the corresponding curves in the rise and transverse directions.In addition,the theoretical results were examined by the finite element simulation.Results indicated that the theoretical analysis was very close to the finite element simulation when the strain was not too high,which confirmed the validity of theoretical analysis.At the same time,the anisotropy was shown to have a significant effect on the mechanical properties of open-cell foams.As the anisotropy ratio increased,the compressive stress was improved in the rise direction but dropped in the transverse direction under the same strain.
On the origins of anomalous elastic moduli and failure strains of GaP nanowires
Yashinski, M. S.; Gutiérrez, H. R.; Muhlstein, C. L.
2017-02-01
Previous reports suggest that Raman peaks in uniaxially loaded nanowires with diamond cubic and zinc blende crystal structures shift at rates that are significantly different from bulk specimens. We have investigated the first order Raman scattering from individual, free-standing, [111] oriented GaP nanowires ranging from 75 to 180 nm in diameter at uniaxial tensile stresses up to 5 GPa. All of the phonon modes were shifted to frequencies lower than previously reported for bulk GaP, and significant splitting of the degenerate transverse optical mode was observed. A general analysis method using single and double Lorentzian fits of the Raman peaks is presented and used to report more accurate values of the phonon deformation potentials (PDPs) that relate uniaxial strains to Raman peak shifts in GaP. A new set of PDPs determined from the nanowires revealed that the they have elastic moduli and failure strains that are consistent with bulk GaP. The analysis method eliminated the anomalous, inconsistent deformation behavior commonly reported in Raman-based strain measurements of nanowires, and can be extended to other materials systems with degenerate phonons.
Simple structures test for elastic-plastic strain acceptance criterion validation
Trimble, T.F. [Electric Boat Corp., Groton, CT (United States); Krech, G.R. [Wyle Labs., Inc., Huntsville, AL (United States)
1997-11-01
A Simple Structures Test Program was performed where several cantilevered beam and fixed-end beam test specimens (fabricated from HY-80 steel) were subjected to a series of analytically predetermined rapidly applied transient dynamic input loads. The primary objective of the test program was to obtain dynamic nonlinear response for simple structures subjected to these load inputs. Data derived from these tests was subsequently used to correlate to analysis predictions to assess the capability to analytically predict elastic-plastic nonlinear material behavior in structures using typical time-dependent (transient) design methods and the ABAQUS finite element analysis code. The installation of a significant amount of instrumentation on these specimens and post-test measurements enabled the monitoring and recording of strain levels, displacements, accelerations, and permanent set. An assessment of modeling parameters such as the element type and mesh refinement was made using these test results. In addition, currently available material models and the incremental time step procedure used in the transient analyses were evaluated. Comparison of test data to analysis results shows that displacements, accelerations, and peak strain can be predicted with a reasonable level of accuracy using detailed solid models of the tested specimens. Permanent set is overpredicted by a factor of approximately two. However, the accuracy of the prediction of permanent set is being enhanced by updating material modeling in the ABAQUS code to account for effects of strain reversal in oscillatory behavior of dynamically loaded specimens.
Zhang, Fan; Wang, Jianchuan; Liu, Shuhong; Du, Yong
2016-10-01
Sn and Sn-based compounds have been attracting a great interest as promising alternative materials for commercial anodes in lithium ion batteries. In this study, the phase evolution of the Li-Sn system during the lithiated processes and the effect of the elastic-strain energies caused by volume change on the phase transition are investigated by means of first-principles calculations. Our calculated results demonstrate that the distorted Li7Sn3 crystal tends to be formed in order to decrease the elastic-strain energy. In addition, our work indicates that the whole lithiated processes under the elastically constrained condition could be classified into two steps. The first step is the two-phase equilibrium process, in which the thermodynamic driving force is large enough to facilitate the phase transition and the plateau voltage could be established. The second step is considered to be the selective equilibrium, in which the thermodynamic driving force is not enough to facilitate the nucleation of the new equilibrium phase due to the elastically constrained conditions and the plateau voltage unformed. Besides, we find that in the Li0.4Sn matrix the nucleation of the αSn is more preferential than the βSn due to the effects of the elastic-strain energies.
Song, Ki Nam [Korea Atomic Energy Research Institute, Daeduk (Korea, Republic of)
1996-03-01
A formula for the elastic stiffness of the leaf type holddown spring assembly with uniformly tapered width from w{sub 0} to w{sub 1} (w{sub 0} < w{sub 1}) has been analytically derived by applying the engineering beam theory and Casiliano`s theory based on strain energy. Elastic stiffnesses for the leaf type holddown springs which are newly designed in the same dimensional design spaces as 14x14 type and 17x17 type KOFA holddown spring assembly have been estimated from the derived formula and also their elastic stiffnesses have been compared with those of KOFA holddown spring assemblies. It is found that elastic stiffnesses of the newly designed leaf type holddown spring assemblies have been about 32-33% about higher than those of KOFA holddown spring assemblies and that effects of axial and shear force on the elastic stiffness have been 0.15-0.21% of the elastic stiffness. Therefore in case that the newly designed holddown spring assemblies have been adapted in KOFA, it is expected that numbers of leaves composing a holddown spring assembly could be lessened by on due to their having a high elastic stiffness and in addition, manufacturing cost of the newly designed holddown spring assembly may be reduced due to easy machinability of each leaf. 4 tabs., 4 figs., 16 refs. (Author) .new.
Strain tensor selection and the elastic theory of incompatible thin sheets
Oshri, Oz; Diamant, Haim
2017-05-01
The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids 57, 762 (2009), 10.1016/j.jmps.2008.12.004]. For a class of simple axisymmetric problems we examine an alternative formulation, defining the strain based on deviations of distances (rather than distances squared) from their rest values. While the two formulations converge in the limit of small slopes and in the limit of an incompressible sheet, for other cases they are found not to be equivalent. The alternative formulation offers several features which are absent in the existing theory. (a) In the case of planar deformations of flat incompatible sheets, it yields linear, exactly solvable, equations of equilibrium. (b) When reduced to uniaxial (one-dimensional) deformations, it coincides with the theory of extensible elastica; in particular, for a uniaxially bent sheet it yields an unstrained cylindrical configuration. (c) It gives a simple criterion determining whether an isometric immersion of an incompatible sheet is at mechanical equilibrium with respect to normal forces. For a reference metric of constant positive Gaussian curvature, a spherical cap is found to satisfy this criterion except in an arbitrarily narrow boundary layer.
Sung Woo Park
2015-03-01
Full Text Available The safety of a multi-span waler beam subjected simultaneously to a distributed load and deflections at its supports can be secured by limiting the maximum stress of the beam to a specific value to prevent the beam from reaching a limit state for failure or collapse. Despite the fact that the vast majority of accidents on construction sites occur at waler beams in retaining wall systems, no safety monitoring model that can consider deflections at the supports of the beam is available. In this paper, a maximum stress estimation model for a waler beam based on average strains measured from vibrating wire strain gauges (VWSGs, the most frequently used sensors in construction field, is presented. The model is derived by defining the relationship between the maximum stress and the average strains measured from VWSGs. In addition to the maximum stress, support reactions, deflections at supports, and the magnitudes of distributed loads for the beam structure can be identified by the estimation model using the average strains. Using simulation tests on two multi-span beams, the performance of the model is evaluated by estimating maximum stress, deflections at supports, support reactions, and the magnitudes of distributed loads.
P. A. Johnson
1996-01-01
Full Text Available Nonlinear elastic response in rock is established as a robust and representative characteristic rock rather than a curiosity. We show measurements of this behaviour from a variety of experiments on rock taken over many orders of magnitude in strain and frequency. The evidence leads to a pattern of unifying behaviour in rock: (1 Nonlinear response in rock is ubiquitous. (2 The response takes place over a large frequency interval (dc to 105 kHz at least. (3 The response not only occurs, as is commonly appreciated, large strains but also at small strains where this behaviour and the manifestations of this behaviour are commonly disregarded.
A.H. Curiale (Ariel H.); G. Vegas-Sanchez-Ferrero (Gonzalo); J.G. Bosch (Hans); S. Aja-Fernández (Santiago)
2015-01-01
textabstractThe strain and strain-rate measures are commonly used for the analysis and assessment of regional myocardial function. In echocardiography (EC), the strain analysis became possible using Tissue Doppler Imaging (TDI). Unfortunately, this modality shows an important limitation: the angle
A.H. Curiale (Ariel H.); G. Vegas-Sanchez-Ferrero (Gonzalo); J.G. Bosch (Johan); S. Aja-Fernández (Santiago)
2015-01-01
textabstractThe strain and strain-rate measures are commonly used for the analysis and assessment of regional myocardial function. In echocardiography (EC), the strain analysis became possible using Tissue Doppler Imaging (TDI). Unfortunately, this modality shows an important limitation: the angle b
McCarty, K.F. (Sandia National Laboratories, Livermore, California 94550 (United States))
1999-09-01
We address whether the elastic strain-energy theory (minimizing the Gibbs energy of a stressed crystal) of McKenzie and co-workers [D. R. McKenzie and M. M. M. Bilek, J. Vac. Sci. Technol. A [bold 16], 2733 (1998)] adequately explains the preferred orientation observed in carbon and BN films. In the formalism, the Gibbs energy of the cubic materials diamond and cubic boron includes the strain that occurs when the phases form, through specific structural transformations, from graphitic precursors. This treatment violates the requirement of thermodynamics that the Gibbs energy be a path-independent, state function. If the cubic phases are treated using the same (path-independent) formalism applied to the graphitic materials, the crystallographic orientation of lowest Gibbs energy is not that observed experimentally. For graphitic (hexagonal) carbon and BN, an elastic strain approach seems inappropriate because the compressive stresses in energetically deposited films are orders of magnitude higher than the elastic limit of the materials. Furthermore, using the known elastic constants of either ordered or disordered graphitic materials, the theory does not predict the orientation observed by experiment. [copyright] [ital 1999 American Vacuum Society.
Song, Ki Nam [Korea Atomic Energy Research Institute, Daeduk (Korea, Republic of)
1996-03-01
A formula to evaluate the elastic stiffness of the leaf type holddown spring (HDS)assembly with uniformly tapered thickness from t{sub 0} to t{sub 1} (t{sub 0} < t{sub 1}) has been analytically derived by applying the engineering beam theory and Casiliano`s theorem based on strain energies due to bending moment, shear and axial force. Comparisons on the elastic stiffnesses have been made with test results and evaluated values from the derived formula for the 14x14 and 17x17 type KOFA HDS, and it has found that most of the differences were in the range of 1-2% of the evaluated elastic stiffnesses and that the elastic stiffness of the HDS was mainly caused by bending moment because effects of shear and axial forces on the elastic stiffness were in the range of 0.09-0.16%. And in addition, it has found that the derived formula could be applicable to HDS designed by Westinghouse. Therefore, the derived formula could be applicable to evaluating the elastic stiffness of any HDS with tapered thickness only with the informations of the geometric data and material properties of leaf springs regardness of the manufacturing companies. 8 tabs., 4 figs., 22 refs. (Author) .new.
Danesi, Valentina; Erani, Paolo; Brandolini, Nicola; Juszczyk, Mateusz M; Cristofolini, Luca
2016-10-01
The vertebral strength and strain can be assessed in vitro by both using isolated vertebrae and sets of three adjacent vertebrae (the central one is loaded through the disks). Our goal was to elucidate if testing single-vertebra-specimens in the elastic regime provides different surface strains to three-vertebrae-segments. Twelve three-vertebrae sets were extracted from thoracolumbar human spines. To measure the principal strains, the central vertebra of each segment was prepared with eight strain-gauges. The sets were tested mechanically, allowing comparison of the surface strains between the two boundary conditions: first when the same vertebra was loaded through the disks (three-vertebrae-segment) and then with the endplates embedded in cement (single-vertebra). They were all subjected to four nondestructive tests (compression, traction, torsion clockwise, and counterclockwise). The magnitude of principal strains differed significantly between the two boundary conditions. For axial loading, the largest principal strains (along vertebral axis) were significantly higher when the same vertebra was tested isolated compared to the three-vertebrae-segment. Conversely, circumferential strains decreased significantly in the single vertebrae compared to the three-vertebrae-segment, with some variations exceeding 100% of the strain magnitude, including changes from tension to compression. For torsion, the differences between boundary conditions were smaller. This study shows that, in the elastic regime, when the vertebra is loaded through a cement pot, the surface strains differ from when it is loaded through the disks. Therefore, when single vertebrae are tested, surface strain should be taken with caution.
A coupled BEM-FEM method for finite strain magneto-elastic boundary-value problems
Nedjar, B.
2016-12-01
The first objective of this contribution is the formulation of nonlinear problems in magneto-elasticity involving finite geometry of the surrounding free space. More specifically for the magnetic part of the problem, the surrounding free space is described by means of a boundary integral equation for which boundary elements are used that are appropriately coupled with the finite element discretization used inside the material. The second objective is to develop a numerical strategy to solve the strongly coupled magneto-mechanics problem at hand. Herein we provide a staggered scheme consisting of a magnetostatic resolution employing the above coupled BEM-FEM procedure at fixed deformation, followed by a mechanical resolution at fixed magnetic fields. This decoupled method renders the whole solution strategy very appealing since, among others, the first BEM-FEM resolution is linear for some prototype models, and the remaining mechanical resolution is analogous to nowadays classical nonlinear elastostatic problems in the finite strain range. Some nonlinear boundary-value problems are simulated to demonstrate the applicability of the proposed framework.
Xu-Sheng Zhang; Chi Zhang; Wei-Jia Zeng
2016-01-01
Objective:To find the value of elastic strain ratio detection by transvaginal elastography in diagnosis of cervical carcinoma and judgment of illness.Methods:A total of 178 cases of women receiving vaginal ultrasound in our hospital from August 2011 to June 2014 were selected as research subjects, obtained cervical tissue block received pathological examination, and according to pathological results, all research subjects were divided into cervical carcinoma group 51 cases, benign cervical lesion group 78 cases and healthy control group 49 cases. Elastography pressure release index and elastic strain ratio, protein expression of CDK8, Ki-67, P53, Pin1 and Cyclin D1 in cervical tissue, serum tumor maker levels, serum COX-2, MMP-9, SCCAg, Apo-1/Fas and S-TK1 levels of all subjects were detected, and the correlation between elastic strain ratio and above cervical carcinoma-related indicator values was further analyzed.Results:Elastography pressure release index and elastic strain ratio of cervical carcinoma group were higher than those of benign cervical lesion group and healthy control group; protein expression levels of CDK8, Ki-67, P53, Pin1 and Cyclin D1 in cervical tissue of cervical carcinoma group were higher than those of benign cervical lesion group and healthy control group; serum CA125, Cyfra21-1, CA724 and CEA levels of cervical carcinoma group were higher than those of benign cervical lesion group and healthy control group; serum COX-2, MMP-9, SCCAg, Apo-1/Fas and S-TK1 levels of cervical carcinoma group were higher than those of benign cervical lesion group and healthy control group; elastic strain ratio had positive correlation with protein expression levels of CDK8, Ki-67, P53, Pin1 and Cyclin D1 in cervical tissue as well as CA125, Cyfra21-1, CA724, CEA, COX-2, MMP-9, SCCAg, Apo-1/Fas and S-TK1 levels in serum.Conclusion:Elastic strain ratio detected by transvaginal elastography can be used as the effective means for diagnosis of cervical carcinoma
NEELAM KUMARI
2012-11-01
Full Text Available The Biot linearized theory for fluid saturated porous materials is used to study the plane strain deformation of an isotropic, homogeneous, poroelastPic half space in welded contact with a homogeneous, transversely isotropic, elastic half space caused by an inclined line-load in elastic half space. The integral expressions for the displacements and stresses in the two half spaces in welded contact are obtained from the corresponding expressions for an unbounded transversely isotropic elastic and poroelastic medium by applying boundary conditions at the interface. The integrals for the inclined line-load are solved analytically for the limiting casei.e. undrained conditions in high frequency limit. The undrained displacements, stresses and pore pressure are shown graphically. Expression for the pore pressure is also calculated for undrained conditions in the high frequency limit.
Le Page, Yvon; Saxe, Paul
2002-03-01
A symmetry-general approach for the least-squares, therefore precise, extraction of elastic coefficients for strained materials is reported. It analyzes stresses calculated ab initio for properly selected strains. The problem, its implementation, and its solution strategy all differ radically from a previous energy-strain approach that we published last year, but the normal equations turn out to be amenable to the same constrainment scheme that makes both approaches symmetry general. The symmetry considerations governing the automated selection of appropriately strained models and their Cartesian systems are detailed. The extension to materials under general stress is discussed and implemented. VASP was used for ab initio calculation of stresses. A comprehensive range of examples includes a triclinic material (kyanite) and simple materials with a range of symmetries at zero pressure, MgO under hydrostatic pressure, Ti4As3 under [001] uniaxial strain, and Si under [001] uniaxial stress. The MgO case agrees with recent experimental work including elastic coefficients as well as their first and second derivatives. The curves of elastic coefficients for Si show a gradual increase in the 33 compliance coefficient, leading to a collapse of the material at -11.7 GPa, compared with -12.0 GPa experimentally. Interpretation of results for Be using two approximations [local density (LDA), generalized gradient (GGA)], two approaches (stress strain and energy strain), two potential types (projector augmented wave and ultrasoft), and two quantum engines (VASP and ORESTES) expose the utmost importance of the cell data used for the elastic calculations and the lesser importance of the other factors. For stiffness at relaxed cell data, differences are shown to originate mostly in the considerable overestimation of the residual compressive stresses at x-ray cell data by LDA, resulting in a smaller relaxed cell, thus larger values for diagonal stiffness coefficients. The symmetry
Levine, Lyle E; Okoro, Chukwudi; Xu, Ruqing
2015-11-01
Nondestructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 µm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components.
Sedighi, Hamid M.
2014-02-01
This paper presents the impact of vibrational amplitude on the dynamic pull-in instability and fundamental frequency of actuated microbeams by introducing the second order frequency-amplitude relationship. The nonlinear governing equation of microbeam predeformed by an electric force including the fringing field effect, based on the strain gradient elasticity theory is considered. The predicted results of the strain gradient elasticity theory are compared with the outcomes that arise from the classical and modified couple stress theory. The influences of basic nondimensional parameters on the pull-in instability as well as the natural frequency are investigated by a powerful asymptotic approach namely the Parameter Expansion Method (PEM). It is demonstrated that two terms in series expansions are sufficient to produce an acceptable solution of the microstructure. The phase portrait of the microstructure shows that by increasing the actuation voltage parameter, the stable center point loses its stability and coalesces with unstable saddle node.
Hudetz, A G; Monos, E
1981-01-01
Three-dimensional quasi-static mechanical measurements were carried out on cylindrical segments of the dog carotid and iliac arteries for determination of the passive anisotropic elastic properties of the vessel wall. On the basis of passive characteristics of outer diameter vs. intraluminal pressure, and axial extending force vs. intraluminal pressure, picked up at various fixed initial vascular length values, the incremental Young moduli and poisson ratios of the vessel wall were calculated in the 0--33 kPa (0--250 mm Hg) pressure range. The strain energy function of the arteries was approximated by polynomial and exponential models. We found that an exponential energy function with 4-parameters gives more accurate results than the 7- or 12-parameter polynomial functions. According to the results the axial modulus reaches higher values than the tangential and radial moduli at a low tangential stretch level, while at high tangential stretch the tangential modulus is the highest in both carotid and iliac arteries. After elevation of the initial tangential stretch the increase in the tangential modulus is the most pronounced, while the values of radial and axial moduli increased less. A change in the initial axial stretch influences the axial and radial moduli to a similar extent, but has no substantial effect on the value of the tangential modulus. The values of corresponding poisson ratios depend in a similar way on the initial deformation state. The different behaviour of the two Poisson ratios characterizing the mechanical coupling between tangential and axial directions, indicates that the structural coupling between the two main directions is asymmetrical. It is assumed that this property of the passive vascular structure can be explained by the network arrangement of collagen fibres in the vessel wall.
Hanson, David E
2011-08-07
Based on recent molecular dynamics and ab initio simulations of small isoprene molecules, we propose a new ansatz for rubber elasticity. We envision a network chain as a series of independent molecular kinks, each comprised of a small number of backbone units, and the strain as being imposed along the contour of the chain. We treat chain extension in three distinct force regimes: (Ia) near zero strain, where we assume that the chain is extended within a well defined tube, with all of the kinks participating simultaneously as entropic elastic springs, (II) when the chain becomes sensibly straight, giving rise to a purely enthalpic stretching force (until bond rupture occurs) and, (Ib) a linear entropic regime, between regimes Ia and II, in which a force limit is imposed by tube deformation. In this intermediate regime, the molecular kinks are assumed to be gradually straightened until the chain becomes a series of straight segments between entanglements. We assume that there exists a tube deformation tension limit that is inversely proportional to the chain path tortuosity. Here we report the results of numerical simulations of explicit three-dimensional, periodic, polyisoprene networks, using these extension-only force models. At low strain, crosslink nodes are moved affinely, up to an arbitrary node force limit. Above this limit, non-affine motion of the nodes is allowed to relax unbalanced chain forces. Our simulation results are in good agreement with tensile stress vs. strain experiments.
Bedolla Pantoja, Marco A; Abbott, Nicholas L
2016-05-25
We report the fabrication of chemically patterned microwells that enable the rapid and facile preparation (by spin coating and patterned dewetting) of thin films of liquid crystals (LCs) that have precise thicknesses (0.7-30 μm), are supported on chemically defined substrates, and have free upper surfaces. We use these microwells to prepare elastically strained nematic LC films supported on silica glass, gold, or polystyrene substrates and thereby characterize the response of the strained LC films to vapors of toluene. We report that low concentrations of toluene vapor (LC to lower the anchoring energy of the LC on these substrates, thus allowing the elastic energy of the strained LC film to drive the LC films through an orientational transition. The central role of the toluene-induced change in surface anchoring energy is supported by additional experiments in which the response of the nematic LC to changes in film thickness and substrate identity are quantified. A simple thermodynamic model captures these trends and yielded estimates of anchoring energies (8-22 μJ/m(2)). Significantly, the orientational transitions observed in these strained LC thin films occur at concentrations of toluene vapor that are almost 1 order of magnitude below those which lead to bulk phase transitions, and they are not triggered by exposure to water vapor. Overall, these results hint at principles for the design of responsive LC-based materials that can be triggered by concentrations of aromatic, volatile organic compounds that are relevant to human health.
Liu Yu-Min; Yu Zhong-Yuan; Ren Xiao-Min
2009-01-01
Based on the continuum elastic theory, this paper presents a finite element analysis to investigate the influences of elastic anisotropy and thickness of spacing layer on the strain field distribution and band edges (both conduction band and valence band) of the InAs/GaAs conical shaped quantum dots. To illustrate these effects, we give detailed comparisons with the circumstances of isolated and stacking quantum dot for both anisotropic and isotropic elastic characteristics. The results show that, in realistic materials design and theoretical predication performances of the optoelectronie devices, both the elastic anisotropy and thickness of the spacing layer of stacked quantum dot should be taken into consideration.
Ziółkowski, Andrzej
2016-09-01
An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition
Ziółkowski, Andrzej
2017-01-01
An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition
Prediction of Maximum Strain in Finocyl Port Case-bonded Solid Propellants under Pressure Loading
Himanshu Shekhar
2006-07-01
Full Text Available Finite element analysis of case-bonded solid propellants in finocyl port configuration hasbeen carried out using finite element method. The parametric studies have also been conductedfor loading conditions, material properties, and geometrical configurations. The results arepresented in the form of a universal power law, which can be utilised for primary assessmentof peak strain in any finocyl port propellant configuration without using finite element software.This eliminates dependence on finite element software for structural integrity analysis of solidpropellants in finocyl port configuration under port pressurisation. The results obtained by finiteelement analysis and power law are in close agreement.
An experimental method to obtain the elastic strain energy function from torsion-tension tests
Peng, S. T. J.; Landel, R. F.
1976-01-01
It is shown that by employing a torsion-tension test, it is possible to have a complete mapping near the origin of the two principal strain invariants associated with the rate of change of the strain energy function. However, the mathematical representation of the twist moment and normal forces vs strain and the strain energy function are complex. This problem is solved by using a set of solid cylindrical bars with different diameters such that the difference in diameter of two successive bars is small. The stress-strain equations can be grossly oversimplified by considering differences in twist moment and normal force as a function of difference in radius.
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Mandsberg, Lotte Frigaard
2008-01-01
with an exponentially decaying function of the time between observations is suggested. A model with a full covariance structure containing OD-dependent variance and an autocorrelation structure is compared to a model with variance only and with no variance or correlation implemented. It is shown that the model...... are used for parameter estimation. The data is log-transformed such that a linear model can be applied. The transformation changes the variance structure, and hence an OD-dependent variance is implemented in the model. The autocorrelation in the data is demonstrated, and a correlation model...... that best describes data is a model taking into account the full covariance structure. An inference study is made in order to determine whether the growth rate of the five bacteria strains is the same. After applying a likelihood-ratio test to models with a full covariance structure, it is concluded...
Solving the problem of elasticity for round thick plates at axially symmetric strain
Oleksiy Hvertsev
2016-12-01
Full Text Available An exact solution of the equations of elasticity for round plates loaded axially symmetric. The problem of bending round plates, which are under the influence of normal forces attached to any law to load any type of resistance. It is shown that pasture circular plate under axially symmetric load leads to appearance of temperature field.
Small Strain Compatibility Conditions of an Elastic Solid in Cylindrical Coordinates
2013-04-01
Intermediate Mechanics of Materials, McGraw-Hill, New York, 2001. 4. Timoshenko , S. P., Goodier, J. N., Theory of Elasticity, 3rd Ed., McGraw-Hill, New York...1970. 5. Timoshenko , S. P., Woinowsky-Krieger, S., Theory of Plates and Shells, 2nd Ed., McGraw- Hill, New York, 1959. 6. Boresi, Arthur P
Nakayama, M; Ariji, Y; Nishiyama, W; Ariji, E
2015-01-01
To verify the use of a single coupling agent as a reference to obtain the elasticity index (EI) ratios and to investigate the EI ratios of the masseter muscles of healthy volunteers. Muscle phantoms with known elasticity (20, 40 and 60 kPa in the Young's modulus) were examined by strain-type sonoelastography using a coupling agent as the reference. Eight examiners tested soft (with 7 kPa) and hard (with 40 kpa) reference coupling agents separately. The correlation coefficients were determined between the EI ratio and Young's modulus of muscle phantoms. The interclass correlation coefficients were calculated for inter- and intraexaminer agreement. Strong correlations were found between the EI ratios and Young's modulus for both soft and hard references. The variations of the EI ratios were larger with soft coupling agents than those with hard coupling agents, and they increased in phantoms with 60 kPa elasticity. There were no differences in the EI ratios of the masseter muscle at rest between males and females or between the right and left sides. The ratio increased during clenching. The hard reference coupling agent was suitable for obtaining EI ratio of the masseter muscle. No differences were found in the EI ratios of the masseter muscle either between sexes or between the right and left sides at rest, and the ratios increased with the widening of their variations during clenching.
PREDICTION OF MAXIMUM CREEP STRAIN OF HIGH PERFORMANCE STEEL FIBER REINFORCED CONCRETE
Mishina Alexandra Vasil'evna
2012-12-01
Full Text Available The strongest research potential is demonstrated by the areas of application of high performance steel fiber reinforced concrete (HPSFRC. The research of its rheological characteristics is very important for the purposes of understanding its behaviour. This article is an overview of an experimental study of UHSSFRC. The study was carried out in the form of lasting creep tests of HPSFRC prism specimen, loaded by stresses of varied intensity. The loading was performed at different ages: 7, 14, 28 and 90 days after concreting. The stress intensity was 0.3 and 0.6 Rb; it was identified on the basis of short-term crush tests of similar prism-shaped specimen, performed on the same day. As a result, values of ultimate creep strains and ultimate specific creep of HPSFRC were identified. The data was used to construct an experimental diagramme of the ultimate specific creep on the basis of the HPSFRC loading age if exposed to various stresses. The research has resulted in the identification of a theoretical relationship that may serve as the basis for the high-precision projection of the pattern of changes in the ultimate specific creep of HPSFRC, depending on the age of loading and the stress intensity.
Erlings, J.G.; Groot, H.W. de; Nauta, J.
1987-01-01
A procedure is presented with which the roles of elastic and elastic-plastic straining in stress corrosion cracking (SCC) and hydrogen embrittlement (HE) can be determined. Premature failure of 3.5% Ni steels in sour and sweet environments due to SCC was only found when slow plastic straining was applied. With purely elastic slow straining the material remained crack-free, even in a buffered NACE solution. Depending on the sourness of the environment, the API 5L X60 pipeline material did not always need plastic straining to suffer HE cracking. Under none of the test conditions studied was hardened material susceptible to SCC or HE cracking. The non-hardened material tested was not susceptible to SCC in the various CO/sub 2/- and/or H/sub 2/S-containing media used.
Du, Minshu; Wan, Qiong; Wang, Zhongqiang; Cui, Lishan
2016-08-01
The application of elastic strain is a promising approach for tuning bandgap of semiconductors; however, the attainment of a simple method for introducing strain has been a major challenge. Here, martensitic surface relief of FeNiCoTi substrate was utilized to tensilely strain TiO2 nanofilm successfully. The elastic strain effects of photocatalysis were also investigated. It was showed that tensile strain reduced the bandgap of TiO2 nanofilm by 50 meV and contributed to a 33.8% faster photodegradation rate of methyl orange, also the photocurrent of the water oxidation reaction of strained TiO2 was 1.4 times as high as that of unstrained nanofilm.
Wu, Jian-Ying; Cervera, Miguel
2017-04-20
Damage-induced strain softening is of vital importance for the modeling of localized failure in frictional-cohesive materials. This paper addresses strain localization of damaging solids and the resulting consistent frictional-cohesive crack models. As a supplement to the framework recently established for stress-based continuum material models in rate form (Wu and Cervera 2015, 2016), several classical strain-based damage models, expressed usually in total and secant format, are considered. Upon strain localization of such damaging solids, Maxwell's kinematics of a strong (or regularized) discontinuity has to be reproduced by the inelastic damage strains, which are defined by a bounded characteristic tensor and an unbounded scalar related to the damage variable. This kinematic constraint yields a set of nonlinear equations from which the discontinuity orientation and damage-type localized cohesive relations can be derived. It is found that for the "Simó and Ju 1987" isotropic damage model, the localization angles and the resulting cohesive model heavily depend on lateral deformations usually ignored in classical crack models for quasi-brittle solids. To remedy this inconsistency, a modified damage model is proposed. Its strain localization analysis naturally results in a consistent frictional-cohesive crack model of damage type, which can be regularized as a classical smeared crack model. The analytical results are numerically verified by the recently-proposed mixed stabilized finite element method, regarding a singly-perforated plate under uniaxial tension. Remarkably, for all of the damage models discussed in this work, the numerically-obtained localization angles agree almost exactly with the closed-form results. This agreement, on the one hand, consolidates the strain localization analysis based on Maxwell's kinematics and, on the other hand, illustrates versatility of the mixed stabilized finite element method.
Strain-rate Dependence of Elastic Modulus Reveals Silver Nanoparticle Induced Cytotoxicity.
Caporizzo, Matthew Alexander; Roco, Charles M; Ferrer, Maria Carme Coll; Grady, Martha E; Parrish, Emmabeth; Eckmann, David M; Composto, Russell John
Force-displacement measurements are taken at different rates with an atomic force microscope to assess the correlation between cell health and cell viscoelasticity in THP-1 cells that have been treated with a novel drug carrier. A variable indentation-rate viscoelastic analysis, VIVA, is employed to identify the relaxation time of the cells that are known to exhibit a frequency dependent stiffness. The VIVA agrees with a fluorescent viability assay. This indicates that dextran-lysozyme drug carriers are biocompatible and deliver concentrated toxic material (rhodamine or silver nanoparticles) to the cytoplasm of THP-1 cells. By modelling the frequency dependence of the elastic modulus, the VIVA provides three metrics of cytoplasmic viscoelasticity: a low frequency modulus, a high frequency modulus and viscosity. The signature of cytotoxicity by rhodamine or silver exposure is a frequency independent twofold increase in the elastic modulus and cytoplasmic viscosity, while the cytoskeletal relaxation time remains unchanged. This is consistent with the known toxic mechanism of silver nanoparticles, where metabolic stress causes an increase in the rigidity of the cytoplasm. A variable indentation-rate viscoelastic analysis is presented as a straightforward method to promote the self-consistent comparison between cells. This is paramount to the development of early diagnosis and treatment of disease.
A finite element implementation of surface elasticity at finite strains using the deal.II library
McBride, Andrew; Steinmann, Paul; Reddy, B Daya
2015-01-01
The potentially significant role of the surface of an elastic body in the overall response of the continuum can be described using the mature theory of surface elasticity. The objective of this contribution is to detail the finite element approximation of the underlying governing equations (both in the volume and on its surface) and their solution using the open-source finite element library deal.II. The fully-nonlinear (geometric and material) setting is considered. The nonlinear problem is solved using a Newton--Raphson procedure wherein the tangent contributions from the volume and surface are computed exactly. The finite element formulation is implemented within the total Lagrangian framework and a Bubnov-Galerkin spatial discretization of the volume and the surface employed. The surface is assumed material. A map between the degrees of freedom on the surface and on the boundary of the volume is used to allocate the contribution from the surface to the global system matrix and residual vector. The deal.II...
Befus, M; Mukherjee, D V; Herzig, C T A; Lowy, F D; Larson, E
2017-07-01
Prisons/jails are thought to amplify the transmission of Staphylococcus aureus (SA) particularly methicillin-resistant SA infection and colonisation. Two independently pooled cross-sectional samples of detainees being admitted or discharged from two New York State maximum-security prisons were used to explore this concept. Private interviews of participants were conducted, during which the anterior nares and oropharynx were sampled and assessed for SA colonisation. Log-binomial regression and correspondence analysis (CA) were used to evaluate the prevalence of colonisation at entry as compared with discharge. Approximately 51% of admitted (N = 404) and 41% of discharged (N = 439) female detainees were colonised with SA. Among males, 59% of those admitted (N = 427) and 49% of those discharged (N = 393) were colonised. Females had a statistically significant higher prevalence (1·26: P = 0·003) whereas males showed no significant difference (1·06; P = 0·003) in SA prevalence between entry and discharge. CA demonstrated that some strains, such as spa types t571 and t002, might have an affinity for certain mucosal sites. Contrary to our hypothesis, the prison setting did not amplify SA transmission, and CA proved to be a useful tool in describing the population structure of strains according to time and/or mucosal site.
Existence of solutions for the anti-plane stress for a new class of “strain-limiting” elastic bodies
Bulíček, Miroslav
2015-04-21
© 2015, Springer-Verlag Berlin Heidelberg. The main purpose of this study is to establish the existence of a weak solution to the anti-plane stress problem on V-notch domains for a class of recently proposed new models that could describe elastic materials in which the stress can increase unboundedly while the strain yet remains small. We shall also investigate the qualitative properties of the solution that is established. Although the equations governing the deformation that are being considered share certain similarities with the minimal surface problem, the boundary conditions and the presence of an additional model parameter that appears in the equation and its specific range makes the problem, as well as the result, different from those associated with the minimal surface problem.
Stress-Strain State Of Elastic Plate With An Arbitrary Smooth Notch
Kuz Ihor
2015-12-01
Full Text Available The paper contains comparing calculations of the stress fields in an elastic plate with notch along the arc of a circle, ellipse or parabola obtained by analytic method based on complex Kolosov-Muskhelishvili potentials and by numerical variation-difference method. These fields differ by no more than 2%, which, in particular, indicates the reliability of such numerical implementation. This discrepancy can be explained by the fact that in the analytical solution domain is unbounded, while the numerical calculation was carried out, obviously, for a finite field. The given stresses at the top of the notch along the arc of an ellipse or a parabola significantly increase with increasing of the relative depth of the notch (while increasing its depth or decreasing width.
The nonconforming linear strain tetrahedron for a large deformation elasticity problem
Hansbo, Peter; Larsson, Fredrik
2016-12-01
In this paper we investigate the performance of the nonconforming linear strain tetrahedron element introduced by Hansbo (Comput Methods Appl Mech Eng 200(9-12):1311-1316, 2011; J Numer Methods Eng 91(10):1105-1114, 2012). This approximation uses midpoints of edges on tetrahedra in three dimensions with either point continuity or mean continuity along edges of the tetrahedra. Since it contains (rotated) bilinear terms it performs substantially better than the standard constant strain element in bending. It also allows for under-integration in the form of one point Gauss integration of volumetric terms in near incompressible situations. We combine under-integration of the volumetric terms with houglass stabilization for the isochoric terms.
The nonconforming linear strain tetrahedron for a large deformation elasticity problem
Hansbo, Peter; Larsson, Fredrik
2016-08-01
In this paper we investigate the performance of the nonconforming linear strain tetrahedron element introduced by Hansbo (Comput Methods Appl Mech Eng 200(9-12):1311-1316, 2011; J Numer Methods Eng 91(10):1105-1114, 2012). This approximation uses midpoints of edges on tetrahedra in three dimensions with either point continuity or mean continuity along edges of the tetrahedra. Since it contains (rotated) bilinear terms it performs substantially better than the standard constant strain element in bending. It also allows for under-integration in the form of one point Gauss integration of volumetric terms in near incompressible situations. We combine under-integration of the volumetric terms with houglass stabilization for the isochoric terms.
Chakraborty, Bidisha; Heyde, Brecht; Alessandrini, Martino; D'hooge, Jan
2016-04-01
Image registration techniques using free-form deformation models have shown promising results for 3D myocardial strain estimation from ultrasound. However, the use of this technique has mostly been limited to research institutes due to the high computational demand, which is primarily due to the computational load of the regularization term ensuring spatially smooth cardiac strain estimates. Indeed, this term typically requires evaluating derivatives of the transformation field numerically in each voxel of the image during every iteration of the optimization process. In this paper, we replace this time-consuming step with a closed-form solution directly associated with the transformation field resulting in a speed up factor of ~10-60,000, for a typical 3D B-mode image of 2503 and 5003 voxels, depending upon the size and the parametrization of the transformation field. The performance of the numeric and the analytic solutions was contrasted by computing tracking and strain accuracy on two realistic synthetic 3D cardiac ultrasound sequences, mimicking two ischemic motion patterns. Mean and standard deviation of the displacement errors over the cardiac cycle for the numeric and analytic solutions were 0.68+/-0.40 mm and 0.75+/-0.43 mm respectively. Correlations for the radial, longitudinal and circumferential strain components at end-systole were 0.89, 0.83 and 0.95 versus 0.90, 0.88 and 0.92 for the numeric and analytic regularization respectively. The analytic solution matched the performance of the numeric solution as no statistically significant differences (p>0.05) were found when expressed in terms of bias or limits-of-agreement.
Eggers, G. L.; Lewis, K. W.; Simons, F. J.
2012-12-01
Venus has undergone a markedly different evolution than Earth. Its tectonics do not resemble the plate-tectonic system observed on Earth, and many surface features—such as tesserae and coronae—lack terrestrial equivalents. To understand Venus' tectonics is to understand its lithosphere. Lithospheric parameters such as the effective elastic thickness have previously been estimated from the correlation between topography and gravity anomalies, either in the space domain or the spectral domain (where admittance or coherence functions are estimated). Correlation and spectral analyses that have been obtained on Venus have been limited by geometry (typically, only rectangular or circular data windows were used), and most have lacked robust error estimates. There are two levels of error: the first being how well the correlation, admittance or coherence can be estimated; the second and most important, how well the lithospheric elastic thickness can be estimated from those. The first type of error is well understood, via classical analyses of resolution, bias and variance in multivariate spectral analysis. Understanding this error leads to constructive approaches of performing the spectral analysis, via multi-taper methods (which reduce variance) with well-chosen optimal tapers (to reduce bias). The second type of error requires a complete analysis of the coupled system of differential equations that describes how certain inputs (the unobservable initial loading by topography at various interfaces) are being mapped to the output (final, measurable topography and gravity anomalies). The equations of flexure have one unknown: the flexural rigidity or effective elastic thickness—the parameter of interest. Fortunately, we have recently come to a full understanding of this second type of error, and derived a maximum-likelihood estimation (MLE) method that results in unbiased and minimum-variance estimates of the flexural rigidity under a variety of initial
Xuebin Wang
2005-01-01
A mechanical model is proposed for the system of elastic beam and strain-softening pillar where strain localization is initiated at peak shear stress. To obtain the plastic deformation of the pillar due to the shear slips of multiple shear bands, the pillar is divided into several narrow slices where compressive deformation is treated as uniformity. In the light of the compatibility condition of deformation, the total compressive displacement of the pillar is equal to the displacement of the beam in the middle span. An insta bility criterion is derived analytically based on the energy principle using a known size of localization band according to gradientdependent plasticity. The main advantage of the present model is that the effects of the constitutive parameters of rock and the geometrical size of structure are reflected in the criterion. The condition that the derivative of distributed load with respect to the deflection of the beam in the middle span is less than zero is not only equivalent to, but also even more concise in form than the instability criterion. To study the influences of constitutive parameters and geometrical size on stability, some examples are presented.
The influence of elastic strain on the early stages of decomposition in Cu–1.7at% Fe
Rademacher, Thomas
2009-04-01
The initial stage of decomposition of homogenized Cu-1.7 at% Fe at 722 K was investigated by means of field ion microscopy (FIM), atom probe tomography (APT) and computer-assisted field ion image tomography (cFIIT). The agglomeration of atoms depending on time could be investigated and the growth of precipitates with a diameter of few nanometers was observed during ongoing nucleation. For the cFIIT measurements, an improved reconstruction algorithm was developed. Employing cFIIT in combination with FIM images, alignments of precipitates mainly in < 100 > directions were found. Besides, a general experimental concept to evaluate strain-related effects on the position of the proximate precipitate will be introduced. These analyses of the APT and cFIIT data show tendencies of a preferred < 100 > directed configuration as well. This effect can be associated with the elastic anisotropy of the Cu matrix (f.c.c.) to accommodate the volume misfit of precipitates. In accordance with previous model calculations, a preferred nucleation in < 100 > directions with respect to existing clusters can be concluded. For such cluster arrangements strain energy reduction is largest for precipitates adapting their sizes. Thus, additional stabilization against coarsening can be inferred for < 100 > alignments which result in the observed effects. (C) 2008 Published by Elsevier B.V.
I. K. Badalakha
2009-12-01
Full Text Available The article presents the results of solving several problems of a flat deformation of elastic infinitely long massifs of different width and limited thickness. Various cases of conditions at the massif/base contact. The relationships between stressed and strained states previously suggested by the author, which differ from the generalized Hooke’s law, are used in the solutions.
Evertz, T. [Salzgitter Flachstahl GmbH, Salzgitter (Germany); Sonne, H.M. [ThyssenKrupp Stahl AG, Duisburg (Germany); Steinbeck, G. [Stahlinstitut VDEh, Duesseldorf (Germany); Engl, B. [MgF Magnesium Flachprodukte GmbH, Freiberg (Germany)
2004-08-01
Within the scope of a common research project of the steel and automotive industry, 20 sheet steels have been investigated to obtain input data for FE-analysis. In detail, characteristical elastic, plastic and fatique values were determined by several testing institutes for a period of 3 years. Knowledge of dependency of Young's modulus from temperature and orientation is important for spring back at the press shop and stiffness of parts for automotive. Young's modulus was determined by tensile tests in delivered state, after prestraining, heat treatment at room temperature and -40 C and 100 C. Young's modulus is dependent from the orientation to rolling direction and can be classified in groups. Young's modulus of ferritic steels is decreased about 10 % by prestraining of 2 % but recovered after annealing at 170 C. Temperature dependency well known from non destructive tests are confirmed. (Abstract Copyright [2004], Wiley Periodicals, Inc.) [German] Im Rahmen eines gemeinschaftlichen Projektes der Stahl- und Automobilindustrie wurden an insgesamt 20 Staehlen fuer Feinblech Kennwerte fuer die FE-Simulation ermittelt. Im Einzelnen handelte es sich um elastische, plastische und zyklische Kennwerte, die ueber einen Zeitraum von 3 Jahren von unterschiedlichen Pruefstellen erarbeitet wurden. Die Bedeutung des temperatur- und richtungsabhaengigen E-Moduls fuer den Automobilbau ist in der Rueckfederung beim Pressen von Blechen und der Steifigkeit von Automobilteilen begruendet. Der E-Modul wurde mit dem Zugversuch fuer den Anlieferungszustand, nach Vorverformung und teilweise nach Waermebehandlung bei Raumtemperatur sowie bei -40 C und 100 C ermittelt. Der E-Modul ist aufgrund der Walzbedingungen richtungsabhaengig und kann in Gruppen zusammengefasst werden. Bereits eine Vorverformung von 2 % verursacht fuer ferritische Staehle eine Verringerung des E-Moduls um ca. 10 %. Nach einer Waermebehandlung bei 170 C erholt sich der E-Modul weitgehend. Die aus
Kevin J. Maloney
2013-08-01
Full Text Available Ordered periodic microlattices with densities from 0.5 mg/cm3 to 500 mg/cm3 are fabricated by depositing various thin film materials (Au, Cu, Ni, SiO2, poly(C8H4F4 onto sacrificial polymer lattice templates. Young's modulus and strength are measured in compression and the density scaling is determined. At low relative densities, recovery from compressive strains of 50% and higher is observed, independent of lattice material. An analytical model is shown to accurately predict the transition between recoverable “pseudo-superelastic” and irrecoverable plastic deformation for all constituent materials. These materials are of interest for energy storage applications, deployable structures, and for acoustic, shock, and vibration damping.
Gurson-type elastic-plastic damage model based on strain-rate plastic potential
Balan, Tudor; Cazacu, Oana
2013-12-01
Ductile damage is generally described by stress-space analytical potentials. In this contribution, it is shown that strain rate potentials, which are exact conjugate of the stress-based potentials, can be equally used to describe the dilatational response of porous metals. This framework is particularly appropriate for porous materials with matrix described by complex yield criteria for which a closed-form expression of the stress-based potential is not available. Illustration of the new approach is done for porous metals containing randomly distributed spherical voids in a von Mises elasto-plastic matrix. Furthermore, a general time integration algorithm for simulation of the mechanical response using this new formulation is developed and implemented in Abaqus/Standard. The proposed model and algorithm are validated with respect to the Abaqus built-in GTN model, which is based on a stress potential, through the simulation of a tensile test on a round bar.
Elastic Deformation in Yield Zones for the Elastic-Plastic Plane Strain Problems%弹塑性变形中的弹性效应
田常录; 那日苏
2007-01-01
In the solution procedures of elastic-plastic problems the elastic deformation in yield zones was generally omitted due to the mathematical difficulty,and some simplified constitutive equations such as the incompressible model are widely employed in the classical plasticity. The analogy results derived in this work are compared with those of the common elastic-plastic methods, and the merit of the analogy results and the improvements in some respects are presented. Based on the basic stress element,the effects of elasticity in different stress states of non-linear elastic-plastic problems are evaluated in detail.%由于数学上的困难,弹塑性问题分析中一般忽略弹性变形.而且,求解时对本构方程的一些简化方法如不可压缩假设等被广泛采用.本文分析了一种比拟解答的优点和其在某些方面的改进,并以平面应变下的弹塑性单元体为例,详细计算和分析了不同应力状态下弹塑性变形过程中的弹性效应.
Wielewski, Euan J.; Boyce, Donald; Park, Jun-Sang; Miller, M P; Dawson, Paul
2017-03-01
Determining reliable single crystal material parameters for complex polycrystalline materials is a significant challenge for the materials community. In this work, a novel methodology for determining those parameters is outlined and successfully applied to the titanium alloy, Ti-6Al-4V. Utilizing the results from a lattice strain pole figure experiment conducted at the Cornell High Energy Synchrotron Source, an iterative approach is used to optimize the single crystal elastic moduli by comparing experimental and simulated lattice strain pole figures at discrete load steps during a uniaxial tensile test. Due to the large number of unique measurements taken during the experiments, comparisons were made by using the discrete spherical harmonic modes of both the experimental and simulated lattice strain pole figures, allowing the complete pole figures to be used to determine the single crystal elastic moduli. (C) 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Wang, Z.; Rudraraju, S.; Garikipati, K.
2016-09-01
We present a field formulation for defects that draws from the classical representation of the cores as force dipoles. We write these dipoles as singular distributions. Exploiting the key insight that the variational setting is the only appropriate one for the theory of distributions, we arrive at universally applicable weak forms for defects in nonlinear elasticity. Remarkably, the standard, Galerkin finite element method yields numerical solutions for the elastic fields of defects that, when parameterized suitably, match very well with classical, linearized elasticity solutions. The true potential of our approach, however, lies in its easy extension to generate solutions to elastic fields of defects in the regime of nonlinear elasticity, and even more notably for Toupin's theory of gradient elasticity at finite strains (Toupin Arch. Ration. Mech. Anal., 11 (1962) 385). In computing these solutions we adopt recent numerical work on an isogeometric analytic framework that enabled the first three-dimensional solutions to general boundary value problems of Toupin's theory (Rudraraju et al. Comput. Methods Appl. Mech. Eng., 278 (2014) 705). We first present exhaustive solutions to point defects, edge and screw dislocations, and a study on the energetics of interacting dislocations. Then, to demonstrate the generality and potential of our treatment, we apply it to other complex dislocation configurations, including loops and low-angle grain boundaries.
Sahmani, Saeid; Bahrami, Mohsen [Amirkabir University of Technology, Tehran (Iran, Islamic Republic of)
2015-01-15
In the current paper, dynamic stability analysis of microbeams subjected to piezoelectric voltage is presented in which the microbeam is integrated with piezoelectric layers on the lower and upper surfaces. Both of the flutter and divergence instabilities of microbeams with clamped-clamped and clamped-free boundary conditions are predicted corresponding to various values of applied voltage. To take size effect into account, the classical Timoshenko beam theory in conjunction with strain gradient elasticity theory is utilized to develop nonclassical beam model containing three additional internal length scale parameters. By using Hamilton's principle, the higher-order governing differential equations and associated boundary conditions are derived. Afterward, generalized differential quadrature method is employed to discretize the size-dependent governing differential equations along with clamped-clamped and clamped-free end supports. The critical piezoelectric voltages corresponding to various values dimensionless length scale parameter are evaluated and compared with those predicted by the classical beam theory. It is revealed that in the case of clamped-free boundary conditions, the both of flutter and divergence instabilities occur. However, for the clamped-clamped microbeams, only divergence instability takes place.
Tsuzuki, Kentaro; Hasegawa, Hideyuki; Kanai, Hiroshi; Ichiki, Masataka; Tezuka, Fumiaki
2008-05-01
Pathologic changes in arterial walls significantly influence their mechanical properties. We have developed a correlation-based method, the phased tracking method [H. Kanai et al.: IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43 (1996) 791], for measurement of the regional elasticity of the arterial wall. Using this method, elasticity distributions of lipids, blood clots, fibrous tissue, and calcified tissue were measured in vitro by experiments on excised arteries (mean±SD: lipids 89±47 kPa, blood clots 131 ±56 kPa, fibrous tissue 1022±1040 kPa, calcified tissue 2267 ±1228 kPa) [H. Kanai et al.: Circulation 107 (2003) 3018; J. Inagaki et al.: Jpn. J. Appl. Phys. 44 (2005) 4593]. It was found that arterial tissues can be classified into soft tissues (lipids and blood clots) and hard tissues (fibrous tissue and calcified tissue) on the basis of their elasticity. However, there are large overlaps between elasticity distributions of lipids and blood clots and those of fibrous tissue and calcified tissue. Thus, it was difficult to differentiate lipids from blood clots and fibrous tissue from calcified tissue by simply thresholding elasticity value. Therefore, we previously proposed a method by classifying the elasticity distribution in each region of interest (ROI) (not a single pixel) in an elasticity image into lipids, blood clots, fibrous tissue, or calcified tissue based on a likelihood function for each tissue [J. Inagaki et al.: Jpn. J. Appl. Phys. 44 (2006) 4732]. In our previous study, the optimum size of an ROI was determined to be 1,500 µm in the arterial radial direction and 1,500 µm in the arterial longitudinal direction [K. Tsuzuki et al.: Ultrasound Med. Biol. 34 (2008) 573]. In this study, the threshold for the likelihood function used in the tissue classification was set by evaluating the variance in the ultrasonic measurement of radial strain. The recognition rate was improved from 50 to 54% by the proposed thresholding.
Hiroshi Suzuki
2016-01-01
Full Text Available Elastic deformation behaviors of as-cast and annealed eutectic and hypoeutectic Zr–Cu–Al bulk metallic glasses (BMG were investigated on a basis of different strain-scales, determined by X-ray scattering and the strain gauge. The microscopic strains determined by Direct-space method and Reciprocal-space method were compared with the macroscopic strain measured by the strain gauge, and the difference in the deformation mechanism between eutectic and hypoeutectic Zr–Cu–Al BMGs was investigated by their correlation. The eutectic Zr50Cu40Al10 BMG obtains more homogeneous microstructure by free-volume annihilation after annealing, improving a resistance to deformation but degrading ductility because of a decrease in the volume fraction of weakly-bonded regions with relatively high mobility. On the other hand, the as-cast hypoeutectic Zr60Cu30Al10 BMG originally has homogeneous microstructure but loses its structural and elastic homogeneities because of nanocluster formation after annealing. Such structural changes by annealing might develop unique mechanical properties showing no degradations of ductility and toughness for the structural-relaxed hypoeutectic Zr60Cu30Al10 BMGs.
Zhang, Bao; Arola, Dwayne D; Roys, Steve; Gullapalli, Rao P
2011-08-01
The use of magnetic resonance (MR) imaging in conjunction with an endorectal coil is currently the clinical standard for the diagnosis of prostate cancer because of the increased sensitivity and specificity of this approach. However, imaging in this manner provides images and spectra of the prostate in the deformed state because of the insertion of the endorectal coil. Such deformation may lead to uncertainties in the localization of prostate cancer during therapy. We propose a novel 3-D elastic registration procedure that is based on the minimization of a physically motivated strain energy function that requires the identification of similar features (points, curves, or surfaces) in the source and target images. The Gauss-Seidel method was used in the numerical implementation of the registration algorithm. The registration procedure was validated on synthetic digital images, MR images from prostate phantom, and MR images obtained on patients. The registration error, assessed by averaging the displacement of a fiducial landmark in the target to its corresponding point in the registered image, was 0.2 ± 0.1 pixels on synthetic images. On the prostate phantom and patient data, the registration errors were 1.0 ± 0.6 pixels (0.6 ± 0.4 mm) and 1.8 ± 0.7 pixels (1.1 ± 0.4 mm), respectively. Registration also improved image similarity (normalized cross-correlation) from 0.72 ± 0.10 to 0.96 ± 0.03 on patient data. Registration results on digital images, phantom, and prostate data in vivo demonstrate that the registration procedure can be used to significantly improve both the accuracy of localized therapies such as brachytherapy or external beam therapy and can be valuable in the longitudinal follow-up of patients after therapy.
Mutungi, Gabriel
2003-01-01
The effects of adding either 25 mM inorganic phosphate (Pi) or its structural analogue arsenate (ASi) on both the maximum Ca2+ activated tension (Po) and passive muscle visco-elasticity (P2 tension) were investigated at 10 degrees C, using segments of single, chemically skinned rat muscle fibres. Whilst the results confirmed some previous findings on the effects of Pi on Po, they also showed that the addition of 25 mM ASi led to a large (approximately 50%) but completely reversible depression of Po in both the fast and slow twitch rat muscle fibres. Moreover, the depression of Po by ASi was greater at low than at high pH values. Examined in the presence of Dextran T-500, the passive tension and sarcomere length responses to a ramp stretch were found to be qualitatively and quantitatively similar to those previously reported in intact rat muscle fibres. Thus, the tension response to a ramp stretch, in the presence and absence of either 25 mM Pi or ASi, consisted of a viscous (P1), a visco-elastic (P2) and an elastic (P3) tension. However, the addition of either 25 mM Pi or ASi led to approximately 15-18% increase in the amplitude of the visco-elastic (P2) tension but had little or no effect on the amplitudes of the other two tension components (viscous, P1 and elastic, P3 tensions). Furthermore, neither compound significantly altered the relaxation rate of the passive muscle visco-elasticity (P2 tension). These results show that Po (arising from cycling cross-bridges) and passive muscle visco-elasticity (P2 tension) are affected differently by both Pi and ASi and suggest that they may not share a common structural basis. The possibility that passive muscle visco-elasticity (P2 tension) arises from the gap-(titin) filament (as suggested previously by Mutungi and Ranatunga, 1996b J Physiol 496: 827-837) and that Pi and ASi increase its amplitude by interacting with the PEVK region of the filament are discussed.
CHENG Feng-Feng; FA Tao; WANG Xin-Qiang; YAO Shu-De
2012-01-01
Dislocation information and strain-related tetragonal distortion as well as crystalline qualities of a 2-μm-thick InN film grown by molecular beam epitaxy (MBE) are characterized by Rutherford backscattering/channeling (RBS/C) and synchrotron radiation x-ray diffraction (SR-XRD).The minimum yield xmin=2.5％ deduced from the RBS/C results indicates a fairly good crystalline quality.From the SR-XRD results,we obtain the values of the screw and edge densities to be ρscrew =7.0027 X 109 and ρedge =8.6115 × 109 cm-2,respectively.The tetragonal distortion of the sample is found to be -0.27 ％ by angular scans,which is close to the -0.28 ％ derived by SR-XRD.The value of ｜e(⊥)/e‖｜ =0.6742 implies that the InN layer is much stiffer along the a axis than that along the c axis,where e‖ is the parallel elastic strain,and e⊥ is the perpendicular elastic strain.Photoluminescence results reveal a main peak of 0.653eV with the linewidth of 60meV,additional shoulder band could be due to impurities and related defects.%Dislocation information and strain-related tetragonal distortion as well as crystalline qualities of a 2-μm-thick InN film grown by molecular beam epitaxy (MBE) are characterized by Rutherford backscattering/'channeling (RBS/C) and synchrotron radiation x-ray diffraction (SR-XRD). The minimum yield Xmin=2.5% deduced from the RBS/C results indicates a fairly good crystalline quality. From the SR-XRD results, we obtain the values of the screw and edge densities to be pscrew = 7.0027 ×109 and pedge = 8.6115 ×109 cm-2, respectively. The tetragonal distortion of the sample is found to be-0.27% by angular scans, which is close to the -0.28 % derived by SR-XRD. The value of |e⊥/e|| | = 0.6742 implies that the InN layer is much stiffer along the a axis than that along the c axis, where e|| is the parallel elastic strain, and e⊥ is the perpendicular elastic strain. Photoluminescence results reveal a main peak of 0.653eV with the linewidth of 60me
Elastic properties of suspended black phosphorus nanosheets
Wang, Jia-Ying; Li, Yang; Zhen, Liang; Xu, Cheng-Yan, E-mail: cy-xu@hit.edu.cn [School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001 (China); MOE Key Laboratory of Micro-systems and Micro-structures Manufacturing, Harbin Institute of Technology, Harbin 150080 (China); Zhan, Zhao-Yao [Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714 (China); Li, Tie [Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050 (China)
2016-01-04
The mechanical properties of black phosphorus (BP) nanosheets suspended over circular holes were measured by an atomic force microscope nanoindentation method. The continuum mechanic model was introduced to calculate the elastic modulus and pretension of BP nanosheets with thicknesses ranging from 14.3 to 34 nm. Elastic modulus of BP nanosheets declines with thickness, and the maximum value is 276 ± 32.4 GPa. Besides, the effective strain of BP ranges from 8 to 17% with a breaking strength of 25 GPa. Our results show that BP nanosheets serve as a promising candidate for flexible electronic applications.
Sung Woo Park; Byung Kwan Oh; Hyo Seon Park
2015-01-01
The safety of a multi-span waler beam subjected simultaneously to a distributed load and deflections at its supports can be secured by limiting the maximum stress of the beam to a specific value to prevent the beam from reaching a limit state for failure or collapse. Despite the fact that the vast majority of accidents on construction sites occur at waler beams in retaining wall systems, no safety monitoring model that can consider deflections at the supports of the beam is available. In this...
Peng, Qing; De, Suvranu
2014-10-21
Silicane is a fully hydrogenated silicene-a counterpart of graphene-having promising applications in hydrogen storage with capacities larger than 6 wt%. Knowledge of its elastic limit is critical in its applications as well as tailoring its electronic properties by strain. Here we investigate the mechanical response of silicane to various strains using first-principles calculations based on density functional theory. We illustrate that non-linear elastic behavior is prominent in two-dimensional nanomaterials as opposed to bulk materials. The elastic limits defined by ultimate tensile strains are 0.22, 0.28, and 0.25 along armchair, zigzag, and biaxial directions, respectively, an increase of 29%, 33%, and 24% respectively in reference to silicene. The in-plane stiffness and Poisson ratio are reduced by a factor of 16% and 26%, respectively. However, hydrogenation/dehydrogenation has little effect on its ultimate tensile strengths. We obtained high order elastic constants for a rigorous continuum description of the nonlinear elastic response. The limitation of second, third, fourth, and fifth order elastic constants are in the strain range of 0.02, 0.08, and 0.13, and 0.21, respectively. The pressure effect on the second order elastic constants and Poisson's ratio were predicted from the third order elastic constants. Our results could provide a safe guide for promising applications and strain-engineering the functions and properties of silicane monolayers.
Hanson, David E.; Barber, John L.; Subramanian, Gopinath
2013-12-01
Molecular networks comprised of crosslinked cis-1,4 polyisoprene, often referred to as "natural rubber," are one of the most common systems for the study of rubber elasticity. Under moderate tensile or compressive strain, network chains begin to assume straighter paths, as local molecular kinks are removed. Isoprene units along the chain backbone are mechanically forced from their equilibrium distributions of 18 possible rotational states into a smaller subset of states, restricted to more linear conformations with the greatest end-to-end distances. There are two consequences to this change: both the configurational entropy and average internal energy decrease. We find that the change in entropy, and resulting change in free energy, gives rise to an elastic force. We derive an expression for a chain extension force constant that we have incorporated in an explicit, three-dimensional meso-scale network simulation code. Using this force model, our simulations predict a macroscopic stress-strain relationship that closely matches published experimental values. We also predict a slight increase in temperature resulting from the change in average internal energy in the affected isoprene units that is consistent with experiments.
Sankaranarayanan, Subramanian K. R. S.; Bhethanabotla, Venkat R.; Joseph, Babu
2007-10-01
Molecular dynamics simulation is used to investigate the mechanical properties of infinitely long, cylindrical bimetallic Pd-Pt nanowires, with an approximate diameter of 1.4nm and two different compositions (25% and 50% Pt). The nanowires are subjected to uniaxial tensile strain along the [001] axis with varying strain rates of 0.05%ps-1 , and 5.0%ps-1 , at simulation temperatures of 50 and 300K , to study the effects of strain rates and thermal conditions on the deformation characteristics and mechanical properties of the nanowire. The deformation and rupture mechanism of these nanowires is explored in detail. Comparisons to the behavior exhibited by pure Pd and Pt nanowires of similar diameter are also made. The effect of lattice mismatch on the observed deformation modes in bimetallic nanowires is also discussed. Our simulations indicate that Pd-Pt alloy nanowires of various compositions, with little lattice mismatch between Pd and Pt atoms, undergo similar deformation and rupture upon uniaxial stretching. It is found that yielding and fracture mechanisms depend on the applied strain rate as well as atomic arrangement and temperature. At low temperature and strain rate, where crystal order and stability are highly preserved, the calculated stress-strain response of pure Pt and Pd as well as Pd-Pt alloy nanowires showed clear periodic, stepwise dislocation-relaxation behavior. Crystalline to amorphous transformation takes place at high strain rates (5%ps-1) , with amorphous melting detected at 300K . Deformation of nanowires at higher strain rates and low temperature, where the superplasticity characteristic is significantly enhanced, results in the development of a multishell helical structure. Mechanical properties of the alloy nanowires are significantly different from those of bulk phase and are dictated by the applied strain rate, temperature, alloy composition, as well as the structural rearrangement associated with nanowire elongation. We find that Young
Reinen, Dirk
2012-04-16
Cations in 6-coordination with orbitally degenerate E(g) ground states, such as Cu(2+) and low-spin Co(2+), play an important role in coordination chemistry-in particular, in modern complex biochemistry. The stereochemistry and the binding properties within the basic polyhedra are the subject of pronounced modifications due to vibronic coupling in such cases, but may be also significantly influenced by what is usually called an imposed strain. The latter effect makes allowance for the general observation that the host sites into which the Jahn-Teller unstable centers are substituted are seldom of O(h) symmetry and built from six equal ligands. Hence, the finally observed molecular and binding structure of the pseudo-octahedral complex is the result of the combined action of vibronic coupling and strain. The closer analysis of host-site strain effects demands to distinguish between elastic strain components, which modify the force constant of the vibronically active (here, ε(g)) vibration, and binding strain perturbations, which take account of possibly present ligands with different binding properties. A symmetry-met semiempirical strain model on such a basis is presented and a corresponding formulation within the vibronic coupling formalism is given, on the molecular level. Well-established model examples of Cu(2+) in octahedral fluoride coordination in various host solids, where a great variety of experimental results is available, are given. The derived parameters allow a detailed characterization of the structural and energy qualities of the Jahn-Teller centers, and might help to steer these properties in cases where synthesis strategies are needed. The proposed strain concept is more complex than that of Ham [F. S. Ham, Electron Paramagnetic Resonance; Plenum Press: New York, 1972; F. S. Ham, Phys. Rev. 1965, A138, 1727]; the advantage is that it is directly tied to the structure and energy of the Jahn-Teller complex in focus, although more data (experimental
Li, Yang; Deng, You-Bin; Bi, Xiao-Jun; Liu, Ya-Ni; Zhang, Jun; Li, Li
2016-07-01
Reduced artery elasticity and reduced myocardial strain were present in patients with bicuspid aortic valve (BAV). Their relation to dilation of proximal aorta is unclear. We aimed to study their relation to dilation of proximal aorta. We studied 57 BAV patients categorized into 2 subgroup according to proximal ascending aortic dimensions (nondilated strain, distensibility and stiffness index were derived. Left ventricular myocardial strain were acquired with speckle-tracking echocardiography. BAV patients with dilation of proximal ascending aorta had lower aortic strain (4.1 ± 4.2 % vs. 7.1 ± 3.5 %) and carotid strain (4.8 ± 1.9 % vs. 10.6 ± 4.2 %), lower aortic distensibility (1.4 ± 1.5 cm(2) dyn(-1) 10(-6) vs. 2.5 ± 1.5 cm(2) dyn(-1) 10(-6)) and carotid distensibility (1.6 ± 0.7 cm(2) dyn(-1) 10(-6) vs. 3.9 ± 2.4 cm(2) dyn(-1) 10(-6)), higher aortic stiffness index (19.7 ± 14.1 vs. 8.3 ± 4.9) and carotid stiffness index (12.2 ± 8.5 vs. 5.0 ± 2.2), and lower global circumferential (-15.9 ± 5.8 % vs. -19.1 ± 4.1 %), radial (19.3 ± 11.6 % vs. 29.8 ± 14.9 %) and longitudinal (-15.7 ± 3.4 % vs. -18.4 ± 3.4 %) compared with those without dilation of proximal ascending aorta. All mean values are different to p myocardial strain in BAV patients, supporting the need for detailed and extensive vascular and cardiac surveillance in BAV patients.
Béland, Laurent Karim; Machado-Charry, Eduardo; Pochet, Pascal; Mousseau, Normand
2014-10-01
We investigate Ge mixing at the Si(001) surface and characterize the 2×N Si(001) reconstruction by means of hybrid quantum and molecular mechanics calculations (QM/MM). Avoiding fake elastic dampening, this scheme allows to correctly take into account long-range deformation induced by reconstructed and defective surfaces. We focus in particular on the dimer vacancy line (DVL) and its interaction with Ge adatoms. We first show that calculated formation energies for these defects are highly dependent on the choice of chemical potential and that the latter must be chosen carefully. Characterizing the effect of the DVL on the deformation field, we also find that the DVL favors Ge segregation in the fourth layer close to the DVL. Using the activation-relaxation technique (ART nouveau) and QM/MM, we show that a complex diffusion path permits the substitution of the Ge atom in the fourth layer, with barriers compatible with mixing observed at intermediate temperature. We also show that the use of QM/MM results in much more significant corrections at the saddle points (up to 0.5 eV) that at minima, demonstrating its importance for describing kinetics correctly.
Ungár, Tamás; Harjo, Stefanus; Kawasaki, Takuro; Tomota, Yo; Ribárik, Gábor; Shi, Zengmin
2017-01-01
Based on high-resolution neutron diffraction experiments, we will show that in lath martensite steels, the initially homogeneous dislocation structure, i.e., homogeneous on the length scale of grain size, is disrupted by plastic deformation, which, in turn, produces a composite on the length scale of martensite lath packets. The diffraction patterns of plastically strained martensitic steel reveal characteristically asymmetric peak profiles in the same way as has been observed in materials with heterogeneous dislocation structures. The quasi homogeneous lath structure, formed by quenching, is disrupted by plastic deformation producing a composite structure. Lath packets oriented favorably or unfavorably for dislocation glide become soft or hard. Two lath packet types develop by work softening or work hardening in which the dislocation densities become smaller or larger compared to the initial average dislocation density. The decomposition into soft and hard lath packets is accompanied by load redistribution and the formation of long-range internal stresses between the two lath packet types. The composite behavior of plastically deformed lath martensite opens a new way to understand the elastic-plastic response in this class of materials.
Jamalpoor, A.; Ahmadi-Savadkoohi, A.; Hosseini-Hashemi, Sh
2016-10-01
This paper deals with the theoretical analysis of free vibration and biaxial buckling of magneto-electro-elastic (MEE) microplate resting on Kelvin-Voigt visco-Pasternak foundation and subjected to initial external electric and magnetic potentials, using modified strain gradient theory (MSGT). Kirchhoff plate model and Hamilton’s principle are employed to extract the governing equations of motion. Governing equations were analytically solved to obtain clear closed-form expression for complex natural frequencies and buckling loads using Navier’s approach. Numerical results are presented to reveal variations of natural frequency and buckling load ratio of MEE microplate against different amounts of the length scale parameter, initial external electric and magnetic potentials, aspect ratio, damping and transverse and shear stiffness parameters of the visco-Pasternak foundation, length to thickness ratio, microplate thickness and higher modes. Numerical results of this study illustrate that by increasing thickness-to-material length scale parameter ratio, both natural frequency and buckling load ratio predicted by MSGT and modified couple stress theory are reduced because the non-dimensional length scale parameter tends to decrease the stiffness of structures and make them more flexible. In addition, results show that initial external electric and initial external magnetic potentials have no considerable influence on the buckling load ratio and frequency of MEE microplate as the microplate thickness increases.
李鹏阳; 陈欢; 王世军; 王权岱; 傅卫平
2015-01-01
The influence of surface contact friction heat on the failure and the life of the parts was studied .The thermal stress of elastic-plastic surface contact was calculated using Fortran language ,the contact surface temperature distribution and the influence of friction heat on the surface pressure distribution were analyzed ,and the subsurface of the Mises stress field and the influence of plastic strain of the contact surface were discussed .The results show :With the increase of surface friction heat flux , the surface maximum pressure is increased .The maximum stress under the surface is decreased and the maximum stress zone of subsurface is always moving gradually to the contact surface .The contact surface temperature increases with the increase of sliding speed .The location of highest temperature point slowly shifts ,with increase of sliding speed ,to the sliding velocity direction .%研究了降低表面接触摩擦热对材料失效和零件寿命的影响。应用Fortran编程语言对弹塑性表面接触中产生的热应力进行了计算，分析了接触表面温度分布及摩擦热对接触表面压力分布、表面下米塞斯应力场及塑性应变的影响。分析结果表明：随着表面摩擦热流的增加，表面上最大接触压力逐渐变大，而表面下最大应力值逐渐减小，最大应力区域逐渐向接触表面上移动。接触表面温度的大小随滑动速度的提高而升高，且最高温度点的位置随滑动速度的提高缓慢向滑动速度方向偏移。
Role of phonon scattering by elastic strain field in thermoelectric Sr1−xYxTiO3−δ
Bhattacharya, S.
2014-06-12
Perovskite-type SrTiO3-δ ceramics are multifunctional materials with significant potential as n-type thermoelectric (TE) materials. The electronic and thermal transport properties of spark plasma sintered polycrystalline Sr1-xYxTiO3-δ (x=0.05, 0.075, 0.1) ceramics are systematically investigated from (15-800) K. The Sr0.9Y0.1TiO3-δ simultaneously exhibits a large Seebeck coefficient, α>-80μV/K and moderately high electrical resistivity, ρ∼0.8mΩ-cm at a carrier concentration of ∼1021cm-3 at 300K resulting in a high TE power factor defined herein as (α2σT)∼0.84W/m-K at 760K. Despite the similar atomic masses of Sr (87.6g/mol) and Y (88.9g/mol), the lattice thermal conductivity (κL) of Sr1-xY xTiO3-δ is significantly reduced with increased Y-doping, owing to the smaller ionic radii of Y3+ (∼1.23Å, coordination number 12) compared to Sr2+ (∼1.44Å, coordination number 12) ions. In order to understand the thermal conductivity reduction mechanism, the κL in the Sr1-xY xTiO3-δ series are phenomenologically modeled with a modified Callaway\\'s equation from 30-600K. Phonon scattering by elastic strain field due to ionic radii mismatch is found to be the prominent scattering mechanism in reducing κL of these materials. In addition, the effect of Y-doping on the elastic moduli of Sr1-xY xTiO3-δ (x=0, 0.1) is investigated using resonant ultrasound spectroscopy, which exhibits an anomaly in x=0.1 in the temperature range 300-600K. As a result, the phonon mean free path is found to be further reduced in the Sr0.9Y0.1TiO3-δ compared to that of SrTiO3-δ, resulting in a considerably low thermal conductivity κ∼2.7W/m-K at 760K. Finally, we report a thermoelectric figure of merit (ZT)∼0.3 at 760K in the Sr0.9Y 0.1TiO3-δ, the highest ZT value reported in the Y-doped SrTiO3 ceramics thus far. © 2014 AIP Publishing LLC.
Hofmann, Felix; Song, Xu; Abbey, Brian; Jun, Tea-Sung; Korsunsky, Alexander M
2012-05-01
An understanding of the mechanical response of modern engineering alloys to complex loading conditions is essential for the design of load-bearing components in high-performance safety-critical aerospace applications. A detailed knowledge of how material behaviour is modified by fatigue and the ability to predict failure reliably are vital for enhanced component performance. Unlike macroscopic bulk properties (e.g. stiffness, yield stress, etc.) that depend on the average behaviour of many grains, material failure is governed by `weakest link'-type mechanisms. It is strongly dependent on the anisotropic single-crystal elastic-plastic behaviour, local morphology and microstructure, and grain-to-grain interactions. For the development and validation of models that capture these complex phenomena, the ability to probe deformation behaviour at the micro-scale is key. The diffraction of highly penetrating synchrotron X-rays is well suited to this purpose and micro-beam Laue diffraction is a particularly powerful tool that has emerged in recent years. Typically it uses photon energies of 5-25 keV, limiting penetration into the material, so that only thin samples or near-surface regions can be studied. In this paper the development of high-energy transmission Laue (HETL) micro-beam X-ray diffraction is described, extending the micro-beam Laue technique to significantly higher photon energies (50-150 keV). It allows the probing of thicker sample sections, with the potential for grain-level characterization of real engineering components. The new HETL technique is used to study the deformation behaviour of individual grains in a large-grained polycrystalline nickel sample during in situ tensile loading. Refinement of the Laue diffraction patterns yields lattice orientations and qualitative information about elastic strains. After deformation, bands of high lattice misorientation can be identified in the sample. Orientation spread within individual scattering volumes is
Fernandez-Saez, J.; Luna de, S.; Rubio, L.; Perez-Castellanos, J. L.; Navarro, C.
2001-07-01
An earlier paper dealt with the experimental techniques used to determine the dynamic fracture properties of linear elastic materials. Here we describe those most commonly used as elastoplastic materials, limiting the study to the initiation fracture toughness at the intermediate strain rate (of around 10''2 s''-1). In this case the inertial forces are negligible and it is possible to apply the static solutions. With this stipulation, the analysis can be based on the methods of testing in static conditions. The dynamic case differs basically, from the static one, in the influence of the strain rate on the properties of the material. (Author) 57 refs.
Oline, L.; Medaglia, J.
1972-01-01
The dynamic finite element method was used to investigate elastic stress waves in a plate. Strain displacement and stress strain relations are discussed along with the stiffness and mass matrix. The results of studying point load, and distributed load over small, intermediate, and large radii are reported. The derivation of finite element matrices, and the derivation of lumped and consistent matrices for one dimensional problems with Laplace transfer solutions are included. The computer program JMMSPALL is also included.
Strain Limits within the Scope of the Integrity Assessment of Piping Systems
Mutz, Alexander [EnBW, Durlacher Allee 93, Karlsruhe 76131 (Germany)
2008-07-01
Allowable stresses in nuclear power plant piping resulting from loading conditions to be considered in Germany are determined on the basis of the German Safety Standards of the Nuclear Safety Standards Commission, KTA. The limitation of the different stress categories within the analysis of the mechanical behaviour is based on a linear elastic material behaviour. Because of the ductile material used in high energy nuclear piping, a more realistic assessment can be performed on the basis of allowable strains using elastic plastic material behaviour. In the present work comparison between the analysis of piping systems considering the elastic material model and the actual elastic plastic material behaviour is performed. The possibilities of allocating plastic strains to calculated elastic stresses is discussed. A parametric study on straight pipes with the actual elastic plastic material model under pure bending is the basis of deriving the elastic plastic strains for the calculated elastic stresses. Strain limits are suggested which correspond to the different stress categories. The aim is to utilize the deformation possibilities of ductile materials used in German nuclear piping and the allocation of maximum strains to different load categories. Keywords: strain limit, ductile material, stress category. (author)
Gatel, C., E-mail: gatel@cemes.fr [CNRS, CEMES (Centre d' Elaboration des Materiaux et d' Etudes Structurales), BP 94347, 29 rue J. Marvig, 31055 Toulouse (France)] [Universite de Toulouse, UPS, 31055 Toulouse (France); Tang, H.; Crestou, C.; Ponchet, A. [CNRS, CEMES (Centre d' Elaboration des Materiaux et d' Etudes Structurales), BP 94347, 29 rue J. Marvig, 31055 Toulouse (France)] [Universite de Toulouse, UPS, 31055 Toulouse (France); Bertru, N.; Dore, F.; Folliot, H. [FOTON-LENS-INSA, 20 av. des Buttes de Coesmes, CS 14315, 35043 Rennes (France)
2010-05-15
Elastic strain has been investigated by transmission electron microscopy in nanometric InAs layers grown on Ga{sub 0.47}In{sub 0.53}As/InP(0 0 1) by molecular beam epitaxy using a residual Sb flux. Deposits of 10 and 15 monolayers of InAs (3 and 4.5 nm) remain elastically stressed with a two-dimensional growth mode. The out-of-plane strain in the layers is analyzed by cross-sectional high-resolution electron microscopy. A distortion of the substrate below and on top of the InAs layers is detected and is attributed to a significant surface relaxation effect due to thinning. Surface relaxation is modeled by three-dimensional finite element modeling. An additional relaxation effect is obtained when the sample is not infinite along the direction perpendicular to the thinning. This effect enhances the buffer distortion of the buffers below and on top of the strained layers. Taking into account thin foil effects, the experimental out-of-plane strain is in excellent agreement with the theoretical value calculated for a pure InAs layer (i.e. 0.035), demonstrating the high level of strain and stress in the layers.
李莲明; 李治平; 车艳
2011-01-01
When the rock is deformed by pressure decreasing in the formation, it is difficult to study the non-linear elasticity deformation rock volumetric strain. According to the power relationship between the non-elastic deformation rock elastic modelling quantity and effective pressure, this paper establishes the theoretic expressions between rock volumetric strain and effective pressure under the surface experiment conditions and the formation conditions, proposese a new method of the “Trial Calculation & Iteration”used to study the non-linear elasticity deformation rock volumetric strain quantitatively, calculates the a and b values of the rock non-linear elasticity deformation constants by means of the experiment databetween the non-linear elasticity rock volumetric strain and the effective pressure, and forecastes the non-linear elasticity deformation rock volumetric strain quantitatively. The application of this method indicates that the relative errors between the predictive values of the non-linear rock volumetric strain, rock porosity under the surface experiment conditions & rock porosity of the formation pressure decrease and the experiment values or the predictive values using experiment data of them should be less than or equal to 7.39％,0.80％ & 3.92％ and preferable consistance, and that it is possible to convert from the experimental data of the surface conditions to the data of reservoir conditions. This method provides an effective way to calculate the non-linear elasticity deformation rock volumetric strain quantitatively.%砂岩气藏地层压力下降岩石发生非线弹性变形时,定量研究非线弹性岩石体积应变的大小是个难点.由非线弹性岩石弹性模量与有效压力满足的乘幂关系,推导了地面实验和地层条件岩石体积应变理论关系,提出了一种定量研究岩石体积应变的试算迭代法,并结合岩石变形实验岩石体积应变与有效压力变化数据,求取了岩
Girill, T. R.
1972-01-01
The Boyle-Mariotte gas law was formulated in terms of pneumatic springs," subsumed by Hooke under his own stress-strain relation, and generally regarded as a law of elasticity. The subsequent development of Boyle's principle and elasticity provide thought-provoking test cases for Kuhn's notations of paradigm and puzzle solving in physics.…
Yu, Betty; Kang, Soo-Young; Akthakul, Ariya; Ramadurai, Nithin; Pilkenton, Morgan; Patel, Alpesh; Nashat, Amir; Anderson, Daniel G.; Sakamoto, Fernanda H.; Gilchrest, Barbara A.; Anderson, R. Rox; Langer, Robert
2016-08-01
We report the synthesis and application of an elastic, wearable crosslinked polymer layer (XPL) that mimics the properties of normal, youthful skin. XPL is made of a tunable polysiloxane-based material that can be engineered with specific elasticity, contractility, adhesion, tensile strength and occlusivity. XPL can be topically applied, rapidly curing at the skin interface without the need for heat- or light-mediated activation. In a pilot human study, we examined the performance of a prototype XPL that has a tensile modulus matching normal skin responses at low strain (<40%), and that withstands elongations exceeding 250%, elastically recoiling with minimal strain-energy loss on repeated deformation. The application of XPL to the herniated lower eyelid fat pads of 12 subjects resulted in an average 2-grade decrease in herniation appearance in a 5-point severity scale. The XPL platform may offer advanced solutions to compromised skin barrier function, pharmaceutical delivery and wound dressings.
Renaud, Guillaume; Talmant, Maryline; Marrelec, Guillaume
2016-01-01
International audience; The nonlinear elasticity of solids at the microstrain level has been recently studied by applying dynamic acousto-elastic testing. It is the analog of conventional quasi-static acousto-elastic experiments but the strain-dependence (or stress-dependence) of ultrasonic wave-speed is measured with an applied strain ranging from 10−7 to 10−5 and produced by a stationary elastic wave. In conventional quasi-static acousto-elastic experiments, the strain is applied in a quasi...
Cowgill, E.; Gold, R. D.; Arrowsmith, R.; Friedrich, A. M.
2015-12-01
In elastic rebound theory, hazard increases as interseismic strain rebuilds after rupture. This model is challenged by the temporal variation in the pacing of major earthquakes that is both predicted by mechanical models and suggested by some long paleoseismic records (e.g., 1-3). However, the extent of such behavior remains unclear due to a lack of long (5-25 ky) records of fault slip. Using Monte Carlo analysis of 11 offset landforms, we determined a 16-ky record of fault slip for the active, left-lateral Altyn Tagh fault, which bounds the NW margin of the Tibetan Plateau. This history reveals a pulse of accelerated slip between 6.4 and 6.0 ka, during which the fault slipped 9 +14/-2 m at a rate of 23 +35/-5 mm/y, or ~3x the 16 ky average of 8.1 +1.2/-0.9mm/y. These two modes of earthquake behavior suggest temporal variation in the rates of stress storage and release. The simplest explanation for the pulse is a cluster of 2-8 Mw > 7.5 earthquakes. Such supercyclicity has been reported for the Sunda (4) and Cascadia (3) megathrusts, but contrasts with steady slip along the strike-slip Alpine fault (5), for example. A second possibility is that the pulse reflects a single, unusually large rupture. However, this Black Swan event is unlikely: empirical scaling relationships require a Mw 8.2 rupture of the entire 1200-km-long ATF to produce 7 m of average slip. Likewise, Coulomb stress change from rupture on the adjacent North Altyn fault is of modest magnitude and overlap with the ATF. Poor temporal correlation between precipitation and the slip pulse argues against climatically modulated changes in surface loading (lakes/ice) or pore-fluid pressure. "Paleoslip" studies such as this sacrifice the single-event resolution of paleoseismology in exchange for long records that quantify both the timing and magnitude of fault slip averaged over multiple ruptures, and are essential for documenting temporal variations in fault slip as we begin to use calibrated physical
Approaching the ideal elastic limit of metallic glasses
Tian, Lin; Cheng, Yong-Qiang; Shan, Zhi-Wei; Li, Ju; Cheng-cai WANG; Han, Xiao-dong; Sun, Jun; Ma, Evan
2012-01-01
The ideal elastic limit is the upper bound to the stress and elastic strain a material can withstand. This intrinsic property has been widely studied for crystalline metals, both theoretically and experimentally. For metallic glasses, however, the ideal elastic limit remains poorly characterized and understood. Here we show that the elastic strain limit and the corresponding strength of submicron-sized metallic glass specimens are about twice as high as the already impressive elastic limit ob...
邵卓平; 祝山
2001-01-01
The elastic constants of wood of Cunninghamia lanceolata was determined and the limits of orthotropic model adopted for wood was studied. The results showed that the elastic constants of wood could be determined by means of electric resistance-strain gauges,and the constants was satisfied to the limits of orthotropic.%测试杉木的弹性常数，研究木材采用正交各向异性体模型的限制条件。结果表明，可以采用电阻应变法以单轴压缩试件测定木材弹性常数；所测木材弹性常数满足正交各向异性材料的限制条件。
Thresiamma Philip; Menon, C S; Indulekha, K.
2006-01-01
The second and third-order elastic constants and pressure derivatives of second- order elastic constants of trigonal LiNbO3 (lithium niobate) have been obtained using the deformation theory. The strain energy density estimated using finite strain elasticity is compared with the strain dependent lattice energy density obtained from the elastic continuum model approximation. The second-order elastic constants and the non-vanishing third-order elastic constants along with the pressure derivative...
Kinkhabwala, Ali
2013-01-01
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation: Which candidate distribution provides the best fit to the observed data?, (2) Goodness-of-fit: How concordant is this distribution with the observed data?, and (3) Uncertainty: How concordant are other candidate distributions with the observed data? A simple unified approach for univariate data that addresses these traditionally distinct statistical notions is presented called "maximum fidelity". Maximum fidelity is a strict frequentist approach that is fundamentally based on model concordance with the observed data. The fidelity statistic is a general information measure based on the coordinate-independent cumulative distribution and critical yet previously neglected symmetry considerations. An approximation for the null distribution of the fidelity allows its direct conversi...
Taylor, F. W.; Lavier, L. L.; Thirumalai, K.; Frohlich, C.; Shen, C. C.; Cai, B.; Dibia, E. C.
2016-12-01
Forearc vertical motions provide a window into processes occurring on the underlying seismogenic zone. On the Western Solomons forearc coral microatolls are living tide gauges that have recorded decimeter-scale relative sea-level changes over the past century, some of which we interpret as being tectonic in origin. Several microatolls show that a segment of the outer forearc subsided 10-15 cm in the 1920-1943 and 1951-1963 periods. In each case subsidence terminated in uplift of a similar amount that appears to have occurred within the time span of one year. Subsidence again started in about 1973 and reached 10-20 cm after which there was ≥65 cm of coseismic uplift during the 1 April 2007 Mw 8.1 megathrust earthquake. The base of this coral still lives so that annual density bands in the coral provide the above ages in calendar years. This location has undergone very little longer-term net uplift so that we infer that the entire 65 cm of coseismic uplift is recovery of stored elastic strain rather than permanent deformation. Until 2007 the instrumental record indicated that this segment was aseismic for teleseismically detectable events. We interpret the small 1915-1943 and 1951-1963 subsidence episodes and subsequent uplifts as intervals of temporary locking on the underlying seismogenic zone that ended in slow slip events. However, the final 65 cm of 2007 coseismic uplift suggests that a much larger amount of elastic strain must have accumulated in this vicinity before these corals lived and was stored until 2007. Unlike the previous subsidence-uplift cycles, the final accumulation of elastic strain after about 1973 may have triggered the 2007 megathrust rupture.
Sinha, S
2003-01-01
In recent years molecular elasticity has emerged as an active area of research: there are experiments that probe mechanical properties of single biomolecules such as DNA and Actin, with a view to understanding the role of elasticity of these polymers in biological processes such as transcription and protein-induced DNA bending. Single molecule elasticity has thus emerged as an area where there is a rich cross-fertilization of ideas between biologists, chemists and theoretical physicists. In this article we present a perspective on this field of research.
Küntz, M.; Dyskin, A.; Lavallée, P.
1998-01-01
A steady-state flow method is used to examine micromechanisms of brittle failure in 2D elastic cracked media submitted to uniaxial compressive stress. The steady-state flow experiments were conducted with an incompressible Newtonian fluid in a Hele Shaw cell. Thin linear rubber inclusions were
Integrodifferential relations in linear elasticity
Kostin, Georgy V
2012-01-01
This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements.It also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering.
Elastic properties of solids at high pressure
Vekilov, Yu Kh; Krasilnikov, O. M.; Lugovskoy, A. V.
2015-11-01
This review examines the elastic response of solids under load. The definitions of isothermal and adiabatic elastic constants of ( n≥2) for a loaded crystal are given. For the case of hydrostatic pressure, two techniques are proposed for calculating the second-, third-, and fourth-order elastic constants from the energy-strain and stress-strain relations. As an example, using the proposed approach within the framework of the density functional theory, the second- to fourth-order elastic constants of bcc tungsten are calculated for the pressure range of 0-600 GPa.
Strength and elastic properties of sandstone under different testing conditions
CHEN Yun-ping; WANG Si-jing; WANG En-zhi
2007-01-01
A laboratory experimental program performed on Wuhan sandstones was presented under monotonic loading, partial cyclic loading during loading path and sine wave cyclic loading with different strain rates to compare uniaxial compression strength and elastic properties (elastic modulus and Poisson ratio) under different conditions and influence of pore fluid on them. When the loading strain rates are 10-5, 10-4 and 10-3/s, uniaxial compression strengths of dry sandstones are 82.3, 126.6 and 141.6 MPa,respectively, and that of water saturated sandstones are 70.5, 108.3 and 124.1 MPa, respectively. The above results show that the uniaxial compression strength increases with the increase of strain rate, however, variation of softening coefficient is insignificant.Under monotonic loading condition, tangent modulus increases with an increment of stress (strain) to a maximum value at a certain stress level, beyond which it starts to decline. Under the partial cyclic loading during loading path condition, unloading or reloading modulus is larger than loading modulus, and unloading and reloading moduli are almost constants with respect to stress level,especially unloading modulus. Under the sine wave cyclic loading condition, tangent modulus and Poisson ratio display asymmetric 'X' shape with various strain, and the average unloading modulus is larger than the average loading modulus.
Vliet, Jurg; Wel, Steven; Dowd, Dara
2011-01-01
While it's always been possible to run Java applications on Amazon EC2, Amazon's Elastic Beanstalk makes the process easier-especially if you understand how it works beneath the surface. This concise, hands-on book not only walks you through Beanstalk for deploying and managing web applications in the cloud, you'll also learn how to use this AWS tool in other phases of development. Ideal if you're a developer familiar with Java applications or AWS, Elastic Beanstalk provides step-by-step instructions and numerous code samples for building cloud applications on Beanstalk that can handle lots
Kiatgamolchai, S
2000-01-01
gamma has the bowl shape with the minimum at x approx 0.25-0.3. These characteristics suggest a possible influence of alloy disorder scattering. The mobilities and activation energies of the carriers in the boron-doped cap vary between samples and this is believed to be due to boron-spike near the Si/Si-substrate interface, in some samples. The source of electron-like carrier is presently unknown. Magnetotransport properties of modulation-doped p-type Si sub 1 sub - sub x Ge sub x /Si and Si sub 1 sub - sub x Ge sub x /Si sub 1 sub - sub y Ge sub y heterostructures were studied, in the magnetic field range 0-12 T, and in the temperature range 0.35-300 K. The experimental data within the classical regime have been analysed by mobility spectrum analysis, in order to separate the influences of different parallel conduction paths. A new method of mobility spectrum analysis has been developed by the based on the concept of maximum-entropy, and this computation has been shown to overcome several drawbacks or limita...
Feng, Guo-Hua; Huang, Wei-Lun
2014-12-01
This paper presents a smart tuning-fork-shaped ionic polymer metal composite (IPMC) clamping actuator for biomedical applications. The two fingers of the actuator, which perform the clamping motion, can be electrically controlled through a unique electrode design on the IPMC material. The generated displacement or strain of the fingers can be sensed using an integrated soft strain-gage sensor. The IPMC actuator and associated soft strain gage were fabricated using a micromachining technique. A 13.5×4×2 mm(3) actuator was shaped from Nafion solution and a selectively grown metal electrode formed the active region. The strain gage consisted of patterned copper foil and polyethylene as a substrate. The relationship between the strain gage voltage output and the displacement at the front end of the actuator's fingers was characterized. The equivalent Young's modulus, 13.65 MPa, of the soft-strain-gage-integrated IPMC finger was analyzed. The produced clamping force exhibited a linear increasing rate of 1.07 mN/s, based on a dc driving voltage of 7 V. Using the developed actuator to clamp soft matter and simultaneously acquire its Young's modulus was achieved. This demonstrated the feasibility of the palpation function and the potential use of the actuator in minimally invasive surgery.
Vassiliev, Dmitri
2017-04-01
We consider an infinite three-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis that gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory, we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension three are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the talk is an explicit construction of a class of time-dependent solutions that we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed-form solutions is a non-trivial fact given that our system of Euler-Lagrange equations is highly nonlinear. We also consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations. The talk is based on the paper [1]. [1] C.G.Boehmer, R.J.Downes and D.Vassiliev, Rotational elasticity, Quarterly Journal of Mechanics and Applied Mathematics, 2011, vol. 64, p. 415-439. The paper is a heavily revised version of preprint https://arxiv.org/abs/1008.3833
Pasta Elasticity: Molecular dynamics simulations of nuclear pasta deformations
Caplan, M. E.; Horowitz, C. J.; Berry, D. K.
2015-04-01
Nuclear pasta is expected in the inner crust of neutron stars at densities near the nuclear saturation density. In this work, the elastic properties of pasta are calculated from large scale molecular dynamics simulations by deforming the simulation volume. Our model uses a semi-classical two-nucleon potential that reproduces nuclear saturation. We report the shear modulus and breaking strain of a variety of pasta phases for different temperatures, densities, and proton fractions. The presence of pasta in neutron stars could have significant effects on crustal oscillations and could be inferred from observations of soft-gamma repeaters. Additionally, these elastic parameters will enable us to improve estimates of the maximum size and lifetime of ``mountains'' on the crust, which could efficiently radiate gravitational waves.
Hilbert complexes of nonlinear elasticity
Angoshtari, Arzhang; Yavari, Arash
2016-12-01
We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.
Extremal Overall Elastic Response of Polycrystalline Materials
Bendsøe, Martin P; Lipton, Robert
1996-01-01
Polycrystalline materials comprised of grains obtained froma single anisotropic material are considered in the frameworkof linear elasticity. No assumptions on the symmetry of thepolycrystal are made. We subject the material to independentexternal strain and stress fields with prescribed mean...
The structure of the linear anisotropic elastic symmetries
Cowin, S. C.; Mehrabadi, M. M.
1992-10-01
AN INSIGHTFUL, STRUCTURALLY appealing and potentially utilitarian formulation of the anisotropic form of the linear Hooke's law due to Lord Kelvin was independently rediscovered by R YCHLEWSKI (1984, Prikl. Mat. Mekh.48, 303) and M EHRABADI and C OWIN (1990, Q. J. Mech. appl. Math.43, 14). The eigenvectors of the three-dimensional fourth-rank anisotropic elasticity tensor, considered as a second-rank tensor in six-dimensional space, are called eigentensors when projected back into three-dimensional space. The maximum number of eigentensors for any elastic symmetry is therefore six. The concept of an eigentensor was introduced by K ELVIN (1856, Phil. Trans. R. Soc.166, 481) who called eigentensors "the principal types of stress or of strain". Kelvin determined the eigentensors for many elastic symmetries and gave a concise summary of his results in the 9th edition of the Encyclopaedia Britannica (1878). The eigentensors for a linear isotropic elastic material are familiar. They are the deviatoric second-rank tensor and a tensor proportional to the unit tensor, the spherical, hydrostatic or dilatational part of the tensor. M EHRABADI and C OWIN (1990, Q. J. Mech. appl. Math.43, 14) give explicit forms of the eigentensors for all of the linear elastic symmetries except monoclinic and triclinic symmetry. We discuss two approaches for the determination of eigentensors and illustrate these approaches by partially determining the eigentensors for monoclinic symmetry. With the nature of the eigentensors for monoclinic symmetry known, a rather complete table of the structural properties of all linear elastic symmetries can be constructed. The purpose of this communication is to give the most specifically detailed presentation of the eigenvalues and eigentensors of the Kelvin formulation to date.
NONLINEAR ELASTICITY OF BLOOD ARTERIAL DUCT
黄孟才; 顾忠; 沈俊; 唐复勇
1991-01-01
The paper deals with nonlinear elasticity of blood arterial duct, in which the artery is modeled to bea locally triclinic, transverse isotropic, incorapressible, axisymmetric and thickwalled tube with large deformations, The nonlinear coustitutive relationship of arterial tissues is based on the theorv of Green and Adkins. A nonlinear strain energy density function is introduced for nonlinear stress-strain relationship of second order, in which the coefficient of each term is expressed by means of a Lame’s constant, The elasticity constants are nqcessary to describe such a uonlinear finite strain etastieity of the second order, These constants are determined by means of the stress-strain increment theory.
Schichtel, N; Korte, C; Hesse, D; Janek, J
2009-05-07
Ionic transport in solids parallel to grain or phase boundaries is usually strongly enhanced compared to the bulk. Transport perpendicular to an interface (across an interface) is often much slower. Therefore in modern micro- and nanoscaled devices, a severe influence on the ionic/atomic transport properties can be expected due to the high density of interfaces.Transport processes in boundaries of ionic materials are still not understood on an atomic scale. In most of the studies on ionic materials the interfacial transport properties are explained by the influence of space charge regions. Here we discuss the influence of interfacial strain at semicoherent or coherent heterophase boundaries on ionic transport along these interfaces in ionic materials. A qualitative model is introduced for (untilted and untwisted) hetero phase boundaries. For experimental verification, the interfacial oxygen ionic conductivity of different multilayer systems consisting of cubic ZrO(2) stabilised by aliovalent dopands (YSZ, CSZ) and an insulating oxide is investigated as a function of structural mismatch. Recent results on extremely fast ionic conduction in YSZ/SrTiO(3) thin film systems ("colossal ionic concuctivity at interfaces") is discussed from the viewpoint of strain effects.
Oscillatory Structure of Elastic Precursor in Shocked Crystalline Solids: A Molecular Dynamics Study
Zybin, Sergey; Zhakhovskii, Vasilii; Elert, Mark; White, Carter T.
2003-03-01
Molecular dynamics simulations are used to study the structure of elastic precursors of shock waves propagating through crystalline solids in different directions. Both rare gas and diamond crystals were studied using Lennard-Jones and reactive empirical bond order potentials respectively. Elastic precursors were found to exhibit an oscillatory profile for various directions and different shock strengths ranging from a pure elastic wave to an elastic-plastic shock splitting to a shock wave with melting. These oscillations originate from collisions of atomic planes in the shock direction bouncing against each other as in one-dimensional chain. After the oscillations fade, and the shear stress achieves its sustained maximum value, plastic deformation develops. These effects are strongly influenced by the orientation dependence of shear stress under high strain rate at the shock front. Our simulations also show that a stationary combination of elastic precursor with plastic wave could exist in moderate and even melting shock waves. The oscillatory structure of the elastic precursor might play an important role in the initiation of shock-induced chemical reactions in crystalline solids.
Micromechanical modeling of damage in periodic composites using strain gradient plasticity
Azizi, Reza
2012-01-01
Damage evolution at the fiber matrix interface in Metal Matrix Composites (MMCs) is studied using strain gradient theory of plasticity. The study includes the rate independent formulation of energetic strain gradient plasticity for the matrix, purely elastic model for the fiber and cohesive zone...... model under simple shear and transverse uniaxial tension using plane strain and periodic boundary conditions. The result of the overall response curve, effective plastic strain, effective stress and higher order stress distributions are shown. The effect of the material length scale, maximum stress...
Complex variable methods in elasticity
England, A H
2003-01-01
The plane strain and generalized plane stress boundary value problems of linear elasticity are the focus of this graduate-level text, which formulates and solves these problems by employing complex variable theory. The text presents detailed descriptions of the three basic methods that rely on series representation, Cauchy integral representation, and the solution via continuation. Its five-part treatment covers functions of a complex variable, the basic equations of two-dimensional elasticity, plane and half-plane problems, regions with circular boundaries, and regions with curvilinear bounda
Renaud, Guillaume; Talmant, Maryline; Marrelec, Guillaume
2016-10-01
The nonlinear elasticity of solids at the microstrain level has been recently studied by applying dynamic acousto-elastic testing. It is the analog of conventional quasi-static acousto-elastic experiments but the strain-dependence (or stress-dependence) of ultrasonic wave-speed is measured with an applied strain ranging from 10-7 to 10-5 and produced by a stationary elastic wave. In conventional quasi-static acousto-elastic experiments, the strain is applied in a quasi-static manner; it exceeds 10-4 and can reach 10-2. In this work, we apply dynamic acousto-elastic testing to measure the third-order elastic constants of two isotropic materials: polymethyl methacrylate and dry Berea sandstone. The peak amplitude of the dynamic applied strain is 8 × 10-6. The method is shown to be particularly suitable for materials exhibiting large elastic nonlinearity like sandstones, since the measurement is performed in the domain of validity of the third-order hyperelastic model. In contrast, conventional quasi-static acousto-elastic experiments in such materials are often performed outside the domain of validity of the third-order hyperelastic model and the stress-dependence of the ultrasonic wave-speed must be extrapolated at zero stress, leading to approximate values of the third-order elastic constants. The uncertainty of the evaluation of the third-order elastic constants is assessed by repeating multiple times the measurements and with Monte-Carlo simulations. The obtained values of the Murnaghan third-order elastic constants are l = -73 GPa ± 9%, m = -34 GPa ± 9%, and n = -61 GPa ± 10% for polymethyl methacrylate, and l = -17 000 GPa ± 20%, m = -11 000 GPa ± 10%, and n = -30 000 GPa ± 20% for dry Berea sandstone.
Thresiamma Phlip; Menon, C S; Indulekha, K.
2005-01-01
The second- and third-order elastic constants of trigonal calcite have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The seven second-order elastic constants and the...
Anisotropic Elastic Properties of Muscle-like Nematic Elastomers
Ratna, Banahalii; Thomseniii, Donald L.; Shenoy, Devanand; Srinivasan, Amritha; Keller, Patrick
2001-03-01
De Gennes suggested in 1997 that the liquid crystal elastomers are an excellent framework to mimic muscular action. We have prepared anisotropic freestanding films of nematic elastomers from laterally attached side-chain polymers that show muscle-like mechanical properties. The orientational order of the liquid crystal side groups imposes a conformational anisotropy in the polymer backbone. When the order parameter drops at the nematic-isotropic phase transition, there is a concomitant loss of order in the backbone which results in a contraction of the film in the direction of the director orientation. Dynamic mechanical data along directions parallel and perpendicular to the optic axis, show anisotropic stress-strain behavior. The film exhibits soft elasticity when strained in the perpendicular direction when the liquid crystal mesogens reorient without appreciable stress build up. Thermostrictive studies in the parallel direction show 40constriction at the nematic-isotropic phase transition. Isometric studies show that the elastic energy stored is purely entropic in origin and the elastomer acts like a spring with unusually large spring constant at the NI transition. The maximum stress measured is 300kPa. A strain rate of 5s-1 is estimated from shear relaxation studies.
Elastic deformation and energy loss of flapping fly wings.
Lehmann, Fritz-Olaf; Gorb, Stanislav; Nasir, Nazri; Schützner, Peter
2011-09-01
During flight, the wings of many insects undergo considerable shape changes in spanwise and chordwise directions. We determined the origin of spanwise wing deformation by combining measurements on segmental wing stiffness of the blowfly Calliphora vicina in the ventral and dorsal directions with numerical modelling of instantaneous aerodynamic and inertial forces within the stroke cycle using a two-dimensional unsteady blade elementary approach. We completed this approach by an experimental study on the wing's rotational axis during stroke reversal. The wing's local flexural stiffness ranges from 30 to 40 nN m(2) near the root, whereas the distal wing parts are highly compliant (0.6 to 2.2 nN m(2)). Local bending moments during wing flapping peak near the wing root at the beginning of each half stroke due to both aerodynamic and inertial forces, producing a maximum wing tip deflection of up to 46 deg. Blowfly wings store up to 2.30 μJ elastic potential energy that converts into a mean wing deformation power of 27.3 μW. This value equates to approximately 5.9 and 2.3% of the inertial and aerodynamic power requirements for flight in this animal, respectively. Wing elasticity measurements suggest that approximately 20% or 0.46 μJ of elastic potential energy cannot be recovered within each half stroke. Local strain energy increases from tip to root, matching the distribution of the wing's elastic protein resilin, whereas local strain energy density varies little in the spanwise direction. This study demonstrates a source of mechanical energy loss in fly flight owing to spanwise wing bending at the stroke reversals, even in cases in which aerodynamic power exceeds inertial power. Despite lower stiffness estimates, our findings are widely consistent with previous stiffness measurements on insect wings but highlight the relationship between local flexural stiffness, wing deformation power and energy expenditure in flapping insect wings.
Storage and recovery of elastic potential energy powers ballistic prey capture in toads.
Lappin, A Kristopher; Monroy, Jenna A; Pilarski, Jason Q; Zepnewski, Eric D; Pierotti, David J; Nishikawa, Kiisa C
2006-07-01
Ballistic tongue projection in toads is a remarkably fast and powerful movement. The goals of this study were to: (1) quantify in vivo power output and activity of the depressor mandibulae muscles that are responsible for ballistic mouth opening, which powers tongue projection; (2) quantify the elastic properties of the depressor mandibulae muscles and their series connective tissues using in situ muscle stimulation and force-lever studies; and (3) develop and test an elastic recoil model, based on the observed elastic properties of the depressor mandibulae muscles and series connective tissues, that accounts for displacement, velocity, acceleration and power output during ballistic mouth opening in toads. The results demonstrate that the depressor mandibulae muscles of toads are active for up to 250 ms prior to mouth opening. During this time, strains of up to 21.4% muscle resting length (ML) develop in the muscles and series connective tissues. At maximum isometric force, series connective tissues develop strains up to 14% ML, and the muscle itself develops strains up to 17.5% ML. When the mouth opens rapidly, the peak instantaneous power output of the depressor mandibulae muscles and series connective tissues can reach 9600 W kg(-1). The results suggest that: (1) elastic recoil of muscle itself can contribute significantly to the power of ballistic movements; (2) strain in series elastic elements of the depressor mandibulae muscle is too large to be borne entirely by the cross bridges and the actin-myosin filament lattice; and (3) central nervous control of ballistic tongue projection in toads likely requires the specification of relatively few parameters.
Twelve Elastic Constants of Betula platyphylla Suk.
Wang Liyu; Lu Zhenyou
2004-01-01
Wood elastic constants are needed to describe the elastic behaviors of wood and be taken as an important design parameter for wood-based composite materials and structural materials. This paper clarified the relationships between compliance coefficients and engineering elastic constants combined with orthotropic properties of wood, and twelve elastic constants of Betula platyphylla Suk. were measured by electrical strain gauges. Spreading the adhesive quantity cannot be excessive or too little when the strain flakes were glued. If excessive, the glue layer was too thick which would influence the strain flakes' performance, and if too little, glues plastered were not firm, which could not accurately transmit the strain. Wood as an orthotropic material, its modulus of elasticity and poisson's ratios are related by two formulas:μij /Ei =μji /Ej and μij 0.95) between the reciprocal of elastic modulus MOE-1 and the square of the ratio of depth to length (h/l)2, which indicate that shear modulus values measured were reliable by three point bending experiment.
Isogeometric design of elastic arches for maximum fundamental frequency
Nagy, A.P.; Abdalla, M.M.; Gürdal, Z.
2010-01-01
The isogeometric paradigm is aimed at unifying the geometric and analysis descriptions of engineering problems. This unification is brought about by employing the same basis functions describing the geometry to approximate the physical response. Non-uniform rational B-splines (NURBS) are commonly us
Zhao, Xin
2013-05-01
Elastic rods have been studied intensively since the 18th century. Even now the theory of elastic rods is still developing and enjoying popularity in computer graphics and physical-based simulation. Elastic rods also draw attention from architects. Architectural structures, NODUS, were constructed by elastic rods as a new method of form-finding. We study discrete models of elastic rods and NODUS structures. We also develop computational tools to find the equilibria of elastic rods and the shape of NODUS. Applications of elastic rods in forming torus knot and closing Bishop frame are included in this thesis.
王赟; 张玉贵; 许小凯
2013-01-01
Abstract The maximum vitrinite reflectance of coal is an important parameter to estimate coal rank and distinguish coal quality,which has important application in methane exploration and production,coal mining,chemical and metallurgical industry.Sampling in the field and measuring in lab is the most conventional method to get coal rank and its vitrinite reflectance.In this paper,the relationships between maximum vitrinite reflectance with seismic properties and elastic parameters were introduced through reflectance and ultrasonic measurement in the lab on six different metamorphic kinds of coals,including maximum vitrinite reflectance,volatile matter percent,traveling time of pressure wave and shear wave.Through analyzing these testing data,it can be concluded that there is a fine correlation between the maximum vitrinite reflectance and seismic properties,especially the density and P-wave velocity.And it can be deduced that it will be possible to predict coal rank with seismic data.%煤镜质组反射率是评价煤阶、区分煤种的重要参数之一,在煤层气勘探与开发、采煤、化工和冶金中有着重要的应用.以往煤阶的评价单纯通过巷道和钻孔取芯的煤样实验室测试分析获得,受取样点有限限制.本文通过6种不同变质程度煤的挥发分和镜质组最大反射率的测试,配合煤样的超声弹性测量,探讨了镜质组最大反射率与地震属性参数—波速、密度和弹性模量之间的相关性.研究发现:煤镜质组最大反射率与地震属性参数均存在较好的线性正相关,其中以密度与纵波速度的相关程度最高.从而为利用煤田地震预测镜质组最大反射率,进而预测煤阶的三维立体分布提供了试验与物理依据.
Estimating of the Elastic Properties of the Composite with Anisotropic Ball Inclusions
V. S. Zarubin
2014-01-01
Full Text Available Scope composites as structural materials sensing mechanical stresses are largely determined by a complex of their elastic properties. Described in the article of review papers devoted to the elastic properties of the composite, it follows that the problem of theoretical evaluation of these characteristics, remains relevant. When considering composites reinforced with spherical inclusions, most famous works of the composite matrix and the inclusion is considered to be isotropic. However, for use as inclusions of metal particles and nanostructured elements often need to consider the anisotropy of the elastic characteristics.In the article for a composite with anisotropic spherical inclusions built two types of estimates of values of the bulk modulus and shear modulus . As background information used elastic properties of the matrix and the inclusions and their content by volume in the composite.The first type is classified as two-sided estimates of desired values that are based on the dual variational formulation of the linear elasticity problem of an inhomogeneous solid body containing alternative functionals (Lagrange and Castigliano. These functionals on the true distribution of strains and stresses in an inhomogeneous body reach the same meaning extremes (minimum and maximum respectively. On the convergence of the distribution of the Lagrange functional application allows you to get an upper bound of desired values, and the use of functional Castigliano - their lower bound.The second type of assessment is built by self-consistency, this method allows for the interaction of a single particle on or matrix composite with a homogeneous isotropic medium having measured the elastic moduli. Averaging over the volume of the composite disturbances arising strains and stresses in the inclusions and matrix particles makes it possible to obtain the calculated dependences for the bulk modulus and shear modulus of the composite. Comparison of these
Parameters testing and non-liner hyper-elastic strain modeling for soft tissue%软组织非线性物理建模及其参数测定
王洪瑞; 董斌
2012-01-01
The human soft tissue modeling is still a bottleneck for realistic soft tissue simulation. A novel soft tissue modeling method is proposed to improve the reality in this paper. Firstly, the volume-spring mass model is employed, and the biomechanics method is used to build the force model of the soft tissue. Then the springs is modeled with the non-liner hyper-elastic strain energy function for bio-tissues, the parameters of the model is calculated with the values tested by the ex vivo experiment on pig liver tissue, and the soft tissue model based on the physical character is obtained. The utility of improving the reality of virtual surgery system is verified by the experiment.%对现有虚拟手术中人体软组织建模方法进行了分析,针对目前软组织建模真实性还有待提高的问题,提出了一种新的软组织建模方法.首先,在引入体弹簧质点模型的基础上,利用生物力学方法建立了适合软组织力学仿真的模型.然后通过非线性超弹性应变能方程对弹簧力建模,并根据真实肝脏软组织物理特性的测量结果求解模型参数,得到基于物理特性的软组织模型.通过实验验证,该方法在提升虚拟手术触觉沉浸感方面具有可行性和有效性.
Jessamine P Winer
Full Text Available Most tissue cells grown in sparse cultures on linearly elastic substrates typically display a small, round phenotype on soft substrates and become increasingly spread as the modulus of the substrate increases until their spread area reaches a maximum value. As cell density increases, individual cells retain the same stiffness-dependent differences unless they are very close or in molecular contact. On nonlinear strain-stiffening fibrin gels, the same cell types become maximally spread even when the low strain elastic modulus would predict a round morphology, and cells are influenced by the presence of neighbors hundreds of microns away. Time lapse microscopy reveals that fibroblasts and human mesenchymal stem cells on fibrin deform the substrate by several microns up to five cell lengths away from their plasma membrane through a force limited mechanism. Atomic force microscopy and rheology confirm that these strains locally and globally stiffen the gel, depending on cell density, and this effect leads to long distance cell-cell communication and alignment. Thus cells are acutely responsive to the nonlinear elasticity of their substrates and can manipulate this rheological property to induce patterning.
Karimi, Alireza; Navidbakhsh, Mahdi
2014-07-01
There are different stress-strain definitions to measure the mechanical properties of the brain tissue. However, there is no agreement as to which stress-strain definition should be employed to measure the mechanical properties of the brain tissue at both the longitudinal and circumferential directions. It is worth knowing that an optimize stress-strain definition of the brain tissue at different loading directions may have implications for neuronavigation and surgery simulation through haptic devices. This study is aimed to conduct a comparative study on different results are given by the various definitions of stress-strain and to recommend a specific definition when testing brain tissues. Prepared cylindrical samples are excised from the parietal lobes of rats' brains and experimentally tested by applying load on both the longitudinal and circumferential directions. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) are used to determine the elastic modulus, maximum stress and strain. The highest non-linear stress-strain relation is observed for the Almansi-Hamel strain definition and it may overestimate the elastic modulus at different stress definitions at both the longitudinal and circumferential directions. The Green-St. Venant strain definition fails to address the non-linear stress-strain relation using different definitions of stress and triggers an underestimation of the elastic modulus. The results suggest the application of the true stress-true strain definition for characterization of the brain tissues mechanics since it gives more accurate measurements of the tissue's response using the instantaneous values.
Finite element simulation of stress intensity factors in elastic-plastic crack growth
ALSHOAIBI Abdulnaser M.; ARIFFIN Ahmad Kamal
2006-01-01
A finite element program developed elastic-plastic crack propagation simulation using Fortran language. At each propagation step, the adaptive mesh is automatically refined based on a posteriori h-type refinement using norm stress error estimator. A rosette of quarter-point elements is then constructed around the crack tip to facilitate the prediction of crack growth based on the maximum normal stress criterion and to calculate stress intensity factors under plane stress and plane strain conditions.Crack was modelled to propagate through the inter-element in the mesh. Some examples are presented to show the results of the implementation.
Inelastic strain in the seismogenic zone, Kyushu, Japan inferred from focal mechanism of earthquakes
Matsumoto, Satoshi; Nishimura, Takuya
2016-04-01
Strain in the seismogenic zone of the crust is a key parameter to understand crustal dynamics. GNSS data provide us with great information about deformation rate at the surface, which have been investigated by many researches and modeled kinematic behavior as elastic medium. Generally, strain in the earth's medium consists with elastic and inelastic ones. The two kinds of strain result different effects on the stress field. Therefore, detecting inelastic strain is important to know state of stress in the crust as well as elastic one. Inelastic strain is caused by such as fault creep, viscoelastic response, and earthquakes. Here, we showed the inelastic strain in the seismogenic zone of Kyushu, Japan from seismic moments and focal mechanisms data by counting Kostrov's sum in the spatial bins. Seismic moment tensors about 9000 earthquakes with magnitude greater than 2 for 13.5 years were obtained from seismic network data in Kyushu Island and F-net catalog. Total released moment at every spatial bin with 0.15 x 0.15 degree in latitude and longitude was estimated and then strain rate was calculated from the moment, compliance of the medium, and volume of the bin. The estimated maximum strain rate achieves 10^-7 strain/year. This strain rate is comparable with that from GNSS data. However, the strain rate mainly revealed the different principal direction from the one of GNSS. On the other hand, the directions were similar to the behavior of active faults in Kyushu. The result in this study showed that inelastic strain due to earthquakes is enough large, suggesting that the effect should be considered for modeling crustal dynamics.
On the algebraic structure of isotropic generalized elasticity theories
Auffray, Nicolas
2013-01-01
In this paper the algebraic structure of the isotropic nth-order gradient elasticity is investigated. In the classical isotropic elasticity it is well-known that the constitutive relation can be broken down into two uncoupled relations between elementary part of the strain and the stress tensors (deviatoric and spherical). In this paper we demonstrate that this result can not be generalized and since 2nd-order isotropic elasticity there exist couplings between elementary parts of higher-order strain and stress tensors. Therefore, and in certain way, nth-order isotropic elasticity have the same kind of algebraic structure as anisotropic classical elasticity. This structure is investigated in the case of 2nd-order isotropic elasticity, and moduli characterizing the behavior are provided.
Ho, Kai-Yu; Keyak, Joyce H; Powers, Christopher M
2014-01-03
Elevated bone principal strain (an indicator of potential bone injury) resulting from reduced cartilage thickness has been suggested to contribute to patellofemoral symptoms. However, research linking patella bone strain, articular cartilage thickness, and patellofemoral pain (PFP) remains limited. The primary purpose was to determine whether females with PFP exhibit elevated patella bone strain when compared to pain-free controls. A secondary objective was to determine the influence of patella cartilage thickness on patella bone strain. Ten females with PFP and 10 gender, age, and activity-matched pain-free controls participated. Patella bone strain fields were quantified utilizing subject-specific finite element (FE) models of the patellofemoral joint (PFJ). Input parameters for the FE model included (1) PFJ geometry, (2) elastic moduli of the patella bone, (3) weight-bearing PFJ kinematics, and (4) quadriceps muscle forces. Using quasi-static simulations, peak and average minimum principal strains as well as peak and average maximum principal strains were quantified. Cartilage thickness was quantified by computing the perpendicular distance between opposing voxels defining the cartilage edges on axial plane magnetic resonance images. Compared to the pain-free controls, individuals with PFP exhibited increased peak and average minimum and maximum principal strain magnitudes in the patella. Additionally, patella cartilage thickness was negatively associated with peak minimum principal patella strain and peak maximum principal patella strain. The elevated bone strain magnitudes resulting from reduced cartilage thickness may contribute to patellofemoral symptoms and bone injury in persons with PFP. © 2013 Published by Elsevier Ltd.
Elastic constants of the human lens capsule.
Fisher, R F
1969-03-01
1. A technique is described whereby the elasticity of the human lens capsule has been determined at birth and throughout life. This technique requires three separate determinations: (a) thickness; (b) stress and strain; (c) Poisson's ratio; (a) the capsule was clamped between accurately perforated ground glass plates and its thickness determined by noting the change in depth of focus between Latex spherules adhering to its upper and lower surfaces; (b) the undisturbed capsule was then placed in a specially designed glass distension apparatus and the relationship between volume and pressure recorded when it was distended with isotonic saline. The permeability of the capsule was also measured; (c) in some cases Poisson's ratio was determined by measuring the change of thickness of the capsule and the height to which it rose when distended with isotonic saline at different pressures. An apparatus was designed for this purpose.2. The average thickness of the anterior capsule increases from birth until about the 60th year but thereafter it decreases slightly.3. Poisson's ratio was about 0.47 for both cat and human capsule, and no significant variations with age in human capsule could be detected.4. Corrected volume pressure curves obeyed Hook's law almost to the point of capsule rupture.5. In childhood Young's Modulus of elasticity is about 6 x 10(7) dyn/cm(2) and decreases to 3 x 10(7) dyn/cm(2) at 60 and 1.5 x 10(7) dyn/cm(2) in extreme old age.6. The ultimate tensile stress was 2.3 x 10(7) dyn/cm(2) in young capsules and 0.7 x 10(7) dyn/cm(2) in old ones. The maximum percentage elongation was 29 per cent and independent of age.7. The implications of these findings are discussed in relation to(a) the mechanical properties of the lens capsule;(b) the ageing of the lens capsule and basement membranes; and(c) the decrease in elasticity of the lens capsule as a cause of presbyopia.
Maximum Autocorrelation Factorial Kriging
Nielsen, Allan Aasbjerg; Conradsen, Knut; Pedersen, John L.
2000-01-01
This paper describes maximum autocorrelation factor (MAF) analysis, maximum autocorrelation factorial kriging, and its application to irregularly sampled stream sediment geochemical data from South Greenland. Kriged MAF images are compared with kriged images of varimax rotated factors from...
Elastic Properties of Sedimentary Rocks
Melendez Martinez, Jaime
Sedimentary rocks are an important research topic since such rocks are associated to sources of ground water as well as oil, gas, and mineral reservoirs. In this work, elastic and physical properties of a variety of sedimentary samples that include glacial sediments, carbonates, shales, one evaporite, and one argillite from a variety of locations are investigated. Assuming vertical transverse isotropy, ultrasonic compressional- and shear-waves (at 1 MHz central frequency) were measured as a function of confining pressure on all samples with the exception of glacial samples which were tested assuming isotropy. Tensile strength tests (Brazilian test) were also carried out on selected glacial samples and, in addition, static-train measurements were conducted on shales and argillite samples. Lithological and textural features of samples were obtained through thin section techniques, scanning electron microscopy images and micro-tomography images. X-ray diffraction and X-Ray fluorescence provided the mineralogical oxides content information. Porosity, density, and pore structure were studied by using a mercury intrusion porosimeter and a helium pycnometer. The wide range of porosities of the studied samples (ranging from a minimum of 1% for shales to a maximum 45% for some glacial sediments) influence the measured velocities since high porosity sample shows an noticeable velocity increment as confining pressure increases as a consequence of closure of microcracks and pores, unlike low porosity samples where increment is quasi-lineal. Implementation of Gassmann's relation to ultrasonic velocities obtained from glacial samples has negligible impact on them when assuming water saturated samples, which suggests that state of saturation it is no so important in defining such velocities and instead they are mainly frame-controlled. On the other hand, velocities measured on carbonate and evaporite samples show that samples are at best weak anisotropic, thus the intrinsic
Three-dimensional finite element analysis of critical pre-twist strain angle for torsional axis
ZHOU Guo-feng; LI Xiao-yan; SHI Yao-wu; XU Bin-shi
2005-01-01
A three-dimensional elasto-plastic finite element analysis of pre-twist process for a torsional axis made of 45GrNiMoVA steel, was carried out using a commercial finite element analysis code, MSC MARC 2001. The results show that the critical pre-twist strain angle is 0. 027 rad and the maximum elastic shear stress after pre-twist is 1 694 MPa for the torsional axis.
Thermal elastic deformations of the planet Mercury.
Liu, H.-S.
1972-01-01
The variation in solar heating due to the resonance rotation of Mercury produces periodic elastic deformations on the surface of the planet. The thermal stress and strain fields under Mercury's surface are calculated after certain simplifications. It is found that deformations penetrate to a greater depth than the variation of solar heating, and that the thermal strain on the surface of the planet pulsates with an amplitude of .004 and a period of 176 days.
Thermal elastic deformations of the planet Mercury.
Liu, H.-S.
1972-01-01
The variation in solar heating due to the resonance rotation of Mercury produces periodic elastic deformations on the surface of the planet. The thermal stress and strain fields under Mercury's surface are calculated after certain simplifications. It is found that deformations penetrate to a greater depth than the variation of solar heating, and that the thermal strain on the surface of the planet pulsates with an amplitude of .004 and a period of 176 days.
A multiaxial elastic potential with error-minimizing approximation to rubberlike elasticity
Gu, Zhi-Xiang; Yuan, Lu; Yin, Zheng-Nan; Xiao, Heng
2015-10-01
This study is concerned with a new, explicit approach by means of which forms of the large strain elastic potential for multiaxial rubberlike elasticity may be obtained based on data for a single deformation mode. As a departure from usual studies, here for the first time errors may be estimated and rendered minimal for all possible deformation modes and, furthermore, failure behavior may be incorporated. Numerical examples presented are in accurate agreement with Treloar's well-known data.
Characterizing the elasticity of hollow metal nanowires
Ji Changjiang; Park, Harold S [Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN 37235 (United States)
2007-03-21
We have performed atomistic simulations on solid and hollow copper nanowires to quantify the elastic properties of hollow nanowires (nanoboxes). We analyse variations in the modulus, yield stress and strain for <100> and <110> nanoboxes by varying the amount of bulk material that is removed to create the nanoboxes. We find that, while <100> nanoboxes show no improvement in elastic properties as compared to solid <100>nanowires, <110> nanoboxes can show enhanced elastic properties as compared to solid <110> nanowires. The simulations reveal that the elastic properties of the nanoboxes are strongly dependent on the relative strength of the bulk material that has been removed, as well as the total surface area of the nanoboxes, and indicate the potential of ultralight, high-strength nanomaterials such as nanoboxes.
Maximum Profit Configurations of Commercial Engines
Yiran Chen
2011-01-01
An investigation of commercial engines with finite capacity low- and high-price economic subsystems and a generalized commodity transfer law [n ∝ Δ (P m)] in commodity flow processes, in which effects of the price elasticities of supply and demand are introduced, is presented in this paper. Optimal cycle configurations of commercial engines for maximum profit are obtained by applying optimal control theory. In some special cases, the eventual state—market equilibrium—is solely determined by t...
Application of numerical methods to elasticity imaging.
Castaneda, Benjamin; Ormachea, Juvenal; Rodríguez, Paul; Parker, Kevin J
2013-03-01
Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of clinical applications: cancer diagnosis (prostate, breast, liver), hepatic cirrhosis, renal disease, thyroiditis, arterial plaque evaluation, wall stiffness in arteries, evaluation of thrombosis in veins, and many others. In this context, numerical methods are applied to solve forward and inverse problems implicit in the algorithms in order to estimate viscoelastic linear and nonlinear parameters, especially for quantitative elasticity imaging modalities. In this work, an introduction to elasticity imaging modalities is presented. The working principle of qualitative modalities (sonoelasticity, strain elastography, acoustic radiation force impulse) and quantitative modalities (Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging) will be explained. Subsequently, the areas in which numerical methods can be applied to elasticity imaging are highlighted and discussed. Finally, we present a detailed example of applying total variation and AM-FM techniques to the estimation of elasticity.
Stress Wave Propagation in a Gradient Elastic Medium
赵亚溥; 赵涵; 胡宇群
2002-01-01
The gradient elastic constitutive equation incorporating the second gradient of the strains is used to determinethe monochromatic elastic plane wave propagation in a gradient infinite medium and thin rod. The equationof motion, together with the internal material length, has been derived. Various dispersion relations have beendetermined. We present explicit expressions for the relationship between various wave speeds, wavenumber andinternal material length.
Extremal Overall Elastic Response of Polycrystalline Materials
Bendsøe, Martin P; Lipton, Robert
1997-01-01
Polycrystalline materials comprised of grains obtained from a single anisotropic material are considered in the framework of linear elasticity. No assumptions on the symmetry of the polycrystal are made. We subject the material to independent external strain and stress fields with prescribed mean...
Intracuticular wax fixes and restricts strain in leaf and fruit cuticles.
Khanal, Bishnu Prasad; Grimm, Eckhard; Finger, Sebastian; Blume, Alfred; Knoche, Moritz
2013-10-01
This paper investigates the effects of cuticular wax on the release of strain and on the tensile properties of enzymatically isolated cuticular membranes (CMs) taken from leaves of agave (Agave americana), bush lily (Clivia miniata), holly (Ilex aquifolium), and ivy (Hedera helix) and from fruit of apple (Malus × domestica), pear (Pyrus communis), and tomato (Lycopersicon esculentum). Biaxial strain release was quantified as the decrease in CM disc area following wax extraction. Stiffness, maximum strain and maximum force were determined in uniaxial tensile tests using strips of CM and dewaxed CMs (DCMs). Biaxial strain release, stiffness, and maximum strain, but not maximum force, were linearly related to the amount of wax extracted. Apple CM has the most wax and here the effect of wax extraction was substantially accounted for by the embedded cuticular wax. Heating apple CM to 80°C melted some wax constituents and produced an effect similar to, but smaller than, that resulting from wax extraction. Our results indicate that wax 'fixes' strain, effectively converting reversible elastic into irreversible plastic strain. A consequence of 'fixation' is increased cuticular stiffness.
WANG Xue-bin
2006-01-01
Patterns of shear band, precursors to shear failure occurring in strain-softening stage, axial, lateral and volumetric strains as well as Poisson's ratio of plane strain rock specimens in compression for different heights were investigated by use of Fast Lagrangian Analysis of Continua(FLAC). A material imperfection closer to the lower-left comer of the specimen was prescribed. For finer mesh, the imperfection was modeled by four null elements, while it was modeled by a null element for coarser mesh. FISH functions were written to calculate the entire deformational characteristics of the specimen. In elastic stage, the adopted constitutive relation was linear elastic; in strain-softening stage, a composite Mohr-Coulomb criterion with tension cut-off and a post-peak linear constitutive relation were adopted. Height of rock specimen does not influence shear band's pattern (including the thickness and inclination angle of shear band). The slopes of the post-peak stress-axial strain curve, stress-lateral strain curve,lateral strain-axial strain curve, Poisson's ratio-axial strain curve and volumetric strain-axial strain curve depend on the height. Hence, the slopes of these curves cannot be considered as material properties. Nonlinear deformation prior to the peak stress is a kind of precursors to shear failure, which is less apparent for shorter specimen. For the same axial strain, lower lateral expansion is reached for shorter specimen, leading to lower Poisson's ratio and higher volumetric strain. The maximum volumetric strain of longer specimen is less than that of shorter specimen. The conclusions drawn from numerical results using finer mesh qualitatively agree with those using coarser mesh.
Elastically Decoupling Dark Matter
Kuflik, Eric; Lorier, Nicolas Rey-Le; Tsai, Yu-Dai
2015-01-01
We present a novel dark matter candidate, an Elastically Decoupling Relic (ELDER), which is a cold thermal relic whose present abundance is determined by the cross-section of its elastic scattering on Standard Model particles. The dark matter candidate is predicted to have a mass ranging from a few to a few hundred MeV, and an elastic scattering cross-section with electrons, photons and/or neutrinos in the $10^{-3}-1$ fb range.
Elastically Decoupling Dark Matter.
Kuflik, Eric; Perelstein, Maxim; Lorier, Nicolas Rey-Le; Tsai, Yu-Dai
2016-06-03
We present a novel dark matter candidate, an elastically decoupling relic, which is a cold thermal relic whose present abundance is determined by the cross section of its elastic scattering on standard model particles. The dark matter candidate is predicted to have a mass ranging from a few to a few hundred MeV, and an elastic scattering cross section with electrons, photons and/or neutrinos in the 10^{-3}-1 fb range.
Paro, Alberto
2013-01-01
Written in an engaging, easy-to-follow style, the recipes will help you to extend the capabilities of ElasticSearch to manage your data effectively.If you are a developer who implements ElasticSearch in your web applications, manage data, or have decided to start using ElasticSearch, this book is ideal for you. This book assumes that you've got working knowledge of JSON and Java
Solano-Altamirano, J M; Goldman, Saul
2015-12-01
We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another.
Tartaglia, Angelo
2015-01-01
Starting from some relevant facts concerning the behaviour of the universe over large scale and time span, the analogy between the geometric approach of General Relativ- ity and the classical description of an elastic strained material continuum is discussed. Extending the elastic deformation approach to four dimensions it is shown that the accelerated expansion of the universe is recovered. The strain field of space-time repro- duces properties similar to the ones ascribed to the dark energy currently called in to explain the accelerated expansion. The strain field in the primordial universe behaves as radiation, but asymptotically it reproduces the cosmological constant. Subjecting the theory to a number of cosmological tests confirms the soundness of the approach and gives an optimal value for the one parameter of the model, i.e. the bulk modulus of the space-time continuum. Finally various aspects of the Strained State Cosmology (SSC) are discussed and contrasted with some non-linear massive gravity theor...
Athermal nonlinear elastic constants of amorphous solids.
Karmakar, Smarajit; Lerner, Edan; Procaccia, Itamar
2010-08-01
We derive expressions for the lowest nonlinear elastic constants of amorphous solids in athermal conditions (up to third order), in terms of the interaction potential between the constituent particles. The effect of these constants cannot be disregarded when amorphous solids undergo instabilities such as plastic flow or fracture in the athermal limit; in such situations the elastic response increases enormously, bringing the system much beyond the linear regime. We demonstrate that the existing theory of thermal nonlinear elastic constants converges to our expressions in the limit of zero temperature. We motivate the calculation by discussing two examples in which these nonlinear elastic constants play a crucial role in the context of elastoplasticity of amorphous solids. The first example is the plasticity-induced memory that is typical to amorphous solids (giving rise to the Bauschinger effect). The second example is how to predict the next plastic event from knowledge of the nonlinear elastic constants. Using the results of our calculations we derive a simple differential equation for the lowest eigenvalue of the Hessian matrix in the external strain near mechanical instabilities; this equation predicts how the eigenvalue vanishes at the mechanical instability and the value of the strain where the mechanical instability takes place.
H.B. Motra
2014-12-01
Full Text Available Strain measurement is important in mechanical testing. A wide variety of techniques exists for measuring strain in the tensile test; namely the strain gauge, extensometer, stress and strain determined by machine crosshead motion, Geometric Moire technique, optical strain measurement techniques and others. Each technique has its own advantages and disadvantages. The purpose of this study is to quantitatively compare the strain measurement techniques. To carry out the tensile test experiments for S 235, sixty samples were cut from the web of the I-profile in longitudinal and transverse directions in four different dimensions. The geometry of samples are analysed by 3D scanner and vernier caliper. In addition, the strain values were determined by using strain gauge, extensometer and machine crosshead motion. Three techniques of strain measurement are compared in quantitative manner based on the calculation of mechanical properties (modulus of elasticity, yield strength, tensile strength, percentage elongation at maximum force of structural steel. A statistical information was used for evaluating the results. It is seen that the extensometer and strain gauge provided reliable data, however the extensometer offers several advantages over the strain gauge and crosshead motion for testing structural steel in tension. Furthermore, estimation of measurement uncertainty is presented for the basic material parameters extracted through strain measurement.
Elasticity of some mantle crystal structures. II.
Wang, H.; Simmons, G.
1973-01-01
The single-crystal elastic constants are determined as a function of pressure and temperature for rutile structure germanium dioxide (GeO2). The data are qualitatively similar to those of rutile TiO2 measured by Manghnani (1969). The compressibility in the c direction is less than one-half that in the a direction, the pressure derivative of the shear constant is negative, and the pressure derivative of the bulk modulus has a relatively high value of about 6.2. According to an elastic strain energy theory, the negative shear modulus derivative implies that the kinetic barrier to diffusion decreases with increasing pressure.
Thickness and orientational design for a maximum stiff membrane
Pedersen, Pauli
1990-01-01
Recent results from sensitivity analysis for strain energy with anisotropic elasticity are applied to thickness and orientational design of laminated membranes. Primarily, the first order gradients of the total elastic energy are used in an optimality criteria based method. This traditional method is shown to give slow convergence with respect to design parameters, although the convergence of strain energy is very good. To get a deeper insight into this rather general characteristic, second order derivatives are included and it is shown how they can be obtained by first order sensitivity analysis. Examples of only thickness design, only orientational design, and combined thickness--orientational design are presented.
Effect of uniaxial strain on adatom diffusion across {l_brace}1 1 1{r_brace}-faceted step
Yang Jianyu, E-mail: wuliyangjianyu@yahoo.com.cn [Department of Maths and Physics, Hunan Institute of Engineering, Donghu Street, Xiangtan 411104 (China); Hu Wangyu, E-mail: Wangyuhu2001@yahoo.com.cn [Department of Applied Physics, Hunan University, Changsha 410082 (China); Tang Jianfeng [Department of Applied Physics, Hunan Agricultural University, Changsha 410128 (China)
2011-02-01
Diffusion of Pt adatom across the strained {l_brace}1 1 1{r_brace}-faceted step is studied by embedded atom method along with nudged elastic band method. For adatom on the flat (1 1 1) surface, the anisotropic diffusion behavior is found as the uniaxial strain is imposed. For the strained {l_brace}1 1 1{r_brace}-faceted step, our results show that the maximum energy barrier for adatom crossing step edge remains approximately constant as the strain varied from -1.0% to 1.0%, and there is a rise as the larger uniaxial strain is applied. The calculated energy barrier for adatom diffusion along the step edge increases with increasing tensile strain, and the slope of the straight line is small.
MENG Guo-jie; REN Jin-wei; WU Ji-cang; SHEN Xu-hui
2008-01-01
Based on Taylor series expansion and strain components expressions of elastic mechanics, we derive formulae of strain and rotation tensor for small arrays in spherical coordinates system. By linearization process of the formulae, we also derive expressions of strain components and Euler vector uncertainties respectively for subnets using the law of error propagation. Taking GPS velocity field in Sichuan-Yunnan area as an example, we compute dilation rate and maximum shear strain rate field using the above procedure, and their characteristics are preliminarily carried on. Limits of the strain model for small array are also discussed. We make detailed explanations on small array method and the choice of small arrays. How to set weights of GPS observations are further discussed. Moreover relationship between strain and radius of GPS subnets is also analyzed.
Elastic and thermal expansion asymmetry in dense molecular materials.
Burg, Joseph A; Dauskardt, Reinhold H
2016-09-01
The elastic modulus and coefficient of thermal expansion are fundamental properties of elastically stiff molecular materials and are assumed to be the same (symmetric) under both tension and compression loading. We show that molecular materials can have a marked asymmetric elastic modulus and coefficient of thermal expansion that are inherently related to terminal chemical groups that limit molecular network connectivity. In compression, terminal groups sterically interact to stiffen the network, whereas in tension they interact less and disconnect the network. The existence of asymmetric elastic and thermal expansion behaviour has fundamental implications for computational approaches to molecular materials modelling and practical implications on the thermomechanical strains and associated elastic stresses. We develop a design space to control the degree of elastic asymmetry in molecular materials, a vital step towards understanding their integration into device technologies.
Elastic and thermal expansion asymmetry in dense molecular materials
Burg, Joseph A.; Dauskardt, Reinhold H.
2016-09-01
The elastic modulus and coefficient of thermal expansion are fundamental properties of elastically stiff molecular materials and are assumed to be the same (symmetric) under both tension and compression loading. We show that molecular materials can have a marked asymmetric elastic modulus and coefficient of thermal expansion that are inherently related to terminal chemical groups that limit molecular network connectivity. In compression, terminal groups sterically interact to stiffen the network, whereas in tension they interact less and disconnect the network. The existence of asymmetric elastic and thermal expansion behaviour has fundamental implications for computational approaches to molecular materials modelling and practical implications on the thermomechanical strains and associated elastic stresses. We develop a design space to control the degree of elastic asymmetry in molecular materials, a vital step towards understanding their integration into device technologies.
Elasticity reconstructive imaging by means of stimulated echo MRI.
Chenevert, T L; Skovoroda, A R; O'Donnell, M; Emelianov, S Y
1998-03-01
A method is introduced to measure internal mechanical displacement and strain by means of MRI. Such measurements are needed to reconstruct an image of the elastic Young's modulus. A stimulated echo acquisition sequence with additional gradient pulses encodes internal displacements in response to an externally applied differential deformation. The sequence provides an accurate measure of static displacement by limiting the mechanical transitions to the mixing period of the simulated echo. Elasticity reconstruction involves definition of a region of interest having uniform Young's modulus along its boundary and subsequent solution of the discretized elasticity equilibrium equations. Data acquisition and reconstruction were performed on a urethane rubber phantom of known elastic properties and an ex vivo canine kidney phantom using elastic properties are well represented on Young's modulus images. The long-term objective of this work is to provide a means for remote palpation and elasticity quantitation in deep tissues otherwise inaccessible to manual palpation.
Paro, Alberto
2015-01-01
If you are a developer who implements ElasticSearch in your web applications and want to sharpen your understanding of the core elements and applications, this is the book for you. It is assumed that you've got working knowledge of JSON and, if you want to extend ElasticSearch, of Java and related technologies.
唐立强; 李永东; 刘长海
2004-01-01
A mechanical model was established for mode Ⅱ interfacial crack static growing along an elastic-elastic power law creeping bimaterial interface. For two kinds of boundary conditions on crack faces, traction free and frictional contact, asymptotic solutions of the stress and strain near tip-crack were given. Results derived indicate that the stress and strain have the same singularity, there is not the oscillatory singularity in the field; the creep power-hardening index n and the ratio of Young' s module notably influence the cracktip field in region of elastic power law creeping material and n only influences distribution of stresses and strains in region of elastic material. When n is bigger, the creeping deformation is dominant and stress fields become steady, which does not change with n.Poisson ' s ratio does not affect the distributing of the crack- tip field.
Maximum Autocorrelation Factorial Kriging
Nielsen, Allan Aasbjerg; Conradsen, Knut; Pedersen, John L.; Steenfelt, Agnete
2000-01-01
This paper describes maximum autocorrelation factor (MAF) analysis, maximum autocorrelation factorial kriging, and its application to irregularly sampled stream sediment geochemical data from South Greenland. Kriged MAF images are compared with kriged images of varimax rotated factors from an ordinary non-spatial factor analysis, and they are interpreted in a geological context. It is demonstrated that MAF analysis contrary to ordinary non-spatial factor analysis gives an objective discrimina...
Kh.L. Khamidov
2017-01-01
Full Text Available Strain effect of focal zones on fore-seismic displacements of earth's surface is studied in the paper for real conditions of focus zones of the earthquakes. The width of the interval of maximum displacements is determined by the conditions of potential focus of tectonic earthquake. The solution of elastic problem for half-space with soft inclusion is used. Calculations are conducted also by empirical formulas, obtained for similar stress states. Possible radius of the zone of maximum revelation of strain anomaly is determined on the basis of the growth of rupture scale and change in heterogeneity volume. It is shown that obtained expression covers a wider range of magnitude variations with consideration of the interval of scale change in upcoming rupture-forming zone. In the example of Tashkent (1966 and Gazli (1984 strong ground motions, an analysis of possible strains occurrence on the Earth's surface was conducted.
Tensile Instability in a Thick Elastic Body
Overvelde, Johannes T. B.; Dykstra, David M. J.; de Rooij, Rijk; Weaver, James; Bertoldi, Katia
2016-08-01
A range of instabilities can occur in soft bodies that undergo large deformation. While most of them arise under compressive forces, it has previously been shown analytically that a tensile instability can occur in an elastic block subjected to equitriaxial tension. Guided by this result, we conducted centimeter-scale experiments on thick elastomeric samples under generalized plane strain conditions and observed for the first time this elastic tensile instability. We found that equibiaxial stretching leads to the formation of a wavy pattern, as regions of the sample alternatively flatten and extend in the out-of-plane direction. Our work uncovers a new type of instability that can be triggered in elastic bodies, enlarging the design space for smart structures that harness instabilities to enhance their functionality.
Programmable shape transformation of elastic spherical domes.
Abdullah, Arif M; Braun, Paul V; Hsia, K Jimmy
2016-07-20
We investigate mismatch strain driven programmable shape transformation of spherical domes and report the effects of different geometric and structural characteristics on dome behavior in response to applied mismatch strain. We envision a bilayer dome design where the differential swelling of the inner layer with respect to the passive outer layer in response to changes in dome surroundings (such as the introduction of an organic solvent) introduces mismatch strain within the bilayer system and causes dome shape transformation. Finite element analysis reveals that, in addition to snap-through, spherical domes undergo bifurcation buckling and eventually gradual bending to morph into cylinders with increasing mismatch strain. Besides demonstrating how the snap-through energy barrier depends on the spherical dome shape, our analysis identifies three distinct groups of dome geometries based on their mismatch strain-transformed configuration relationships. Our experiments with polymer-based elastic bilayer domes that exhibit differential swelling in organic solvents qualitatively confirm the finite element predictions. We establish that, in addition to externally applied stimuli (mismatch strain), bilayer spherical dome morphing can be tuned and hence programmed through its geometry and structural characteristics. Incorporation of an elastic instability mechanism such as snap-through within the framework of stimuli-responsive functional devices can improve their response time which is otherwise controlled by diffusion. Hence, our proposed design guidelines can be used to realize deployable, multi-functional, reconfigurable, and therefore, adaptive structures responsive to a diverse set of stimuli across multiple length scales.
Thresiamma Philip
2006-01-01
Full Text Available The second and third-order elastic constants and pressure derivatives of second- order elastic constants of trigonal LiNbO3 (lithium niobate have been obtained using the deformation theory. The strain energy density estimated using finite strain elasticity is compared with the strain dependent lattice energy density obtained from the elastic continuum model approximation. The second-order elastic constants and the non-vanishing third-order elastic constants along with the pressure derivatives of trigonal LiNbO3 are obtained in the present work. The second and third-order elastic constants are compared with available experimental values. The second-order elastic constant C11 which corresponds to the elastic stiffness along the basal plane of the crystal is less than C33 which corresponds to the elastic stiffness tensor component along the c-axis of the crystal. The pressure derivatives, dC'ij/dp obtained in the present work, indicate that trigonal LiNbO3 is compressible. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in LiNbO3. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.
Nonlocal elasticity tensors in dislocation and disclination cores
Taupin, V.; Gbemou, K.; Fressengeas, C.; Capolungo, L.
2017-03-01
Nonlocal elastic constitutive laws are introduced for crystals containing defects such as dislocations and disclinations. In addition to pointwise elastic moduli tensors adequately reflecting the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum and moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. The convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.
Elastic and viscoelastic properties of a type I collagen fiber.
Sopakayang, Ratchada; De Vita, Raffaella; Kwansa, Albert; Freeman, Joseph W
2012-01-21
A new mathematical model is presented to describe the elastic and viscoelastic properties of a single collagen fiber. The model is formulated by accounting for the mechanical contribution of the collagen fiber's main constituents: the microfibrils, the interfibrillar matrix and crosslinks. The collagen fiber is modeled as a linear elastic spring, which represents the mechanical contribution of the microfibrils, and an arrangement in parallel of elastic springs and viscous dashpots, which represent the mechanical contributions of the crosslinks and interfibrillar matrix, respectively. The linear elastic spring and the arrangement in parallel of elastic springs and viscous dashpots are then connected in series. The crosslinks are assumed to gradually break under strain and, consequently, the interfibrillar is assumed to change its viscous properties. Incremental stress relaxation tests are conducted on dry collagen fibers reconstituted from rat tail tendons to determine their elastic and viscoelastic properties. The elastic and total stress-strain curves and the stress relaxation at different levels of strain collected by performing these tests are then used to estimate the parameters of the model and evaluate its predictive capabilities.
Wu, H. I.; Spence, R. D.; Sharpe, P. J.; Goeschl, J. D.
1985-01-01
The traditional bulk elastic modulus approach to plant cell pressure-volume relations is inconsistent with its definition. The relationship between the bulk modulus and Young's modulus that forms the basis of their usual application to cell pressure-volume properties is demonstrated to be physically meaningless. The bulk modulus describes stress/strain relations of solid, homogeneous bodies undergoing small deformations, whereas the plant cell is best described as a thin-shelled, fluid-filled structure with a polymer base. Because cell walls possess a polymer structure, an alternative method of mechanical analysis is presented using polymer elasticity principles. This initial study presents the groundwork of polymer mechanics as would be applied to cell walls and discusses how the matrix and microfibrillar network induce nonlinear stress/strain relationships in the cell wall in response to turgor pressure. In subsequent studies, these concepts will be expanded to include anisotropic expansion as regulated by the microfibrillar network.
Elastic scattering phenomenology
Mackintosh, R.S. [The Open University, School of Physical Sciences, Milton Keynes (United Kingdom)
2017-04-15
We argue that, in many situations, fits to elastic scattering data that were historically, and frequently still are, considered ''good'', are not justifiably so describable. Information about the dynamics of nucleon-nucleus and nucleus-nucleus scattering is lost when elastic scattering phenomenology is insufficiently ambitious. It is argued that in many situations, an alternative approach is appropriate for the phenomenology of nuclear elastic scattering of nucleons and other light nuclei. The approach affords an appropriate means of evaluating folding models, one that fully exploits available empirical data. It is particularly applicable for nucleons and other light ions. (orig.)
Maximum-biomass prediction of homofermentative Lactobacillus.
Cui, Shumao; Zhao, Jianxin; Liu, Xiaoming; Chen, Yong Q; Zhang, Hao; Chen, Wei
2016-07-01
Fed-batch and pH-controlled cultures have been widely used for industrial production of probiotics. The aim of this study was to systematically investigate the relationship between the maximum biomass of different homofermentative Lactobacillus and lactate accumulation, and to develop a prediction equation for the maximum biomass concentration in such cultures. The accumulation of the end products and the depletion of nutrients by various strains were evaluated. In addition, the minimum inhibitory concentrations (MICs) of acid anions for various strains at pH 7.0 were examined. The lactate concentration at the point of complete inhibition was not significantly different from the MIC of lactate for all of the strains, although the inhibition mechanism of lactate and acetate on Lactobacillus rhamnosus was different from the other strains which were inhibited by the osmotic pressure caused by acid anions at pH 7.0. When the lactate concentration accumulated to the MIC, the strains stopped growing. The maximum biomass was closely related to the biomass yield per unit of lactate produced (YX/P) and the MIC (C) of lactate for different homofermentative Lactobacillus. Based on the experimental data obtained using different homofermentative Lactobacillus, a prediction equation was established as follows: Xmax - X0 = (0.59 ± 0.02)·YX/P·C.
Statistical mechanics of elasticity
Weiner, JH
2012-01-01
Advanced, self-contained treatment illustrates general principles and elastic behavior of solids. Topics include thermoelastic behavior of crystalline and polymeric solids, interatomic force laws, behavior of solids, and thermally activated processes. 1983 edition.
Yielding elastic tethers stabilize robust cell adhesion.
Matt J Whitfield
2014-12-01
Full Text Available Many bacteria and eukaryotic cells express adhesive proteins at the end of tethers that elongate reversibly at constant or near constant force, which we refer to as yielding elasticity. Here we address the function of yielding elastic adhesive tethers with Escherichia coli bacteria as a model for cell adhesion, using a combination of experiments and simulations. The adhesive bond kinetics and tether elasticity was modeled in the simulations with realistic biophysical models that were fit to new and previously published single molecule force spectroscopy data. The simulations were validated by comparison to experiments measuring the adhesive behavior of E. coli in flowing fluid. Analysis of the simulations demonstrated that yielding elasticity is required for the bacteria to remain bound in high and variable flow conditions, because it allows the force to be distributed evenly between multiple bonds. In contrast, strain-hardening and linear elastic tethers concentrate force on the most vulnerable bonds, which leads to failure of the entire adhesive contact. Load distribution is especially important to noncovalent receptor-ligand bonds, because they become exponentially shorter lived at higher force above a critical force, even if they form catch bonds. The advantage of yielding is likely to extend to any blood cells or pathogens adhering in flow, or to any situation where bonds are stretched unequally due to surface roughness, unequal native bond lengths, or conditions that act to unzip the bonds.
Maximum likely scale estimation
Loog, Marco; Pedersen, Kim Steenstrup; Markussen, Bo
2005-01-01
A maximum likelihood local scale estimation principle is presented. An actual implementation of the estimation principle uses second order moments of multiple measurements at a fixed location in the image. These measurements consist of Gaussian derivatives possibly taken at several scales and/or ...
Kuc, Rafal
2013-01-01
A practical tutorial that covers the difficult design, implementation, and management of search solutions.Mastering ElasticSearch is aimed at to intermediate users who want to extend their knowledge about ElasticSearch. The topics that are described in the book are detailed, but we assume that you already know the basics, like the query DSL or data indexing. Advanced users will also find this book useful, as the examples are getting deep into the internals where it is needed.
Elastic therapeutic tape: do they have the same material properties?
Boonkerd, Chuanpis; Limroongreungrat, Weerawat
2016-01-01
[Purpose] Elastic therapeutic tape has been widely used for rehabilitation and treatment of sports injuries. Tapes with different elastic properties serve different treatment purposes with inappropriate tension reducing tape effectiveness. Many tapes are available in the market, but studies on tape properties are limited. The aim of this study was to examine the material properties of elastic therapeutic tape. [Subjects and Methods] Brands of elastic therapeutic tape included KinesioTex®, ATex, Mueller, 3M, and ThaiTape. The Material Testing System Insight® 1 Electromechanical Testing Systems was used to apply a tensile force on elastic therapeutic tape. Ten specimens of each brand were tested. Stress, load, and Young’s modulus at 25%, 50%, 75%, 100%, and maximum point were collected. One-way analysis of variance with post hoc testing was used to analyze tape parameters. [Results] Maximum elongation and Young’s modulus at all percentages were significantly different between brands. There were no differences in maximum load and maximum stress. [Conclusion] Mechanical properties are different for commercial elastic therapeutic tapes. Physiotherapists and other clinicians should be aware of mechanical tape properties to correctly apply kinesio tape. PMID:27190472
Elastic therapeutic tape: do they have the same material properties?
Boonkerd, Chuanpis; Limroongreungrat, Weerawat
2016-04-01
[Purpose] Elastic therapeutic tape has been widely used for rehabilitation and treatment of sports injuries. Tapes with different elastic properties serve different treatment purposes with inappropriate tension reducing tape effectiveness. Many tapes are available in the market, but studies on tape properties are limited. The aim of this study was to examine the material properties of elastic therapeutic tape. [Subjects and Methods] Brands of elastic therapeutic tape included KinesioTex(®), ATex, Mueller, 3M, and ThaiTape. The Material Testing System Insight(®) 1 Electromechanical Testing Systems was used to apply a tensile force on elastic therapeutic tape. Ten specimens of each brand were tested. Stress, load, and Young's modulus at 25%, 50%, 75%, 100%, and maximum point were collected. One-way analysis of variance with post hoc testing was used to analyze tape parameters. [Results] Maximum elongation and Young's modulus at all percentages were significantly different between brands. There were no differences in maximum load and maximum stress. [Conclusion] Mechanical properties are different for commercial elastic therapeutic tapes. Physiotherapists and other clinicians should be aware of mechanical tape properties to correctly apply kinesio tape.
Ban, Ehsan; Barocas, Victor H; Shephard, Mark S; Picu, Catalin R
2016-04-01
Fiber networks are assemblies of one-dimensional elements representative of materials with fibrous microstructures such as collagen networks and synthetic nonwovens. The mechanics of random fiber networks has been the focus of numerous studies. However, fiber crimp has been explicitly represented only in few cases. In the present work, the mechanics of cross-linked networks with crimped athermal fibers, with and without an embedding elastic matrix, is studied. The dependence of the effective network stiffness on the fraction of nonstraight fibers and the relative crimp amplitude (or tortuosity) is studied using finite element simulations of networks with sinusoidally curved fibers. A semi-analytic model is developed to predict the dependence of network modulus on the crimp amplitude and the bounds of the stiffness reduction associated with the presence of crimp. The transition from the linear to the nonlinear elastic response of the network is rendered more gradual by the presence of crimp, and the effect of crimp on the network tangent stiffness decreases as strain increases. If the network is embedded in an elastic matrix, the effect of crimp becomes negligible even for very small, biologically relevant matrix stiffness values. However, the distribution of the maximum principal stress in the matrix becomes broader in the presence of crimp relative to the similar system with straight fibers, which indicates an increased probability of matrix failure.
Mitsak, Anna G; Dunn, Andrew M; Hollister, Scott J
2012-07-01
Scaffold tissue engineering strategies for repairing and replacing soft tissue aim to improve reconstructive and corrective surgical techniques whose limitations include suboptimal mechanical properties, fibrous capsule formation and volume loss due to graft resorption. An effective tissue engineering strategy requires a scaffolding material with low elastic modulus that behaves similarly to soft tissue, which has been characterized as a nonlinear elastic material. The material must also have the ability to be manufactured into specifically designed architectures. Poly(glycerol sebacate) (PGS) is a thermoset elastomer that meets these criteria. We hypothesize that the mechanical properties of PGS can be modulated through curing condition and architecture to produce materials with a range of stiffnesses. To evaluate this hypothesis, we manufactured PGS constructs cured under various conditions and having one of two architectures (solid or porous). Specimens were then tensile tested according to ASTM standards and the data were modeled using a nonlinear elastic Neo-Hookean model. Architecture and testing conditions, including elongation rate and wet versus dry conditions, affected the mechanical properties. Increasing curing time and temperature led to increased tangent modulus and decreased maximum strain for solid constructs. Porous constructs had lower nonlinear elastic properties, as did constructs of both architectures tested under simulated physiological conditions (wetted at 37 °C). Both solid and porous PGS specimens could be modeled well with the Neo-Hookean model. Future studies include comparing PGS properties to other biological tissue types and designing and characterizing PGS scaffolds for regenerating these tissues.
On the third- and fourth-order constants of incompressible isotropic elasticity.
Destrade, Michel; Ogden, Raymond W
2010-12-01
Consider the constitutive law for an isotropic elastic solid with the strain-energy function expanded up to the fourth order in the strain and the stress up to the third order in the strain. The stress-strain relation can then be inverted to give the strain in terms of the stress with a view to considering the incompressible limit. For this purpose, use of the logarithmic strain tensor is of particular value. It enables the limiting values of all nine fourth-order elastic constants in the incompressible limit to be evaluated precisely and rigorously. In particular, it is explained why the three constants of fourth-order incompressible elasticity μ, Ā, and D are of the same order of magnitude. Several examples of application of the results follow, including determination of the acoustoelastic coefficients in incompressible solids and the limiting values of the coefficients of nonlinearity for elastic wave propagation.
Maximum information photoelectron metrology
Hockett, P; Wollenhaupt, M; Baumert, T
2015-01-01
Photoelectron interferograms, manifested in photoelectron angular distributions (PADs), are a high-information, coherent observable. In order to obtain the maximum information from angle-resolved photoionization experiments it is desirable to record the full, 3D, photoelectron momentum distribution. Here we apply tomographic reconstruction techniques to obtain such 3D distributions from multiphoton ionization of potassium atoms, and fully analyse the energy and angular content of the 3D data. The PADs obtained as a function of energy indicate good agreement with previous 2D data and detailed analysis [Hockett et. al., Phys. Rev. Lett. 112, 223001 (2014)] over the main spectral features, but also indicate unexpected symmetry-breaking in certain regions of momentum space, thus revealing additional continuum interferences which cannot otherwise be observed. These observations reflect the presence of additional ionization pathways and, most generally, illustrate the power of maximum information measurements of th...
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Indentation of elastically soft and plastically compressible solids
Needleman, A.; Tvergaard, Viggo; Van der Giessen, E.
2015-01-01
The effect of soft elasticity, i.e., a relatively small value of the ratio of Young's modulus to yield strength and plastic compressibility on the indentation of isotropically hardening elastic-viscoplastic solids is investigated. Calculations are carried out for indentation of a perfectly sticking...... rigid sharp indenter into a cylinder modeling indentation of a half space. The material is characterized by a finite strain elastic-viscoplastic constitutive relation that allows for plastic as well as elastic compressibility. Both soft elasticity and plastic compressibility significantly reduce...... the ratio of nominal indentation hardness to yield strength. A linear relation is found between the nominal indentation hardness and the logarithm of the ratio of Young's modulus to yield strength, but with a different coefficient than reported in previous studies. The nominal indentation hardness decreases...
Development of Hard Elastic Solids from Glassy Polymers.
1980-06-10
elastic polypropylene (PP) as reported by Park and Noether 5 The stress-strain behavior for three intermittent cycles to 40% extension is shown in Fig. Zb...system. Such viscoelastic effects have been concluded by Park and Noether 1 5 from more extensive stress relaxation investigations of hard elastic PP...Petermann and H. Gleiter, J. Macromol. Sc.- Phys., B12(4), 523 (1976). 4. H. D. Noether , Intern. J. Polymeric Mater.,. 7, 57 (1979). 5. M. E. Mackay
Aida Rodríguez, Sara; Alcalá, Jorge; Martins Souza, Roberto
2011-03-01
Although the Hertz theory is not applicable in the analysis of the indentation of elastic-plastic materials, it is common practice to incorporate the concept of indenter/specimen combined modulus to consider indenter deformation. The appropriateness was assessed of the use of reduced modulus to incorporate the effect of indenter deformation in the analysis of the indentation with spherical indenters. The analysis based on finite element simulations considered four values of the ratio of the indented material elastic modulus to that of the diamond indenter, E/Ei (0, 0.04, 0.19, 0.39), four values of the ratio of the elastic reduced modulus to the initial yield strength, Er/Y (0, 10, 20, 100), and two values of the ratio of the indenter radius to maximum total displacement, R/δmax (3, 10). Indenter deformation effects are better accounted for by the reduced modulus if the indented material behaves entirely elastically. In this case, identical load-displacement (P - δ) curves are obtained with rigid and elastic spherical indenters for the same elastic reduced modulus. Changes in the ratio E/Ei , from 0 to 0.39, resulted in variations lower than 5% for the load dimensionless functions, lower than 3% in the contact area, Ac , and lower than 5% in the ratio H/Er . However, deformations of the elastic indenter made the actual radius of contact change, even in the indentation of elastic materials. Even though the load dimensionless functions showed only a little increase with the ratio E/Ei , the hardening coefficient and the yield strength could be slightly overestimated when algorithms based on rigid indenters are used. For the unloading curves, the ratio δe/δmax , where δe is the point corresponding to zero load of a straight line with slope S from the point (Pmax, δmax ), varied less than 5% with the ratio E/Ei . Similarly, the relationship between reduced modulus and the unloading indentation curve, expressed by Sneddon's equation, did not reveal the necessity
Energy in elastic fiber embedded in elastic matrix containing incident SH wave
Williams, James H., Jr.; Nagem, Raymond J.
1989-01-01
A single elastic fiber embedded in an infinite elastic matrix is considered. An incident plane SH wave is assumed in the infinite matrix, and an expression is derived for the total energy in the fiber due to the incident SH wave. A nondimensional form of the fiber energy is plotted as a function of the nondimensional wavenumber of the SH wave. It is shown that the fiber energy attains maximum values at specific values of the wavenumber of the incident wave. The results obtained here are interpreted in the context of phenomena observed in acousto-ultrasonic experiments on fiber reinforced composite materials.
Thresiamma Phlip
2005-01-01
Full Text Available The second- and third-order elastic constants of trigonal calcite have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The seven second-order elastic constants and the fourteen non-vanishing third-order elastic constants of trigonal calcite are obtained. The second-order elastic constants C11, which corresponds to the elastic stiffness along the basal plane of the crystal is greater than C33, which corresponds to the elastic stiffness tensor component along the c-axis of the crystal. First order pressure derivatives of the second-order elastic constants of calcite are evaluated. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in calcite. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.
Maximum Likelihood Associative Memories
Gripon, Vincent; Rabbat, Michael
2013-01-01
Associative memories are structures that store data in such a way that it can later be retrieved given only a part of its content -- a sort-of error/erasure-resilience property. They are used in applications ranging from caches and memory management in CPUs to database engines. In this work we study associative memories built on the maximum likelihood principle. We derive minimum residual error rates when the data stored comes from a uniform binary source. Second, we determine the minimum amo...
Maximum likely scale estimation
Loog, Marco; Pedersen, Kim Steenstrup; Markussen, Bo
2005-01-01
A maximum likelihood local scale estimation principle is presented. An actual implementation of the estimation principle uses second order moments of multiple measurements at a fixed location in the image. These measurements consist of Gaussian derivatives possibly taken at several scales and....../or having different derivative orders. Although the principle is applicable to a wide variety of image models, the main focus here is on the Brownian model and its use for scale selection in natural images. Furthermore, in the examples provided, the simplifying assumption is made that the behavior...... of the measurements is completely characterized by all moments up to second order....
Elastic anisotropy of crystals
Christopher M. Kube
2016-09-01
Full Text Available An anisotropy index seeks to quantify how directionally dependent the properties of a system are. In this article, the focus is on quantifying the elastic anisotropy of crystalline materials. Previous elastic anisotropy indices are reviewed and their shortcomings discussed. A new scalar log-Euclidean anisotropy measure AL is proposed, which overcomes these deficiencies. It is based on a distance measure in a log-Euclidean space applied to fourth-rank elastic tensors. AL is an absolute measure of anisotropy where the limiting case of perfect isotropy yields zero. It is a universal measure of anisotropy applicable to all crystalline materials. Specific examples of strong anisotropy are highlighted. A supplementary material provides an anisotropy table giving the values of AL for 2,176 crystallite compounds.
Peselnick, L.; Robie, R.A.
1962-01-01
The recent measurements of the elastic constants of calcite by Reddy and Subrahmanyam (1960) disagree with the values obtained independently by Voigt (1910) and Bhimasenachar (1945). The present authors, using an ultrasonic pulse technique at 3 Mc and 25??C, determined the elastic constants of calcite using the exact equations governing the wave velocities in the single crystal. The results are C11=13.7, C33=8.11, C44=3.50, C12=4.82, C13=5.68, and C14=-2.00, in units of 1011 dyncm2. Independent checks of several of the elastic constants were made employing other directions and polarizations of the wave velocities. With the exception of C13, these values substantially agree with the data of Voigt and Bhimasenachar. ?? 1962 The American Institute of Physics.
Dremin, I M
2012-01-01
When colliding, the high energy hadrons can either produce new particles or scatter elastically without change of their quantum num- bers and other particles produced. Namely elastic scattering of hadrons is considered in this review paper. Even though the inelastic processes dominate at high energies, the elastic scattering constitutes the notice- able part of the total cross section ranging between 18 and 25% with some increase at higher energies. The scattering proceeds mostly at small angles and reveals peculiar dependences at larger angles disclos- ing the geometrical structure of the colliding particles and di?erent dynamical mechanisms. The fast decreasing Gaussian peak at small angles is followed by the exponential (Orear) regime with some shoul- ders and dips and then by the power-like decrease. Results of various theoretical approaches are compared with exper- imental data. Phenomenological models pretending to describe this process are reviewed. The unitarity condition requires the exponen- tial re...
Nematic order by elastic interactions and cellular rigidity sensing
Friedrich, B. M.; Safran, S. A.
2011-01-01
We predict spontaneous nematic order in an ensemble of active force generators with elastic interactions as a minimal model for early nematic alignment of short stress fibers in non-motile, adhered cells. Mean-field theory is formally equivalent to Maier-Saupe theory for a nematic liquid. However, the elastic interactions are long-ranged (and thus depend on cell shape and matrix elasticity) and originate in cell activity. Depending on the density of force generators, we find two regimes of cellular rigidity sensing for which orientational, nematic order of stress fibers depends on matrix rigidity either in a step-like manner or with a maximum at an optimal rigidity.
Hwu, Chyanbin
2010-01-01
As structural elements, anisotropic elastic plates find wide applications in modern technology. The plates here are considered to be subjected to not only in plane load but also transverse load. In other words, both plane and plate bending problems as well as the stretching-bending coupling problems are all explained in this book. In addition to the introduction of the theory of anisotropic elasticity, several important subjects have are discussed in this book such as interfaces, cracks, holes, inclusions, contact problems, piezoelectric materials, thermoelastic problems and boundary element a
Lai, Yun
2011-06-26
Metamaterials can exhibit electromagnetic and elastic characteristics beyond those found in nature. In this work, we present a design of elastic metamaterial that exhibits multiple resonances in its building blocks. Band structure calculations show two negative dispersion bands, of which one supports only compressional waves and thereby blurs the distinction between a fluid and a solid over a finite frequency regime, whereas the other displays super anisotropy-in which compressional waves and shear waves can propagate only along different directions. Such unusual characteristics, well explained by the effective medium theory, have no comparable analogue in conventional solids and may lead to novel applications. © 2011 Macmillan Publishers Limited. All rights reserved.
Mechanics of elastic composites
Cristescu, Nicolaie Dan; Soós, Eugen
2003-01-01
This is a comprehensive, reader-friendly treatment of the theory behind modern elastic composite materials. The treatment includes recently developed results and methods drawn from research papers published in Eastern Europe that until now were unavailable in many western countries. Among the book''s many notable features is the inclusion of more than 400 problems, many of which are solved at the end of the book. Mechanics of Elastic Composites is an outstanding textbook for graduate-level course work and a valuable reference for engineers and researchers. Developed over many years by leading
Rogozinski, Marek
2014-01-01
This book is a detailed, practical, hands-on guide packed with real-life scenarios and examples which will show you how to implement an ElasticSearch search engine on your own websites.If you are a web developer or a user who wants to learn more about ElasticSearch, then this is the book for you. You do not need to know anything about ElastiSeach, Java, or Apache Lucene in order to use this book, though basic knowledge about databases and queries is required.
Effects of Strain Ratio on Fatigue Behavior of G20Mn5QT Cast Steel
韩庆华; 郭琪; 尹越; 邢颖
2016-01-01
Due to traffic and wave actions, cast steel joints are subjected to variable-amplitude fatigue loading, which may cause fatigue problems. The ratio of the minimum strain to the maximum strain(strain ratio)can be em-ployed to analyze the influence of variable-amplitude fatigue both in the elastic and plastic ranges. To evaluate the effect of the strain ratio on G20Mn5QT cast steel, the fatigue tests of smooth specimens were carried out at the strain ratio of 0.1. The cyclic deformation and the relationships between the strain amplitude, the stress amplitude, the Smith, Watson and Topper(SWT)parameter and fatigue life were studied and compared with those at the strain ratio of-1. Compared with other methods, Basquin formula and Solonberg formula provide reliable and appropri-ate ranges ofS-N curve and fatigue limit at different strain ratios respectively. The SWT parameter can be used to predict the fatigue life at other strain ratios accurately.
On elastic moduli and elastic anisotropy in polycrystalline martensitic NiTi
Qiu, S. [Advanced Materials Processing and Analysis Center (AMPAC), Mechanical, Materials and Aerospace Engineering Department, University of Central Florida, Orlando, FL 32816 (United States); Clausen, B. [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Padula, S.A.; Noebe, R.D. [NASA Glenn Research Center, Cleveland, OH 44135 (United States); Vaidyanathan, R., E-mail: raj@mail.ucf.edu [Advanced Materials Processing and Analysis Center (AMPAC), Mechanical, Materials and Aerospace Engineering Department, University of Central Florida, Orlando, FL 32816 (United States)
2011-08-15
A combined experimental and computational effort was undertaken to provide insight into the elastic response of B19' martensitic NiTi variants as they exist in bulk, polycrystalline aggregate form during monotonic tensile and compressive loading. The experimental effort centered on using in situ neutron diffraction during loading to measure elastic moduli in several directions along with an average Young's modulus and a Poisson's ratio. The measurements were compared with predictions from a 30,000 variant, self-consistent polycrystalline deformation model that accounted for the elastic intergranular constraint, and also with predictions of single crystal behavior from previously published ab initio studies. Variant conversion and detwinning processes that influenced the intergranular constraint occurred even at stresses where the macroscopic stress-strain response appeared linear. Direct evidence of these processes was revealed in changes in texture, which were captured in inverse pole figures constructed from the neutron diffraction measurements.
Oestreicher, J H; Frueh, B R
1995-06-01
We built an experimental apparatus to investigate the passive elastic characteristics of orbicularis oculi muscle and examined specimens from normal humans, humans with stable Graves' eye disease, and cynomolgus monkeys. Stress-strain curves were determined and found to be exponential. The elastic modulus (Young's modulus), analogous to the stiffness of the material, was calculated as a function of strain. Elastic modulus as a function of instantaneous stress was linear. Monkey elastic modulus values were determined, but did not allow meaningful interspecies comparison because of the small sample size. No significant difference was found between normal humans and humans with Graves' eye disease with respect to elastic modulus values.
F. TopsÃƒÂ¸e
2001-09-01
Full Text Available Abstract: In its modern formulation, the Maximum Entropy Principle was promoted by E.T. Jaynes, starting in the mid-fifties. The principle dictates that one should look for a distribution, consistent with available information, which maximizes the entropy. However, this principle focuses only on distributions and it appears advantageous to bring information theoretical thinking more prominently into play by also focusing on the "observer" and on coding. This view was brought forward by the second named author in the late seventies and is the view we will follow-up on here. It leads to the consideration of a certain game, the Code Length Game and, via standard game theoretical thinking, to a principle of Game Theoretical Equilibrium. This principle is more basic than the Maximum Entropy Principle in the sense that the search for one type of optimal strategies in the Code Length Game translates directly into the search for distributions with maximum entropy. In the present paper we offer a self-contained and comprehensive treatment of fundamentals of both principles mentioned, based on a study of the Code Length Game. Though new concepts and results are presented, the reading should be instructional and accessible to a rather wide audience, at least if certain mathematical details are left aside at a rst reading. The most frequently studied instance of entropy maximization pertains to the Mean Energy Model which involves a moment constraint related to a given function, here taken to represent "energy". This type of application is very well known from the literature with hundreds of applications pertaining to several different elds and will also here serve as important illustration of the theory. But our approach reaches further, especially regarding the study of continuity properties of the entropy function, and this leads to new results which allow a discussion of models with so-called entropy loss. These results have tempted us to speculate over
Regularized maximum correntropy machine
Wang, Jim Jing-Yan
2015-02-12
In this paper we investigate the usage of regularized correntropy framework for learning of classifiers from noisy labels. The class label predictors learned by minimizing transitional loss functions are sensitive to the noisy and outlying labels of training samples, because the transitional loss functions are equally applied to all the samples. To solve this problem, we propose to learn the class label predictors by maximizing the correntropy between the predicted labels and the true labels of the training samples, under the regularized Maximum Correntropy Criteria (MCC) framework. Moreover, we regularize the predictor parameter to control the complexity of the predictor. The learning problem is formulated by an objective function considering the parameter regularization and MCC simultaneously. By optimizing the objective function alternately, we develop a novel predictor learning algorithm. The experiments on two challenging pattern classification tasks show that it significantly outperforms the machines with transitional loss functions.
bessel functions for axisymmetric elasticity problems of the elastic ...
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ELASTIC HALF SPACE SOIL: A POTENTIAL FUNCTION METHOD. C. C. Ike1 ... OF CIVIL ENGR., ENUGU STATE UNIVERSITY OF SCIENCE AND TECHNOLOGY, ENUGU, ENUGU STATE. ..... Elasticity, Third Edition,McGraw Hill, New York.
Acquired disorders of elastic tissue: Part II. decreased elastic tissue.
Lewis, Kevan G; Bercovitch, Lionel; Dill, Sara W; Robinson-Bostom, Leslie
2004-08-01
Elastic fibers in the extracellular matrix are integral components of dermal connective tissue. The resilience and elasticity required for normal structure and function of the skin are attributable to the network of elastic tissue. Advances in our understanding of elastic tissue physiology provide a foundation for studying the pathogenesis of elastic tissue disorders. Many acquired disorders are nevertheless poorly understood owing to the paucity of reported cases. Several acquired disorders in which loss of dermal elastic tissue produces prominent clinical and histopathologic features have recently been described, including middermal elastolysis, papular elastorrhexis, and pseudoxanthoma-like papillary dermal elastolysis, which must be differentiated from more well-known disorders such as anetoderma, acquired cutis laxa, and acrokeratoelastoidosis. Learning objective At the conclusion of this learning activity, participants should have an understanding of the similarities and differences between acquired disorders of elastic tissue that are characterized by a loss of elastic tissue.
Elastic limit and microplastic response of hardened steels
Zaccone, M.A. (McDonnell Douglas Aerospace Co., St. Louis, MO (United States)); Krauss, G. (Colorado School of Mines, Golden, CO (United States). Dept. of Metallurgical and Materials Engineering)
1993-10-01
Tempered martensite-retained austenite microstructures were produced by direct quenching a series of 41XX medium carbon steels, direct quenching and reheating a series of five 0.8C-Cr-Ni-Mo steels and intercritically austenitizing at various temperatures, and quenching a SAE 52100 steel. All specimens were tempered either at 150 C or at 200 C. Specimens were subjected to compression and tension testing in the microstrain regime to determine the elastic limits and microplastic response of the microstructures. The retained austenite and matrix carbon content of the intercritically austenized specimens were measured by X-ray diffraction and Mossbauer spectroscopy. The elastic limit of the microstructures decreases with increasing amounts of retained austenite. Refining of the austenite distribution increases the elastic limit. Low elastic limits are mainly due to low flow stresses in the austenite and not internal stresses. The elastic limit correlates with the largest austenite free-mean path by a Hall-Petch type equation. The elastic limit increases with decreasing intercritical austenitizing temperature in the SAE 52100 due to a lower carbon content in the matrix reducing the retained austenite levels and retained carbides that refine grain size and, therefore, the austenite distribution in quenched specimens. In the microplastic region, the strain is accommodated by successively smaller austenite regions until the flow strength matches that of the martensite. Reheating and quenching refines the microstructure and renders the austenite unstable in the microplastic regime, causing transformation of the austenite to martensite by a strain-induced mechanism. The transformation of austenite to martensite occurs by a stress-assisted mechanism in medium carbon steels. The low elastic limits in medium carbon steels were due to the inability of the strain from the stress-assisted transformation to balance the plastic strain accumulated in the austenite.
A Membrane Model from Implicit Elasticity Theory
Freed, A. D.; Liao, J.; Einstein, D. R.
2014-01-01
A Fungean solid is derived for membranous materials as a body defined by isotropic response functions whose mathematical structure is that of a Hookean solid where the elastic constants are replaced by functions of state derived from an implicit, thermodynamic, internal-energy function. The theory utilizes Biot’s (1939) definitions for stress and strain that, in 1-dimension, are the stress/strain measures adopted by Fung (1967) when he postulated what is now known as Fung’s law. Our Fungean membrane model is parameterized against a biaxial data set acquired from a porcine pleural membrane subjected to three, sequential, proportional, planar extensions. These data support an isotropic/deviatoric split in the stress and strain-rate hypothesized by our theory. These data also demonstrate that the material response is highly non-linear but, otherwise, mechanically isotropic. These data are described reasonably well by our otherwise simple, four-parameter, material model. PMID:24282079
Yildirim, Ali; Kosger, Pelin; Ozdemir, Gokmen; Sahin, Fezan Mutlu; Ucar, Birsen; Kilic, Zubeyir
2015-09-01
A significant correlation between hypertension history and high blood pressure has been observed with regard to age, race and gender. Investigating carotid intima-media thickness and aortic stiffness prior to the development of hypertension in children of hypertensive parents enabled us to evaluate these patients for subclinical atherosclerosis. We compared carotid intima-media thickness, aortic strain, distensibility, stiffness indices and elastic modulus in 67 normotensive children whose parents had a diagnosis of essential hypertension and 39 normotensive children with no parental history of hypertension. Although there were no significant differences between the two groups in terms of systolic blood pressure, diastolic blood pressure, average blood pressure and pulse pressure (P>0.05), systolic blood pressures were higher among patients 15 years and older in the study group. No significant differences were noted between the control and study groups regarding interventricular septal thickness, left-ventricular posterior wall thickness, left-ventricular systolic and diastolic diameter and aortic annulus diameter (P>0.05). The left atrium diameter was larger in the study group compared with that in the control group, mainly because of the values of the 15-year-old and older children (P=0.01). The mean, maximum and minimum values of carotid intima-media thickness were significantly different in the study group compared with the control group among all age groups (Pchildren of hypertensive parents compared with the control group (P=0.014, P=0.001, respectively). Although there were no differences between the study and control groups regarding aortic strain, aortic distensibility, elastic modulus and stiffness indices (P>0.05), aortic distensibility was lower, and aortic stiffness indices were higher among children 15 years and older in the study group. An increase in the carotid intima-media thickness in all age groups and a decrease in aortic elastic properties in
Mechanical analysis of single myocyte contraction in a 3-D elastic matrix.
John Shaw
Full Text Available BACKGROUND: Cardiac myocytes experience mechanical stress during each heartbeat. Excessive mechanical stresses under pathological conditions cause functional and structural remodeling that lead to heart diseases, yet the precise mechanisms are still incompletely understood. To study the cellular and molecular level mechanotransduction mechanisms, we developed a new 'cell-in-gel' experimental system to exert multiaxial (3-D stresses on a single myocyte during active contraction. METHODS: Isolated myocytes are embedded in an elastic hydrogel to simulate the mechanical environment in myocardium (afterload. When electrically stimulated, the in-gel myocyte contracts while the matrix resists shortening and broadening of the cell, exerting normal and shear stresses on the cell. Here we provide a mechanical analysis, based on the Eshelby inclusion problem, of the 3-D strain and stress inside and outside the single myocyte during contraction in an elastic matrix. RESULTS: (1 The fractional shortening of the myocyte depends on the cell's geometric dimensions and the relative stiffness of the cell to the gel. A slender or softer cell has less fractional shortening. A myocyte of typical dimensions embedded in a gel of similar elastic stiffness can contract only 20% of its load-free value. (2 The longitudinal stress inside the cell is about 15 times the transverse stress level. (3 The traction on the cell surface is highly non-uniform, with a maximum near its ends, showing 'hot spots' at the location of intercalated disks. (4 The mechanical energy expenditure of the myocyte increases with the matrix stiffness in a monotonic and nonlinear manner. CONCLUSION: Our mechanical analyses provide analytic solutions that readily lend themselves to parametric studies. The resulting 3-D mapping of the strain and stress states serve to analyze and interpret ongoing cell-in-gel experiments, and the mathematical model provides an essential tool to decipher and quantify
Elastic anisotropy and low-temperature thermal expansion in the shape memory alloy Cu-Al-Zn.
Kuruvilla, Santhosh Potharay; Menon, C S
2008-04-01
Cu-based shape memory alloys are known for their technologically important pseudo-elastic and shapememory properties, which are intimately associated with the martensitic transformation. A combination of deformation theory and finite-strain elasticity theory has been employed to arrive at the expressions for higher order elastic constants of Cu-Al-Zn based on Keating's approach. The second- and third-order elastic constants are in good agreement with the measurements. The aggregate elastic properties like bulk modulus, pressure derivatives, mode Grüneisen parameters of the elastic waves, low temperature limit of thermal expansion, and the Anderson-Grüneisen parameter are also presented.
A Investigation of the Elastic and Dielectric Anisotropy of Paper.
Fleischman, Elmer Henry, Jr.
This investigation was undertaken to learn more about the way in which fiber orientation and drying restraint affect the elastic and dielectric properties in all three principal directions of paper. It was found that both variables affect the in -plane elastic anisotropy by similar magnitudes. What was surprising, however, was that wet straining has the greatest effect in the z-direction. The z-direction stiffness was reduced 50% as a result of only a moderate 2.4% wet strain in the plane of the sheet. On the other hand, the dielectric anisotropy was affected very little by wet straining. In fact, the dielectric results could be explained in terms of mixture theories. The anisotropy in the dielectric constant when measured at microwave frequencies could largely be explained as being the result of fiber orientation alone without having to assume that the fiber has an anisotropic dielectric constant. From comparison of the elastic and dielectric results, it may be concluded that the mechanism by which wet straining enhances the elastic anisotropy does not involve a large fiber orientation in the direction of wet straining. From a practical standpoint, one could use the dielectric anisotropy measured at microwave frequencies as a measure of the fiber orientation distribution in the sheet. On the basis of the results presented here, this measurement should be quite insensitive to any stresses imposed on the sheet as it dries.
Dynamic Acousto-Elasticity: Pressure and Frequency Dependences in Berea Sandstone.
Riviere, J. V.; Pimienta, L.; Latour, S.; Fortin, J.; Schubnel, A.; Johnson, P. A.
2014-12-01
Nonlinear elasticity is studied at the laboratory scale with the goal of understanding observations at earth scales, for instance during strong ground motion, tidal forcing and earthquake slip processes. Here we report frequency and pressure dependences on elasticity when applying dynamic acousto-elasticity (DAE) of rock samples, analogous to quasi-static acousto-elasticity. DAE allows one to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. We perform DAE on a sample of Berea sandstone subject to 0.5MPa uniaxial load, with sinusoidal oscillating strain amplitudes ranging from 10-6 to 10-5 and at frequencies from 0.1 to 260Hz. In addition, the confining pressure is increased stepwise from 0 to 30MPa. We compare results to previous measurements made at lower (mHz) and higher (kHz) frequencies. Nonlinear elastic parameters corresponding to conditioning effects, third order elastic constants and fourth order elastic constants are quantitatively compared over the pressure and frequency ranges. We observe that the decrease in modulus due to conditioning increases with frequency, suggesting a frequency and/or strain-rate dependence that should be included in nonlinear elastic models of rocks. In agreement with previous measurements, nonlinear elastic effects also decrease with confining pressure, suggesting that nonlinear elastic sources such as micro-cracks, soft bonds and dislocations are turned off as the pressure increases.
A comparison between different finite elements for elastic and aero-elastic analyses.
Mahran, Mohamed; ELsabbagh, Adel; Negm, Hani
2017-11-01
In the present paper, a comparison between five different shell finite elements, including the Linear Triangular Element, Linear Quadrilateral Element, Linear Quadrilateral Element based on deformation modes, 8-node Quadrilateral Element, and 9-Node Quadrilateral Element was presented. The shape functions and the element equations related to each element were presented through a detailed mathematical formulation. Additionally, the Jacobian matrix for the second order derivatives was simplified and used to derive each element's strain-displacement matrix in bending. The elements were compared using carefully selected elastic and aero-elastic bench mark problems, regarding the number of elements needed to reach convergence, the resulting accuracy, and the needed computation time. The best suitable element for elastic free vibration analysis was found to be the Linear Quadrilateral Element with deformation-based shape functions, whereas the most suitable element for stress analysis was the 8-Node Quadrilateral Element, and the most suitable element for aero-elastic analysis was the 9-Node Quadrilateral Element. Although the linear triangular element was the last choice for modal and stress analyses, it establishes more accurate results in aero-elastic analyses, however, with much longer computation time. Additionally, the nine-node quadrilateral element was found to be the best choice for laminated composite plates analysis.
Non-linear elastic deformations
Ogden, R W
1997-01-01
Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.
EFFECTIVE STRESS AND STRAIN IN FINITE DEFORMATION
周喆; 秦伶俐; 黄文彬; 王红卫
2004-01-01
Whether the concept of effective stress and strain in elastic-plastic theory is still valid under the condition of finite deformation was mainly discussed. The uni-axial compression experiments in plane stress and plane strain states were chosen for study. In the two kinds of stress states, the stress- strain curve described by logarithm strain and rotated Kirchhoff stress matches the experiments data better than the curves defined by other stressstrain description.
Bulk solitary waves in elastic solids
Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.
2015-10-01
A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the
Equalized near maximum likelihood detector
2012-01-01
This paper presents new detector that is used to mitigate intersymbol interference introduced by bandlimited channels. This detector is named equalized near maximum likelihood detector which combines nonlinear equalizer and near maximum likelihood detector. Simulation results show that the performance of equalized near maximum likelihood detector is better than the performance of nonlinear equalizer but worse than near maximum likelihood detector.
Cheeseman, Peter; Stutz, John
2005-01-01
A long standing mystery in using Maximum Entropy (MaxEnt) is how to deal with constraints whose values are uncertain. This situation arises when constraint values are estimated from data, because of finite sample sizes. One approach to this problem, advocated by E.T. Jaynes [1], is to ignore this uncertainty, and treat the empirically observed values as exact. We refer to this as the classic MaxEnt approach. Classic MaxEnt gives point probabilities (subject to the given constraints), rather than probability densities. We develop an alternative approach that assumes that the uncertain constraint values are represented by a probability density {e.g: a Gaussian), and this uncertainty yields a MaxEnt posterior probability density. That is, the classic MaxEnt point probabilities are regarded as a multidimensional function of the given constraint values, and uncertainty on these values is transmitted through the MaxEnt function to give uncertainty over the MaXEnt probabilities. We illustrate this approach by explicitly calculating the generalized MaxEnt density for a simple but common case, then show how this can be extended numerically to the general case. This paper expands the generalized MaxEnt concept introduced in a previous paper [3].
Mathematical methods in elasticity imaging
Ammari, Habib; Garnier, Josselin; Wahab, Abdul
2015-01-01
This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertai
Hmiel, A.; Winey, J. M.; Gupta, Y. M.; Desjarlais, M. P.
2016-05-01
Accurate theoretical calculations of the nonlinear elastic response of strong solids (e.g., diamond) constitute a fundamental and important scientific need for understanding the response of such materials and for exploring the potential synthesis and design of novel solids. However, without corresponding experimental data, it is difficult to select between predictions from different theoretical methods. Recently the complete set of third-order elastic constants (TOECs) for diamond was determined experimentally, and the validity of various theoretical approaches to calculate the same may now be assessed. We report on the use of density functional theory (DFT) methods to calculate the six third-order elastic constants of diamond. Two different approaches based on homogeneous deformations were used: (1) an energy-strain fitting approach using a prescribed set of deformations, and (2) a longitudinal stress-strain fitting approach using uniaxial compressive strains along the [100], [110], and [111] directions, together with calculated pressure derivatives of the second-order elastic constants. The latter approach provides a direct comparison to the experimental results. The TOECs calculated using the energy-strain approach differ significantly from the measured TOECs. In contrast, calculations using the longitudinal stress-uniaxial strain approach show good agreement with the measured TOECs and match the experimental values significantly better than the TOECs reported in previous theoretical studies. Our results on diamond have demonstrated that, with proper analysis procedures, first-principles calculations can indeed be used to accurately calculate the TOECs of strong solids.
DYNAMICAL FORMATION OF CAVITY IN A COMPOSED HYPER-ELASTIC SPHERE
任九生; 程昌钧
2004-01-01
The dynamical formation of cavity in a hyper-elastic sphere composed of two materials with the incompressible strain energy function, subjected to a suddenly applied uniform radial tensile boundary dead-load, was studied following the theory of finite deformation dynamics. Besides a trivial solution corresponding to the homogeneous static state, a cavity forms at the center of the sphere when the tensile load is larger than its critical value. An exact differential relation between the cavity radius and the tensile land was obtained. It is proved that the evolution of cavity radius with time displays nonlinear periodic oscillations. The phase diagram for oscillation, the maximum amplitude, the approximate period and the critical load were all discussed.
Farris, Dominic James; Trewartha, Grant; McGuigan, M Polly; Lichtwark, Glen A
2013-02-15
The human Achilles tendon (AT) has often been considered to act as a single elastic structure in series with the muscles of the triceps surae. As such it has been commonly modelled as a Hookean spring of uniform stiffness. However, the free AT and the proximal AT have distinctly different structures that lend themselves to different elastic properties. This study aimed to use three-dimensional freehand ultrasound imaging to determine whether the proximal AT and the free AT exhibit different elastic behaviour during sub-maximal, fixed-end contractions of the triceps surae. Six male and five female participants (mean ± s.d. age=27 ± 5 years) performed fixed position contractions of the plantar-flexors on an isokinetic dynamometer at 50% of their maximum voluntary contraction in this position. Freehand three-dimensional ultrasound imaging was used to reconstruct the free-tendon and proximal AT at rest and during contraction. The free-tendon exhibited significantly (P=0.03) greater longitudinal strain (5.2 ± 1.7%) than the proximal AT (2.6 ± 2.0%). The lesser longitudinal strain of the proximal AT was linked to the fact that it exhibited considerable transverse (orthogonal to the longitudinal direction) strains (5.0 ± 4%). The transverse strain of the proximal AT is likely due to the triceps surae muscles bulging upon contraction, and thus the level of bulging may influence the elastic behaviour of the proximal AT. This might have implications for the understanding of triceps surae muscle-tendon interaction during locomotion, tendon injury mechanics and previous measurements of AT elastic properties.
Approximation by planar elastic curves
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2016-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....
Elastic-plastic finite element simulation for diamond turning process
无
2006-01-01
Using general commercial software, a coupled thermo-mechanieal plane strain larger deformation orthogonal cutting model is developed on the basis of updated Lagrangian formulation in this paper. The workpiece is oxygen free high conductivity copper ( OFHC copper), its flow stress is considered as a function of strain, strain rate and temperature to reflect its realistic changes in physical properties. In order to take into account the cutting edge radius effects of the single crystal diamond tool, rezoning technology is introduced into this simulation model. Diamond turning process is simulated from the initial stage to the steady stage of chip formation, and the distribution of temperature, equivalent stress, residual stress, strain rate and shear angle are obtained. The simulated principal force is compared with published experiment data and they are found to be in good agreement with each other, but poor for thrust force due to no consideration of elastic recovery for machined surface in the elastic-plastic material model.
Modeling of the wave transmission properties of large arteries using nonlinear elastic tubes.
Pythoud, F; Stergiopulos, N; Meister, J J
1994-11-01
We propose a new, simple way of constructing elastic tubes which can be used to model the nonlinear elastic properties of large arteries. The tube models are constructed from a silicon elastomer (Sylgard 184, Dow Corning), which exhibits a nonlinear behavior with increased stiffness at high strains. Tests conducted on different tube models showed that, with the proper choice of geometric parameters, the elastic properties, in terms of area-pressure relation and compliance, can be similar to that of real arteries.
K.R. Arpin; T.F. Trimble
2003-04-01
This testing was undertaken to develop material true stress-true strain curves for elastic-plastic material behavior for use in performing transient analysis. Based on the conclusions of this test, the true stress-true strain curves derived herein are valid for use in elastic-plastic finite element analysis for structures fabricated from these materials. In addition, for the materials tested herein, the ultimate strain values are greater than those values cited as the limits for the elastic-plastic strain acceptance criteria for transient analysis.
Yong, Ee Hou; Nelson, David R; Mahadevan, L
2013-10-25
On microscopic scales, the crystallinity of flexible tethered or cross-linked membranes determines their mechanical response. We show that by controlling the type, number, and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic shell analogs of the classical platonic solids. These morphologies arise via a sharp buckling transition from the sphere which is strongly hysteretic in loading or unloading. We construct a minimal Landau theory for the transition using quadratic and cubic invariants of the spherical harmonic modes. Our approach suggests methods to engineer shape into soft spherical shells using a frozen defect topology.
Williamson, Matthew M.
1995-01-01
This thesis presents the design, construction, control and evaluation of a novel for controlled actuator. Traditional force controlled actuators are designed from the premise that 'Stiffer is better'. This approach gives a high bandwidth system, prone to problems of contact instability, noise, and low power density. The actuator presented in this thesis is designed from the premise that 'Stiffness isn't everything'. The actuator, which incorporates a series elastic element, trades off achievable bandwidth for gains in stable, low noise force control, and protection against shock loads. This thesis reviews related work in robot force control, presents theoretical descriptions of the control and expected performance from a series elastic actuator, and describes the design of a test actuator constructed to gather performance data. Finally the performance of the system is evaluated by comparing the performance data to theoretical predictions.
Introduction to linear elasticity
Gould, Phillip L
2013-01-01
Introduction to Linear Elasticity, 3rd Edition, provides an applications-oriented grounding in the tensor-based theory of elasticity for students in mechanical, civil, aeronautical, and biomedical engineering, as well as materials and earth science. The book is distinct from the traditional text aimed at graduate students in solid mechanics by introducing the subject at a level appropriate for advanced undergraduate and beginning graduate students. The author's presentation allows students to apply the basic notions of stress analysis and move on to advanced work in continuum mechanics, plasticity, plate and shell theory, composite materials, viscoelasticity and finite method analysis. This book also: Emphasizes tensor-based approach while still distilling down to explicit notation Provides introduction to theory of plates, theory of shells, wave propagation, viscoelasticity and plasticity accessible to advanced undergraduate students Appropriate for courses following emerging trend of teaching solid mechan...
Behavior of steel fiber-reinforced high-strength concrete at medium strain rate
Chujie JIAO; Wei SUN; Shi HUAN; Guoping JIANG
2009-01-01
Impact compression experiments for the steel fiber-reinforced high-strength concrete (SFRHSC) at medium strain rate were conducted using the split Hopkinson press bar (SHPB) testing method. The volume fractions of steel fibers of SFRHSC were between 0 and 3%. The experimental results showed that, when the strain rate increased from threshold value to 90 s-1, the maximum stress of SFRHSC increased about 30%, the elastic modulus of SFRHSC increased about 50%, and the increase in the peak strain of SFRHSC was 2-3 times of that in the matrix specimen. The strength and toughness of the matrix were improved remarkably because of the superposition effect of the aggregate high-strength matrix and steel fiber high-strength matrix. As a result, under impact loading, cracks developed in the SFRHSC specimen, but the overall shape of the specimen remained virtually unchanged. However, under similar impact loading, the matrix specimens were almost broken into small pieces.
Maximum Profit Configurations of Commercial Engines
Yiran Chen
2011-06-01
Full Text Available An investigation of commercial engines with finite capacity low- and high-price economic subsystems and a generalized commodity transfer law [n ∝ Δ (P m] in commodity flow processes, in which effects of the price elasticities of supply and demand are introduced, is presented in this paper. Optimal cycle configurations of commercial engines for maximum profit are obtained by applying optimal control theory. In some special cases, the eventual state—market equilibrium—is solely determined by the initial conditions and the inherent characteristics of two subsystems; while the different ways of transfer affect the model in respects of the specific forms of the paths of prices and the instantaneous commodity flow, i.e., the optimal configuration.
Dremin, I. M.
2013-01-01
Colliding high-energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced. We consider the latter case here. Although inelastic processes dominate at high energies, elastic scattering contributes considerably (18-25%) to the total cross section. Its share first decreases and then increases at higher energies. Small-angle scattering prevails at all energies. Some characteristic features can be seen that provide information on the geometrical structure of the colliding particles and the relevant dynamical mechanisms. The steep Gaussian peak at small angles is followed by the exponential (Orear) regime with some shoulders and dips, and then by a power-law decrease. Results from various theoretical approaches are compared with experimental data. Phenomenological models claiming to describe this process are reviewed. The unitarity condition predicts an exponential fall for the differential cross section with an additional substructure to occur exactly between the low momentum transfer diffraction cone and a power-law, hard parton scattering regime under high momentum transfer. Data on the interference of the Coulomb and nuclear parts of amplitudes at extremely small angles provide the value of the real part of the forward scattering amplitude. The real part of the elastic scattering amplitude and the contribution of inelastic processes to the imaginary part of this amplitude (the so-called overlap function) are also discussed. Problems related to the scaling behavior of the differential cross section are considered. The power-law regime at highest momentum transfer is briefly described.
Three-dimensional treatment of nonequilibrium dynamics and higher order elasticity
Lott, Martin; Payan, Cédric; Garnier, Vincent; Vu, Quang A.; Eiras, Jesús N.; Remillieux, Marcel C.; Le Bas, Pierre-Yves; Ulrich, T. J.
2016-04-01
This letter presents a three-dimensional model to describe the complex behavior of nonlinear mesoscopic elastic materials such as rocks and concrete. Assuming isotropy and geometric contraction of principal stress axes under dynamic loading, the expression of elastic wave velocity is derived, based on the second-order elastic constants ( λ , μ ) , third-order elastic constants (l, m, n), and a parameter α of nonclassical nonlinear elasticity resulting from conditioning. We demonstrate that both softening and recovering of the elastic properties under dynamic loading is an isotropic effect related to the strain tensor. The measurement of the conditioning is achieved using three polarized waves. The model allows the evaluation of the third-order elastic constants uncoupled from conditioning and viscoelastic effects. The values obtained are similar to those reported in the literature using quasi-static loading.
Size-Dependent Elastic Modulus and Vibration Frequency of Nanocrystals
Lihong Liang
2011-01-01
Full Text Available The elastic properties and the vibration characterization are important for the stability of materials and devices, especially for nanomaterials with potential and broad application. Nanomaterials show different properties from the corresponding bulk materials; the valid theoretical model about the size effect of the elastic modulus and the vibration frequency is significant to guide the application of nanomaterials. In this paper, a unified analytical model about the size-dependent elastic modulus and vibration frequency of nanocrystalline metals, ceramics and semiconductors is established based on the inherent lattice strain and the binding energy change of nanocrystals compared with the bulk crystals, and the intrinsic correlation between the elasticity and the vibration properties is discussed. The theoretical predictions for Cu, Ag, Si thin films, nanoparticles, and TiO2 nanoparticles agree with the experimental results, the computational simulations, and the other theoretical models.
Elastic response of filamentous networks with compliant crosslinks.
Sharma, A; Sheinman, M; Heidemann, K M; MacKintosh, F C
2013-11-01
Experiments have shown that elasticity of disordered filamentous networks with compliant crosslinks is very different from networks with rigid crosslinks. Here, we model and analyze filamentous networks as a collection of randomly oriented rigid filaments connected to each other by flexible crosslinks that are modeled as wormlike chains. For relatively large extensions we allow for enthalpic stretching of crosslink backbones. We show that for sufficiently high crosslink density, the network linear elastic response is affine on the scale of the filaments' length. The nonlinear regime can become highly nonaffine and is characterized by a divergence of the elastic modulus at finite strain. In contrast to the prior predictions, we do not find an asymptotic regime in which the differential elastic modulus scales linearly with the stress, although an approximate linear dependence can be seen in a transition from entropic to enthalpic regimes. We discuss our results in light of recent experiments.
Elastic response of filamentous networks with compliant crosslinks
Sharma, A; Heidemann, K M; MacKintosh, F C
2013-01-01
Experiments have shown that elasticity of disordered filamentous networks with compliant crosslinks is very different from networks with rigid crosslinks. Here, we model and analyze filamentous networks as a collection of randomly oriented rigid filaments connected to each other by flexible crosslinks that are modeled as worm-like chains. For relatively large extensions we allow for enthalpic stretching of crosslinks' backbones. We show that for sufficiently high crosslink density, the network linear elastic response is affine on the scale of the filaments' length. The nonlinear regime can become highly nonaffine and is characterized by a divergence of the elastic modulus at finite strain. In contrast to the prior predictions, we do not find an asymptotic regime in which the differential elastic modulus scales linearly with the stress, although an approximate linear dependence can be seen in a transition from entropic to enthalpic regimes. We discuss our results in light of the recent experiments.
Rheology elasticity determined by deformation of stretchable molecular trains
肖建华
2008-01-01
The average stretching direction,local rotation angular,and stretching ratio parameters of molecular trains were used to express the rheology deformation.Based on this micro geometrical deformation,the macro deformation of medium was expressed.Then,using intrinsic elasticity concept,the stress-strain relation was obtained.In this theoretic formulation,the response functions of extension ratio and rotation angular were used to express the rheology feature of medium.For medium composed by incompressible molecular trains,the local rotation angular divides rheology deformation into three kinds:viscoelastic deformation or elasticity enhancement,viscoplastic deformation or elasticity degenerate and constant elasticity range.These results explain the experimental features of rheology deformation well.
Model-Based Reconstructive Elasticity Imaging Using Ultrasound
Salavat R. Aglyamov
2007-01-01
Full Text Available Elasticity imaging is a reconstructive imaging technique where tissue motion in response to mechanical excitation is measured using modern imaging systems, and the estimated displacements are then used to reconstruct the spatial distribution of Young's modulus. Here we present an ultrasound elasticity imaging method that utilizes the model-based technique for Young's modulus reconstruction. Based on the geometry of the imaged object, only one axial component of the strain tensor is used. The numerical implementation of the method is highly efficient because the reconstruction is based on an analytic solution of the forward elastic problem. The model-based approach is illustrated using two potential clinical applications: differentiation of liver hemangioma and staging of deep venous thrombosis. Overall, these studies demonstrate that model-based reconstructive elasticity imaging can be used in applications where the geometry of the object and the surrounding tissue is somewhat known and certain assumptions about the pathology can be made.
Spinodal surface instability of soft elastic thin films
Huang, Shi Qing; Feng, Xi Qiao
2008-06-01
When the thicknesses of thin films reduce to microns or even nanometers, surface energy and surface interaction often play a significant role in their deformation behavior and surface morphology. The spinodal surface instability induced by the van der Waals force in a soft elastic thin film perfectly bonded to a rigid substrate is investigated theoretically using the bifurcation theory of elastic structures. The analytical solution is derived for the critical condition of spinodal surface morphology instability by accounting for the competition of the van der Waals interaction energy, elastic strain energy and surface energy. Detailed examinations on the effect of surface energy, thickness and elastic properties of the film show that the characteristic wavelength of the deformation bifurcation mode depends on the film thickness via an exponential relation, with the power index in the range from 0.749 to 1.0. The theoretical solution has a good agreement with relevant experiment results.
Spinodal surface instability of soft elastic thin films
Shi Qing Huang; Xi Qiao Feng
2008-01-01
When the thicknesses of thin films reduce to microns or even nanometers, surface energy and surface interaction often play a significant role in their deformation behavior and surface morphology. The spinodal surface instability induced by the van der Waals force in a soft elastic thin film perfectly bonded to a rigid substrate is investigated theoretically using the bifurcation theory of elastic structures. The analytical solution is derived for the critical condition of spinodal surface morphology instability by accounting for the competition of the van der Waals interaction energy, elastic strain energy and surface energy. Detailed examinations on the effect of surface energy, thickness and elastic propeties of the film show that the characteristic wavelength of the deformation bifurcation mode depends on the film thickness via an exponential relation, with the power index in the range from 0.749 to 1.0. The theoretical solution has a good agreement with relevant experiment results.
Density functional calculations of elastic properties of portlandite, Ca(OH)(2)
Laugesen, Jakob Lund
2005-01-01
The elastic constants of portlandite, Ca(OH)(2), are calculated by use of density functional theory. A lattice optimization of an infinite (periodic boundary conditions) lattice is performed on which strains are applied. The elastic constants are extracted by minimizing Hooke's law of linear...
Effective elastic moduli and interface effects of nano- crystalline materials
无
2002-01-01
Many properties of nanocrystalline materials are associated with interface effects. Based on their microstructural features, the influence of interfaces on the effective elastic property of nanocrystalline materials is investigated. First, the Mori-Tanaka method is employed to determine the overall effective elastic moduli by considering a nanocrystalline material as a binary composite solid consisting of a crystal or inclusion phase with regular lattice connected by an amorphous-like interface or matrix phase. The effects of strain gradients are then examined on the effective elastic property by using the strain gradient theory to analyze a representative unit cell. Two interface mechanisms are elucidated that influence the effective stiffness and other mechanical properties of materials. One is the softening effect due to the distorted atomic structures and the increased atomic spacings in interface regions, and the other is the baffling effect due to the existence of boundary layers near interfaces.
GENERAL EXPRESSIONS OF CONSTITUTIVE EQUATIONS FOR ISOTROPIC ELASTIC DAMAGED MATERIALS
唐雪松; 蒋持平; 郑健龙
2001-01-01
The general expressions of constitutive equations for isotropic elastic damaged materials were derived directly from the basic law of irreversible thermodynamics. The limitations of the classical damage constitutive equation based on the well-known strain equivalence hypothesis were overcome. The relationships between the two elastic isotropic damage models(i. e. single and double scalar damage models)were revealed. When a single scalar damage variable defined according to the microscopic geometry of a damaged material is used to describle the isotropic damage state, the constitutive equations contain two "damage effect functions", which describe the different influences of damage on the two independent elastic constants. The classical damage constitutive equation based on the strain equivalence hypothesis is only the first-order approximation of the general expression.It may be unduly simplified and may fail to describe satisfactorily the damage phenomena of practical materials.
李秀云; 邹春鹏; 姜淑英; 何慧疗; 寇红菊; 张其敏; 赵雅萍
2014-01-01
目的 应用超声二维应变成像检测2型糖尿病患者颈动脉整体圆周应变(CS)、应变率(CSr)和硬度参数(β),探讨其评价颈动脉弹性的临床应用价值.方法 选择2型糖尿病患者60例为病例组,并分为颈动脉内中膜厚度(CIMT)增厚组(34例,1.0 mm＜CIMT≤1.2 mm)和斑块组(26例,CIMT＞ 1.2mm),33例正常人为对照组.在颈总动脉二维短轴图像测量收缩期峰值CS和CSr,根据超声二维应变计算动脉硬度参数β,并将β和CS分别与CIMT进行相关性分析.结果 CIMT增厚组与斑块组CS和CSr均低于对照组(P＜0.01),斑块组CS和CSr低于CIMT增厚组(P＜0.05);CIMT增厚组与斑块组β高于对照组(P＜0.01);斑块组β高于CIMT增厚组(P＜0.01);CS与CIMT显著相关(r =-0.79,P＜0.01),β与CIMT显著相关(r=0.72,P＜0.01).结论 超声二维应变成像能更早地检测出2型糖尿病患者颈动脉受累的信息,2型糖尿病患者颈动脉的变形程度随CIMT增厚而减低,硬度随CIMT增厚而增大.%Objective Three parameters include circumferential strain (CS),circumferential strain rate (CSr) and stiffness parameter (β) were measured to evaluate the elasticity of carotid artery using two-dimensional(2D) strain imaging and evaluate its clinical value in patients with type 2 diabetes mellitus (T2DM).Methods 60 patients with T2DM were collected and divided into carotid intima-midia thickness (CIMT) thickeness group(34 cases,1.0 mm＜CIMT≤1.2 mm) and plaque group(26 case,CIMT＞ 1.2 mm).33 normal people were supplied as control group.The systolic global peak CS and CSr of the carotid artery were obtained from short-axis view of the common carotid artery and the stiffness parameters β was measured using 2D strain imaging.All the parameters were compared among the three groups.Results The CS and CSr were decreased and β was increased in patients with T2DM (P ＜ 0.01),The CS and CSr obtained from the plaque group were less than that of the CIMT thickeness group
A new approach to ultrasonic elasticity imaging
Hoerig, Cameron; Ghaboussi, Jamshid; Fatemi, Mostafa; Insana, Michael F.
2016-04-01
Biomechanical properties of soft tissues can provide information regarding the local health status. Often the cells in pathological tissues can be found to form a stiff extracellular environment, which is a sensitive, early diagnostic indicator of disease. Quasi-static ultrasonic elasticity imaging provides a way to image the mechanical properties of tissues. Strain images provide a map of the relative tissue stiffness, but ambiguities and artifacts limit its diagnostic value. Accurately mapping intrinsic mechanical parameters of a region may increase diagnostic specificity. However, the inverse problem, whereby force and displacement estimates are used to estimate a constitutive matrix, is ill conditioned. Our method avoids many of the issues involved with solving the inverse problem, such as unknown boundary conditions and incomplete information about the stress field, by building an empirical model directly from measured data. Surface force and volumetric displacement data gathered during imaging are used in conjunction with the AutoProgressive method to teach artificial neural networks the stress-strain relationship of tissues. The Autoprogressive algorithm has been successfully used in many civil engineering applications and to estimate ocular pressure and corneal stiffness; here, we are expanding its use to any tissues imaged ultrasonically. We show that force-displacement data recorded with an ultrasound probe and displacements estimated at a few points in the imaged region can be used to estimate the full stress and strain vectors throughout an entire model while only assuming conservation laws. We will also demonstrate methods to parameterize the mechanical properties based on the stress-strain response of trained neural networks. This method is a fundamentally new approach to medical elasticity imaging that for the first time provides full stress and strain vectors from one set of observation data.
Antony, S. J.; Kruyt, N. P.
2009-03-01
The interlink between particle-scale properties and macroscopic behavior of three-dimensional granular media subjected to mechanical loading is studied intensively by scientists and engineers, but not yet well understood. Here we study the role of key particle-scale properties, such as interparticle friction and particle elastic modulus, in the functioning of dual contact force networks, viz., strong and weak contacts, in mobilizing shear strength in dense granular media subjected to quasistatic shearing. The study is based on three-dimensional discrete element method in which particle-scale constitutive relations are based on well-established nonlinear theories of contact mechanics. The underlying distinctive contributions of these force networks to the macroscopic stress tensor of sheared granular media are examined here in detail to find out how particle-scale friction and particle-scale elasticity (or particle-scale stiffness) affect the mechanism of mobilization of macroscopic shear strength and other related properties. We reveal that interparticle friction mobilizes shear strength through bimodal contribution, i.e., through both major and minor principal stresses. However, against expectation, the contribution of particle-scale elasticity is mostly unimodal, i.e., through the minor principal stress component, but hardly by the major principal stress. The packing fraction and the geometric stability of the assemblies (expressed by the mechanical coordination number) increase for decrease in interparticle friction and elasticity of particles. Although peak shear strength increases with interparticle friction, the deviator strain level at which granular systems attain peak shear strength is mostly independent of interparticle friction. Granular assemblies attain peak shear strength (and maximum fabric anisotropy of strong contacts) when a critical value of the mechanical coordination number is attained. Irrespective of the interparticle friction and elasticity
In situ nonlinear elastic behavior of soil observed by DAET
Larmat, Carene [Los Alamos National Laboratory; Renaud, Guillaume [Eramus Medical Center, Rotterdam, The Netherlands; Rutledge, James T. [EES-17: GEOPHYSICS; Lee, Richard C. [Los Alamos National Laboratory; Guyer, Robert A. [Los Alamos National Laboratory; Johnson, Paul A. [Los Alamos National Laboratory
2012-07-05
The key to safe design of critical facilities (strong ground motion in low velocity materials such as soils). Current approaches are predictions from measurements of the elastic non-linear properties of boreholes samples. Need for in-situ, local and complete determination of non-linear properties of soil, rock in response to high-strain motion.
Elastic properties of nonstoichiometric reacted PDMS networks
Skov, Anne Ladegaard; Hansen, Kristoffer Karsten; Sommer-Larsen, Peter;
2003-01-01
The influence of stoichiometry on the elastic modulus of eight-functional end-linked poly(dimethylsiloxane) (PDMS) networks was investigated by extensional rheometry with extensions up to more than 100%, and the stress-strain relation was found to be almost linear-a characteristic property...... obtained for the Mooney-Rivlin constants. It was furthermore found that trapped entanglements dominate when there is an excess of cross-linker, ensuring that all long difunctional DMS chains are bound to the infinite network in both ends....
Karimi, Alireza; Navidbakhsh, Mahdi
2014-12-01
The umbilical cord is part of the fetus and generally includes one umbilical vein (UV) and two umbilical arteries (UAs). As the saphenous vein and UV are the most commonly used veins for the coronary artery disease treatment as a coronary artery bypass graft (CABG), understating the mechanical properties of UV has a key asset in its performance for CABG. However, there is not only a lack of knowledge on the mechanical properties of UV and UA but there is no agreement as to which stress-strain definition should be implemented to measure their mechanical properties. In this study, the UV and UA samples were removed after caesarean from eight individuals and subjected to a series of tensile testing. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were employed to determine the linear mechanical properties of UVs and UAs. The nonlinear mechanical behavior of UV/UA was computationally investigated using hyperelastic material models, such as Ogden and Mooney-Rivlin. The results showed that the effect of varying the stress definition on the maximum stress measurements of the UV/UA is significant but not when calculating the elastic modulus. In the true stress-strain diagram, the maximum strain of UV was 92 % higher, while the elastic modulus and maximum stress were 162 and 42 % lower than that of UA. The Mooney-Rivlin material model was designated to represent the nonlinear mechanical behavior of the UV and UA under uniaxial loading.
Nonlinear elastic behavior of rocks revealed by dynamic acousto-elastic testing
Shokouhi, Parisa; Riviere, Jacques; Guyer, Robert; Johnson, Paul
2017-04-01
Nonlinear elastic behavior of rocks is studied at the laboratory scale with the goal of illuminating observations at the Earth scale, for instance during strong ground motion and earthquake slip processes. A technique called Dynamic Acousto-Elastic Testing (DAET) is used to extract the nonlinear elastic response of disparate rocks (sandstone, granite and soapstone). DAET is the dynamic analogous to standard (quasi-static) acousto-elastic testing. It consists in measuring speed of sound with high-frequency low amplitude pulses (MHz range) across the sample while it is dynamically loaded with a low frequency, large amplitude resonance (kHz range). This particular configuration provides the instantaneous elastic response over a full dynamic cycle and reveals unprecedented details: instantaneous softening, tension/compression asymmetry as well as hysteretic behaviors. The strain-induced modulation of ultrasonic pulse velocities ('fast dynamics') is analyzed to extract nonlinearity parameters. A projection method is used to extract the harmonic content and a careful comparison of the fast dynamics response is made. In order to characterize the rate of elastic recovery ('slow dynamics'), we continue to monitor the ultrasonic wave velocity for about 30 minutes after the low-frequency resonance is turned off. In addition, the frequency, pressure and humidity dependences of the nonlinear parameters are reported for a subset of samples. We find that the nonlinear components can be clustered into two categories, which suggests that two main mechanisms are at play. The first one, related to the second harmonic, is likely related to the opening/closing of microstructural features such as cracks and grain/grain contacts. In contrast, the second mechanism is related to all other nonlinear parameters (transient softening, hysteresis area and higher order harmonics) and may arise from shearing mechanisms at grain interfaces.
On the identification of the eggshell elastic properties under quasistatic compression
Jana Simeonovová
2004-01-01
Full Text Available The problem of the identification of the elastic properties of eggshell, i.e. the evaluation of the Young's modulus and Poisson's ratio is solved. The eggshell is considered as a rotational shell. The experiments on the egg compression under quasistatic loading have been conducted. During these experiments a strain on the eggshell surface has been recorded. By the mutual comparison between experimental and theoretical values of strains the influence of the elastic constants has been demonstrated.
Niehuesbernd, Jörn; Müller, Clemens; Pantleon, Wolfgang;
2013-01-01
. The local grain orientations determined by EBSD measurements were used to calculate the elastic tensors at several positions along the strain gradient. Based on the geometric mean, the calculated local elastic constants were transferred into global ones by appropriate weighting. Ultrasonic measurements were......Severely deformed materials often show strong plastic strain gradients, which can lead to a variety of gradients in microstructure and texture. Since the elastic behavior of a material is in most cases linked to its crystallographic texture, gradients in the elastic properties are also possible....... Consequently, the macroscopic elastic behavior results from the local elastic properties within the gradient. In the present investigation profiles produced by the linear flow splitting process were examined with respect to local and global elastic anisotropy, which develops during the complex forming process...
On some method of the space elevator maximum stress reduction
Ambartsumian S. A.
2007-03-01
Full Text Available The possibility of the realization and exploitation of the space elevator project is connected with a number of complicated problems. One of them are large elastic stresses arising in the space elevator ribbon body, which are considerably bigger that the limit of strength of modern materials. This note is devoted to the solution of problem of maximum stress reduction in the ribbon by the modification of the ribbon cross-section area.
Modeling the elastic energy of alloys: Potential pitfalls of continuum treatments
Baskaran, Arvind; Ratsch, Christian; Smereka, Peter
2015-12-01
Some issues that arise when modeling elastic energy for binary alloys are discussed within the context of a Keating model and density-functional calculations. The Keating model is a simplified atomistic formulation based on modeling elastic interactions of a binary alloy with harmonic springs whose equilibrium length is species dependent. It is demonstrated that the continuum limit for the strain field are the usual equations of linear elasticity for alloys and that they correctly capture the coarse-grained behavior of the displacement field. In addition, it is established that Euler-Lagrange equation of the continuum limit of the elastic energy will yield the same strain field equation. This is the same energy functional that is often used to model elastic effects in binary alloys. However, a direct calculation of the elastic energy atomistic model reveals that the continuum expression for the elastic energy is both qualitatively and quantitatively incorrect. This is because it does not take atomistic scale compositional nonuniformity into account. Importantly, this result also shows that finely mixed alloys tend to have more elastic energy than segregated systems, which is the exact opposite of predictions made by some continuum theories. It is also shown that for strained thin films the traditionally used effective misfit for alloys systematically underestimate the strain energy. In some models, this drawback is handled by including an elastic contribution to the enthalpy of mixing, which is characterized in terms of the continuum concentration. The direct calculation of the atomistic model reveals that this approach suffers serious difficulties. It is demonstrated that elastic contribution to the enthalpy of mixing is nonisotropic and scale dependent. It is also shown that such effects are present in density-functional theory calculations for the Si-Ge system. This work demonstrates that it is critical to include the microscopic arrangements in any elastic
Strain Pattern in Supercooled Liquids
Illing, Bernd; Fritschi, Sebastian; Hajnal, David; Klix, Christian; Keim, Peter; Fuchs, Matthias
2016-11-01
Investigations of strain correlations at the glass transition reveal unexpected phenomena. The shear strain fluctuations show an Eshelby-strain pattern [˜cos (4 θ ) /r2 ], characteristic of elastic response, even in liquids, at long times. We address this using a mode-coupling theory for the strain fluctuations in supercooled liquids and data from both video microscopy of a two-dimensional colloidal glass former and simulations of Brownian hard disks. We show that the long-ranged and long-lived strain signatures follow a scaling law valid close to the glass transition. For large enough viscosities, the Eshelby-strain pattern is visible even on time scales longer than the structural relaxation time τ and after the shear modulus has relaxed to zero.
Mathematical foundations of elasticity
Marsden, Jerrold E
1994-01-01
This advanced-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Prerequisites include a solid background in advanced calculus and the basics of geometry and functional analysis.The first two chapters cover the background geometry ― developed as needed ― and use this discussion to obtain the basic results on kinematics and dynamics of con
Mohammad Derikvand; Ghanbar Ebrahimi
2014-01-01
We studied the effect of loose tenon dimensions on stress and strain distributions in T-shaped mortise and loose tenon (M<) furni-ture joints under uniaxial bending loads, and determined the effects of loose tenon length (30, 45, 60, and 90 mm) and loose tenon thickness (6 and 8 mm) on bending moment capacity of M< joints constructed with polyvinyl acetate (PVAc) adhesive. Stress and strain distributions in joint elements were then estimated for each joint using ANSYS finite element (FE) software. The bending moment capacity of joints increased significantly with thickness and length of the tenon. Based on the FE analysis results, under uniaxial bending, the highest shear stress values were obtained in the middle parts of the tenon, while the highest shear elastic strain values were estimated in glue lines between the tenon sur-faces and walls of the mortise. Shear stress and shear elastic strain values in joint elements generally increased with tenon dimensions and corre-sponding bending moment capacities. There was consistency between predicted maximum shear stress values and failure modes of the joints.
Effective elasticity tensor of a periodic composite
Nunan, Kevin C.; Keller, Joseph B.
THE EFFECTIVE elasticity tensor of a composite is defined to be the four-tensor C which relates the average stress to the average strain. We determine it for an array of rigid spheres centered on the points of a periodic lattice in a homogeneous isotropic elastic medium. We first express C in terms of the traction exerted on a single sphere by the medium, and then derive an integral equation for this traction. We solve this equation numerically for simple, body-centered and face-centered cubic lattices with inclusion concentrations up to 90% of the close-packing concentration. For lattices with cubic symmetry the effective elasticity tensor involves just three parameters, which we compute from the solution for the traction. We obtain approximate asymptotic formulas for low concentrations which agree well with the numerical results. We also derive asymptotic results for C at high inclusion concentrations for arbitrary lattice geometries. We find them to be in good agreement with the numerical results for cubic lattices. For low and moderate concentrations the approximate results of NEMAT- NASSERet al., also agree well with the numerical results for cubic lattices.
Elasticity in Amorphous Solids: Nonlinear or Piecewise Linear?
Dubey, Awadhesh K; Procaccia, Itamar; Shor, Carmel A B Z; Singh, Murari
2016-02-26
Quasistatic strain-controlled measurements of stress versus strain curves in macroscopic amorphous solids result in a nonlinear-looking curve that ends up either in mechanical collapse or in a steady state with fluctuations around a mean stress that remains constant with increasing strain. It is therefore very tempting to fit a nonlinear expansion of the stress in powers of the strain. We argue here that at low temperatures the meaning of such an expansion needs to be reconsidered. We point out the enormous difference between quenched and annealed averages of the stress versus strain curves and propose that a useful description of the mechanical response is given by a stress (or strain) -dependent shear modulus for which a theoretical evaluation exists. The elastic response is piecewise linear rather than nonlinear.
Self-folding miniature elastic electric devices
Miyashita, Shuhei; Meeker, Laura; Tolley, Michael T.; Wood, Robert J.; Rus, Daniela
2014-09-01
Printing functional materials represents a considerable impact on the access to manufacturing technology. In this paper we present a methodology and validation of print-and-self-fold miniature electric devices. Polyvinyl chloride laminated sheets based on metalized polyester film show reliable self-folding processes under a heat application, and it configures 3D electric devices. We exemplify this technique by fabricating fundamental electric devices, namely a resistor, capacitor, and inductor. Namely, we show the development of a self-folded stretchable resistor, variable resistor, capacitive strain sensor, and an actuation mechanism consisting of a folded contractible solenoid coil. Because of their pre-defined kinematic design, these devices feature elasticity, making them suitable as sensors and actuators in flexible circuits. Finally, an RLC circuit obtained from the integration of developed devices is demonstrated, in which the coil based actuator is controlled by reading a capacitive strain sensor.
解兆谦; 张洪武; 陈飙松
2012-01-01
Based on the parametric variational principle, a quadratic programming method is developed for the elastic-plastic finite element analysis of a 3D Cosserat continuum model. Since the classical continuum model which is lack of internal scale parameter suffers from pathological mesh dependence in the strain localization analysis, the governing equations of the Cosserat continuum model are regularized by adding a rotational degrees-of-freedom and internal scale parameters to the conventional continuum model. Numerical examples are calculated to demonstrate the efficiency of the 3D Cosserat finite element model and the stability of the proposed computational algorithm for numerical simulation of strain localization problems. Particularly, the mesh independent results are ensured.%基于参变量变分原理，该文发展了三维Cosserat连续体模型弹塑性有限元分析的二次规划算法。由于Cosserat连续体模型的本构方程中存在材料内尺度参数，该模型可以解决经典连续介质理论在分析应变软化问题时病态的有限元网格依赖性问题。数值结果表明所发展的三维Cosserat连续介质弹塑性有限元模型可以有效的模拟应变局部化现象并且该算法具有很好的数值稳定性，同时获得的数值结果具有良好的非网格依赖性。
Lattice strain of osmium diboride under high pressure and nonhydrostatic stress
Kavner, Abby; Weinberger, Michelle B.; Shahar, Anat; Cumberland, Robert W.; Levine, Jonathan B.; Kaner, Richard B.; Tolbert, Sarah H.
2012-01-01
The lattice strain behavior of osmium diboride—a member of a group of third-row transition metal borides associated with hard/superhard behavior—has been studied using radial diffraction in a diamond anvil cell under high pressure and non-hydrostatic stress. We interpret the average values of the measured lattice strains as a lower-bound to the lattice-plane dependent yield strengths using existing estimates for the elastic constants of OsB2, with a yield strength of 11 GPa at 27.5 GPa of hydrostaticpressure. The measured differential lattice strains show significant plane-dependent anisotropy, with the (101) lattice plane showing the largest differential strain and the (001) lattice plane showing the least strain. At the highest pressure, the a-axis develops a larger compressive strain and supports a larger differential strain than either the b or c axes. This causes an increase in the c/a ratio and a decrease in the a/b ratio especially in the maximum stress direction. The large strength anisotropy of this material points to possible ways to modulate directional mechanical properties by taking advantage of the interplay between aggregate polycrystalline texture with directional mechanical properties.
Strain Growth in Containment Vessels
DONG Q; LI Q M; ZHENG J Y
2006-01-01
Strain growth is a phenomenon observed in containment vessels subjected to internal blast loading.The elastic response of the vessel may become larger in a later stage compared to its response during the initial stage.The dynamic responses of infinitely long cylindrical containment vessels subjected to uniformly-distributed internal blast loading are studied using LS-DYNA.The development of bending modes and the interaction between the breathing mode and bending modes are observed.The methodology developed for dynamic elastic buckling analysis is employed to study the strain growth phenomenon in explosion containment vessels.It is shown that the dynamic instable vibration of a containment vessel is the basic mechanism of strain growth.
Nonlinear elastic behavior of phantom materials for elastography
Pavan, Theo Z; Madsen, Ernest L; Frank, Gary R; Hall, Timothy J [Medical Physics Department, University of Wisconsin, Room 1005, Wisconsin Institutes for Medical Research, 1111 Highland Avenue, Madison, WI 53705 (United States); Adilton O Carneiro, Antonio, E-mail: tjhall@wisc.ed [Departamento de Fisica e Matematica, FFCLRP, Universidade de Sao Paulo, Av. Bandeirantes, 3900, Monte Alegre, Ribeirao Preto, Sao Paulo (Brazil)
2010-05-07
The development of phantom materials for elasticity imaging is reported in this paper. These materials were specifically designed to provide nonlinear stress/strain relationship that can be controlled independently of the small strain shear modulus of the material. The materials are mixtures of agar and gelatin gels. Oil droplet dispersions in these materials provide further control of the small strain shear modulus and the nonlinear parameter of the material. Since these materials are mostly water, they are assumed to be incompressible under typical experimental conditions in elasticity imaging. The Veronda-Westman model for strain energy density provided a good fit to all materials used in this study. Materials with a constant gelatin concentration (3.0% dry weight) but varying agar concentration (0.6-2.8% dry weight) demonstrated the same power law relationship between elastic modulus and agar concentration found for pure agar (1.89 {+-} 0.02), consistent with percolation theory, and provided a consistent nonlinearity parameter of 4.5 {+-} 0.3. The insights provided by this study will form the basis for stable elastography phantoms with stiffness and nonlinear stress/strain relationships in the background that differ from those in the target.
Effect of Intrinsic Ripples on Elasticity of the Graphene Monolayer.
Lee, Seungjun
2015-12-01
The effect of intrinsic ripples on the mechanical response of the graphene monolayer is investigated under uniaxial loading using molecular dynamics (MD) simulations with a focus on nonlinear behavior at a small strain. The calculated stress-strain response shows a nonlinear relation through the entire range without constant slopes as a result of the competition between ripple softening and bond stretching hardening. For a small strain, entropic contribution is dominant due to intrinsic ripples, leading to elasticity softening. As the ripples flatten at increasing strain, the energetic term due to C-C bonds stretching competes with the entropic contribution, followed by energetic dominant deformation. Elasticity softening is enhanced at increased temperature as the ripple amplitude increases. The study shows that the intrinsic ripple of graphene affects elasticity. This result suggests that a change of ripple amplitudes due to various environmental conditions such as temperature, and substrate interactions can lead to a change of the mechanical properties of graphene. The understanding of the rippling effect on the mechanical behavior of 2D materials is useful for strain-based ripple manipulation for their engineering applications.
Polysoaps: Configurations and Elasticity
Halperin, A.
1997-03-01
Simple polymers are very long, flexible, linear molecules. Amphiphiles, soaps, are small molecules comprising of a part that prefers water over oil and a part that prefers oil over water. By combining the two we arrive at an interesting, little explored, class of materials: Polysoaps. These comprise of a water soluble backbone incorporating, at intervals, covalently bound amphiphilic monomers. In water, the polymerised amphiphiles aggregate into self assembled units known as micelles. This induces a dramatic modification of the spatial configurations of the polymers. What were featureless random coils now exhibit intramolecular, hierachial self organisation. Due to this self organisation it is necessary to modify the paradigms describing the large scale behaviour of these polymers: Their configurations, dimensions and elasticity. Understanding the behaviour of these polymers is of practical interest because of their wide range of industrial applications, ranging from cosmetics to paper coating. It is of fundamental interest because polysoaps are characterised by a rugged free energy landscape that is reminiscent of complex systems such as proteins and glasses. The talk concerns theoretical arguments regarding the following issues: (i) The design parameters that govern the spatial configurations of the polysoaps, (ii) The interaction between polysoaps and free amphiphiles, (iii) The effect of the intramolecular self organisation on the elasticity of the chains.
Loewenthal, M.; Loseke, K.; Dow, T.A.; Scattergood, R.O.
1988-12-01
Elastic emission polishing, also called elastic emission machining (EEM), is a process where a stream of abrasive slurry is used to remove material from a substrate and produce damage free surfaces with controlled surface form. It is a noncontacting method utilizing a thick elasto-hydrodynamic film formed between a soft rotating ball and the workpiece to control the flow of the abrasive. An apparatus was built in the Center, which consists of a stationary spindle, a two-axis table for the workpiece, and a pump to circulate the working fluid. The process is controlled by a programmable computer numerical controller (CNC), which presently can operate the spindle speed and movement of the workpiece in one axis only. This apparatus has been used to determine material removal rates on different material samples as a function of time, utilizing zirconium oxide (ZrO{sub 2}) particles suspended in distilled water as the working fluid. By continuing a study of removal rates the process should become predictable, and thus create a new, effective, yet simple tool for ultra-precision mechanical machining of surfaces.
A Large Deformation Model for the Elastic Moduli of Two-dimensional Cellular Materials
HU Guoming; WAN Hui; ZHANG Youlin; BAO Wujun
2006-01-01
We developed a large deformation model for predicting the elastic moduli of two-dimensional cellular materials. This large deformation model was based on the large deflection of the inclined members of the cells of cellular materials. The deflection of the inclined member, the strain of the representative structure and the elastic moduli of two-dimensional cellular materials were expressed using incomplete elliptic integrals. The experimental results show that these elastic moduli are no longer constant at large deformation, but vary significantly with the strain. A comparison was made between this large deformation model and the small deformation model proposed by Gibson and Ashby.
A Home Experiment in Elasticity
Aguirregabiria, J M; Rivas, M
2006-01-01
We analyze a simple problem in elasticity: the \\emph{initial} motion of an elastic bar that after being hanged from an end is suddenly released. In a second problem a point mass is attached on the top of the bar. The analytical solutions uncover some unexpected properties, which can be checked, with a digital camera or camcorder, in an alternative setup in which a spring is substituted for the bar. The theoretical model and the experiments are useful to understand the similarities and differences between the elastic properties of bar and spring. Students can take advantage of the home experiments to improve their understanding of elastic waves.
Modeling of Distributed Sensing of Elastic Waves by Fiber-Optic Interferometry
Just Agbodjan Prince
2016-09-01
Full Text Available This paper deals with the transduction of strain accompanying elastic waves in solids by firmly attached optical fibers. Stretching sections of optical fibers changes the time required by guided light to pass such sections. Exploiting interferometric techniques, highly sensitive fiber-optic strain transducers are feasible based on this fiber-intrinsic effect. The impact on the actual strain conversion of the fiber segment’s shape and size, as well as its inclination to the elastic wavefront is studied. FEM analyses show that severe distortions of the interferometric response occur when the attached fiber length spans a noticeable fraction of the elastic wavelength. Analytical models of strain transduction are presented for typical transducer shapes. They are used to compute input-output relationships for the transduction of narrow-band strain pulses as a function of the mechanical wavelength. The described approach applies to many transducers depending on the distributed interaction with the investigated object.
Evaluation of Compressive Strength and Stiffness of Grouted Soils by Using Elastic Waves
In-Mo Lee
2014-01-01
Full Text Available Cement grouted soils, which consist of particulate soil media and cementation agents, have been widely used for the improvement of the strength and stiffness of weak ground and for the prevention of the leakage of ground water. The strength, elastic modulus, and Poisson’s ratio of grouted soils have been determined by classical destructive methods. However, the performance of grouted soils depends on several parameters such as the distribution of particle size of the particulate soil media, grouting pressure, curing time, curing method, and ground water flow. In this study, elastic wave velocities are used to estimate the strength and elastic modulus, which are generally obtained by classical strength tests. Nondestructive tests by using elastic waves at small strain are conducted before and during classical strength tests at large strain. The test results are compared to identify correlations between the elastic wave velocity measured at small strain and strength and stiffness measured at large strain. The test results show that the strength and stiffness have exponential relationship with elastic wave velocities. This study demonstrates that nondestructive methods by using elastic waves may significantly improve the strength and stiffness evaluation processes of grouted soils.
汪明元; 单治钢; 王亚军; 狄圣杰
2014-01-01
The strain controlled dynamic triaxial tests to measure the dynamic moduli and the damping ratios were conducted on intact marine samples from sea area at Daishan,in Zhoushan Archipelago. The experimental results show that the hysteresis curves of Zhoushan Daishan marine sediments are not completely closed loops and are strain softening. The values of dynamic modulus and damping ratio under certain strain amplitude fluctuate around constant values respectively which are designated as the representative values of the dynamic moduli and damping ratios under the corresponding strain amplitude. As such,relationships between dynamic moduli and strain amplitude and between damping ratio and strain amplitude under different confining pressures are established,which converge asymptotically. Hardin-Drnevich(H-D) model is modified to fit the experimental data. Meanwhile,the resonant column tests are conducted to measure the elastic moduli of the marine sediments under wave loading. The results from two tests show that the marine sediments from Daishan are sensitive to the confining pressure.%为探究舟山岱山海域海底岩土地质层动力学特性，借助GDS动三轴系统对应变控制循环荷载作用下舟山原状海相软土动弹性模量和阻尼比变化规律进行研究。得到舟山岱山海相软土动应力、动应变、动孔压时程曲线以及应力-应变关系曲线，讨论各围压下动弹性模量和阻尼比随动应变幅值的变化趋势。结果表明：舟山岱山海相软土的应力-应变关系曲线为不完全封闭的滞回圈；循环加载过程中土样发生应变软化；同级加载下动弹性模量和阻尼比数据点围绕某恒值作小幅波动，故可采用代表该恒值的均值来表征该级加载下的动弹性模量和阻尼比，由此所得的各围压下动弹性模量-动应变幅值、阻尼比-动应变幅值关系曲线呈收敛趋势；由修正Hardin-Drnevich (H-D)模型建立的应变控制下舟
An elastic mechanics model and computation method for geotechnical material
Zheng Yingren; Gao Hong; Zheng Lushi
2010-01-01
Internal friction characteristic is one of the basic properties of geotechnical materials and it exists in mechanical elements all the time.However,until now internal friction is only considered in limit analysis and plastic mechanics but not included in elastic theory for rocks and soils.We consider that internal friction exists in both elastic state and plastic state of geotechnical materials,so the mechanical unit of friction material is constituted.Based on study results of soil tests,the paper also proposes that cohesion takes effect first and internal friction works gradually with the increment of deformation.By assuming that the friction coefficient is proportional to the strain,the internal friction is computed.At last,by imitating the linear elastic mechanics,the nonlinear elastic mechanics model of friction material is established,where the shear modulus G is not a constant.The new model and the traditional elastic model are used simultaneously to analyze an elastic foundation.The results indicate that the displacements computed by the new model are less than those from the traditional method,which agrees with the fact and shows that the mechanical units of friction material are suitable for geotechnical material.
Measurement of elastic nonlinearity of soft solid with transient elastography
Catheline, S.; Gennisson, J.-L.; Fink, M.
2003-12-01
Transient elastography is a powerful tool to measure the speed of low-frequency shear waves in soft tissues and thus to determine the second-order elastic modulus μ (or the Young's modulus E). In this paper, it is shown how transient elastography can also achieve the measurement of the nonlinear third-order elastic moduli of an Agar-gelatin-based phantom. This method requires speed measurements of polarized elastic waves measured in a statically stressed isotropic medium. A static uniaxial stress induces a hexagonal anisotropy (transverse isotropy) in solids. In the special case of uniaxially stressed isotropic media, the anisotropy is not caused by linear elastic coefficients but by the third-order nonlinear elastic constants, and the medium recovers its isotropic properties as soon as the uniaxial stress disappears. It has already been shown how transient elastography can measure the elastic (second-order) moduli in a media with transverse isotropy such as muscles. Consequently this method, based on the measurement of the speed variations of a low-frequency (50-Hz) polarized shear strain waves as a function of the applied stress, allows one to measure the Landau moduli A, B, C that completely describe the third-order nonlinearity. The several orders of magnitude found among these three constants can be justified from the theoretical expression of the internal energy.
Measurement of elastic nonlinearity of soft solid with transient elastography.
Catheline, S; Gennisson, J L; Fink, M
2003-12-01
Transient elastography is a powerful tool to measure the speed of low-frequency shear waves in soft tissues and thus to determine the second-order elastic modulus mu (or the Young's modulus E). In this paper, it is shown how transient elastography can also achieve the measurement of the nonlinear third-order elastic moduli of an Agar-gelatin-based phantom. This method requires speed measurements of polarized elastic waves measured in a statically stressed isotropic medium. A static uniaxial stress induces a hexagonal anisotropy (transverse isotropy) in solids. In the special case of uniaxially stressed isotropic media, the anisotropy is not caused by linear elastic coefficients but by the third-order nonlinear elastic constants, and the medium recovers its isotropic properties as soon as the uniaxial stress disappears. It has already been shown how transient elastography can measure the elastic (second-order) moduli in a media with transverse isotropy such as muscles. Consequently this method, based on the measurement of the speed variations of a low-frequency (50-Hz) polarized shear strain waves as a function of the applied stress, allows one to measure the Landau moduli A, B, C that completely describe the third-order nonlinearity. The several orders of magnitude found among these three constants can be justified from the theoretical expression of the internal energy.
Measurement of Elastic Modulus of Collagen Type I Single Fiber.
Dutov, Pavel; Antipova, Olga; Varma, Sameer; Orgel, Joseph P R O; Schieber, Jay D
2016-01-01
Collagen fibers are the main components of the extra cellular matrix and the primary contributors to the mechanical properties of tissues. Here we report a novel approach to measure the longitudinal component of the elastic moduli of biological fibers under conditions close to those found in vivo and apply it to type I collagen from rat tail tendon. This approach combines optical tweezers, atomic force microscopy, and exploits Euler-Bernoulli elasticity theory for data analysis. This approach also avoids drying for measurements or visualization, since samples are freshly extracted. Importantly, strains are kept below 0.5%, which appear consistent with the linear elastic regime. We find, surprisingly, that the longitudinal elastic modulus of type I collagen cannot be represented by a single quantity but rather is a distribution that is broader than the uncertainty of our experimental technique. The longitudinal component of the single-fiber elastic modulus is between 100 MPa and 360 MPa for samples extracted from different rats and/or different parts of a single tail. Variations are also observed in the fibril-bundle/fibril diameter with an average of 325±40 nm. Since bending forces depend on the diameter to the fourth power, this variation in diameter is important for estimating the range of elastic moduli. The remaining variations in the modulus may be due to differences in composition of the fibril-bundles, or the extent of the proteoglycans constituting fibril-bundles, or that some single fibrils may be of fibril-bundle size.
Reduction in tendon elasticity from unloading is unrelated to its hypertrophy.
Kinugasa, Ryuta; Hodgson, John A; Edgerton, V Reggie; Shin, David D; Sinha, Shantanu
2010-09-01
Tendinous tissues respond to chronic unloading with adaptive changes in mechanical, elastic, and morphological properties. However, little is known about the changes in the detailed structures of the entire tendinous tissue and whether the change in tendon stiffness is related to morphology. We investigated changes in dimensional (volume, cross-sectional area, segmented lengths) and elastic (Young's modulus) properties of the Achilles tendon and distal aponeurosis in response to chronic unilateral lower limb suspension (ULLS) using velocity encoded phase contrast (VE-PC) and three-dimensional morphometric magnetic resonance imaging (MRI). Five healthy subjects underwent ULLS for 4 wk. Axial morphometric MRI was acquired along the entire length from the calcaneous to the medial gastrocnemius insertion. An oblique sagittal VE-PC MRI was also acquired. The Young's modulus could be calculated from this cine dynamic sequence of velocity encoded images from the slope of the stress-strain curve during the submaximal isometric plantar flexion. After 4 wk of ULLS, we found significant (46.7%) decrease in maximum plantar flexion torque. The total volumes of entire tendinous tissue (determined as the sum of the Achilles tendon and distal aponeurosis) increased significantly by 6.4% (11.9 vs. 12.7 ml) after ULLS. In contrast, Young's modulus decreased significantly by 10.4% (211.7 vs. 189.6 MPa) for the Achilles tendon and 29.0% for the distal aponeurosis (158.8 vs. 113.0 MPa) following ULLS. There was no significant correlation between relative change in volume and Young's modulus with 4 wk of ULLS. It is suggested that, although tendon hypertrophy can be expected to adversely affect tendon stiffness, the absence of any significant correlation between the magnitude of tendon hypertrophy and reduced Young's modulus indicates that dimensional factors were not critical to the elastic properties.
An elastic compound tube model for a single osteon.
Braidotti, P; Branca, F P; Sciubba, E; Stagni, L
1995-04-01
A model is developed whereby the secondary osteon--the dominant microstructural component of the cortical bone tissue--is considered as an n-layered cylinder with internal stresses in linear isotropic elasticity. An exact solution is obtained for a loading condition represented by a tensile-compressive force. The lengthening, the side deformation, and the strain energy of the system are explicitly calculated. The behavior of the main elastic quantities is illustrated by graphs. In particular, the important role played by the parity of the number of lamellae is revealed.
Gray, G.T. III; Idar, D.J.; Blumenthal, W.R.; Cady, C.M.; Peterson, P.D.
1998-12-31
High- and low-strain rate compression data were obtained on several different energetic composites: PBX 9501, X0242-92-4-4, PBXN-9, as well as the polymeric binder used in PBX 9501 and X0242-92-4-4 composites. The effects of energetic-to-binder ratios, different binder systems, and different energetic formulations were investigated. All the energetic composites exhibit increasing elastic modulus, E, maximum flow stresses, {sigma}{sub m}, and strain-at-maximum stress, {var_epsilon}{sub m}, with increasing strain rate at ambient temperature. PBX 9501 displays marginally higher ultimate flow strength than X0242-92-4-4, and significantly higher ultimate compressive strength than PBXN-9 at quasi-static and dynamic strain rates. The failure mode of PBX 9501 and X0242-92-4-4 under high-rate loading changes from a mixture of ductile binder tearing and transgranular cleavage and cracking of the HMX when tested at 20 C to transgranular brittle HMX cleavage and glassy fracture of the binder at {minus}40 C.
Kubo, Keitaro; Kanehisa, Hiroaki; Fukunaga, Tetsuo
2005-05-01
The purposes of this study were to compare the elasticity of tendon and aponeurosis in human knee extensors and ankle plantar flexors in vivo and to examine whether the maximal strain of tendon was correlated to that of aponeurosis. The elongation of tendon and aponeurosis during isometric knee extension (n = 23) and ankle plantar flexion (n = 22), respectively, were determined using a real-time ultrasonic apparatus, while the participants performed ramp isometric contractions up to voluntary maximum. To calculate the strain values from the measured elongation, we measured the respective length of tendon and aponeurosis. For the knee extensors, the maximal strain of aponeurosis (12.1 +/- 2.8 %) was significantly greater than that of the patella tendon (8.3 +/- 2.4 %), p aponeurosis in ankle plantar flexors (2.7 +/- 1.4 %), p plantar flexors there was no significant correlation between maximal strain of tendon and aponeurosis. These results would be important for understanding the different roles of tendon and aponeurosis during human movements and for more accurate muscle modeling.
Engelbrecht, Jüri
2015-01-01
This book addresses the modelling of mechanical waves by asking the right questions about them and trying to find suitable answers. The questions follow the analytical sequence from elementary understandings to complicated cases, following a step-by-step path towards increased knowledge. The focus is on waves in elastic solids, although some examples also concern non-conservative cases for the sake of completeness. Special attention is paid to the understanding of the influence of microstructure, nonlinearity and internal variables in continua. With the help of many mathematical models for describing waves, physical phenomena concerning wave dispersion, nonlinear effects, emergence of solitary waves, scales and hierarchies of waves as well as the governing physical parameters are analysed. Also, the energy balance in waves and non-conservative models with energy influx are discussed. Finally, all answers are interwoven into the canvas of complexity.
Spagnolie, Saverio E.; Lauga, Eric
2010-03-01
Motile eukaryotic cells propel themselves in viscous fluids by passing waves of bending deformation down their flagella. An infinitely long flagellum achieves a hydrodynamically optimal low-Reynolds number locomotion when the angle between its local tangent and the swimming direction remains constant along its length. Optimal flagella therefore adopt the shape of a helix in three dimensions (smooth) and that of a sawtooth in two dimensions (nonsmooth). Physically, biological organisms (or engineered microswimmers) must expend internal energy in order to produce the waves of deformation responsible for the motion. Here we propose a physically motivated derivation of the optimal flagellum shape. We determine analytically and numerically the shape of the flagellar wave which leads to the fastest swimming for a given appropriately defined energetic expenditure. Our novel approach is to define an energy which includes not only the work against the surrounding fluid, but also (1) the energy stored elastically in the bending of the flagellum, (2) the energy stored elastically in the internal sliding of the polymeric filaments which are responsible for the generation of the bending waves (microtubules), and (3) the viscous dissipation due to the presence of an internal fluid. This approach regularizes the optimal sawtooth shape for two-dimensional deformation at the expense of a small loss in hydrodynamic efficiency. The optimal waveforms of finite-size flagella are shown to depend on a competition between rotational motions and bending costs, and we observe a surprising bias toward half-integer wave numbers. Their final hydrodynamic efficiencies are above 6%, significantly larger than those of swimming cells, therefore indicating available room for further biological tuning.
PAGOSA Sample Problem. Elastic Precursor
Weseloh, Wayne N. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Clancy, Sean Patrick [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-02-03
A PAGOSA simulation of a flyer plate impact which produces an elastic precursor wave is examined. The simulation is compared to an analytic theory for the Mie-Grüneisen equation of state and an elastic-perfectly-plastic strength model.
Larkin, A. I.; Khmelnitskii, D. E., E-mail: dekl2@cam.ac.uk [Landau Institute for Theoretical Physics (Russian Federation)
2013-09-15
Friction of elastic bodies is connected with the passing through the metastable states that arise at the contact of surfaces rubbing against each other. Three models are considered that give rise to the metastable states. Friction forces and their dependence on the pressure are calculated. In Appendix A, the contact problem of elasticity theory is solved with adhesion taken into account.
Elastic energy release in great earthquakes and eruptions
Agust eGudmundsson
2014-05-01
Full Text Available The sizes of earthquakes are measured using well-defined, measurable quantities such as seismic moment and released (transformed elastic energy. No similar measures exist for the sizes of volcanic eruptions, making it difficult to compare the energies released in earthquakes and eruptions. Here I provide a new measure of the elastic energy (the potential mechanical energy associated with magma chamber rupture and contraction (shrinkage during an eruption. For earthquakes and eruptions, elastic energy derives from two sources: (1 the strain energy stored in the volcano/fault zone before rupture, and (2 the external applied load (force, pressure, stress, displacement on the volcano/fault zone. From thermodynamic considerations it follows that the elastic energy released or transformed (dU during an eruption is directly proportional to the excess pressure (pe in the magma chamber at the time of rupture multiplied by the volume decrease (-dVc of the chamber, so that . This formula can be used as a basis for a new eruption magnitude scale, based on elastic energy released, which can be related to the moment-magnitude scale for earthquakes. For very large eruptions (>100 km3, the volume of the feeder-dike is negligible, so that the decrease in chamber volume during an eruption corresponds roughly to the associated volume of erupted materials , so that the elastic energy is . Using a typical excess pressures of 5 MPa, it is shown that the largest known eruptions on Earth, such as the explosive La Garita Caldera eruption (27-28 million years ago and largest single (effusive Colombia River basalt lava flows (15-16 million years ago, both of which have estimated volumes of about 5000 km3, released elastic energy of the order of 10EJ. For comparison, the seismic moment of the largest earthquake ever recorded, the M9.5 1960 Chile earthquake, is estimated at 100 ZJ and the associated elastic energy release at 10EJ.
Residual strains in conduit arteries.
Rachev, A; Greenwald, S E
2003-05-01
Residual strains and stresses are those that exist in a body when all external loads are removed. Residual strains in arteries can be characterized by the opening angle of the sector-like cross-section which arises when an unloaded ring segment is radially cut. A review of experimental methods for measuring residual strains and the main results about the variation of the opening angle with arterial localization, age, smooth muscle activity, mechanical environment and certain vascular pathologies are presented and discussed. It is shown that, in addition to their well-established ability to homogenize the stress field in the arterial wall, residual strains make arteries more compliant and thereby improve their performance as elastic reservoirs and ensure more effective local control of the arterial lumen by smooth muscle cells. Finally, evidence that, in some cases, residual strains remain in arteries even after they have been cut radially is discussed.
Cell elasticity determines macrophage function.
Naimish R Patel
Full Text Available Macrophages serve to maintain organ homeostasis in response to challenges from injury, inflammation, malignancy, particulate exposure, or infection. Until now, receptor ligation has been understood as being the central mechanism that regulates macrophage function. Using macrophages of different origins and species, we report that macrophage elasticity is a major determinant of innate macrophage function. Macrophage elasticity is modulated not only by classical biologic activators such as LPS and IFN-γ, but to an equal extent by substrate rigidity and substrate stretch. Macrophage elasticity is dependent upon actin polymerization and small rhoGTPase activation, but functional effects of elasticity are not predicted by examination of gene expression profiles alone. Taken together, these data demonstrate an unanticipated role for cell elasticity as a common pathway by which mechanical and biologic factors determine macrophage function.
GUO Lei; NIE GuoHua
2008-01-01
This paper presents an analytical solution for the elastic fields induced by non-elastic eigenstrains in a plane elliptical inhomogeneity embedded in the orthotropic matrix under tension at infinity and inclined at any angle. The conformal transformation and complex function method for the snisotropic elastic material were used to determine the strain energies in the inhomogeneity and matrix, which were expressed by four undetermined coefficients characterizing the equilibrium boundary of the inhomogeneity due to the acting eigenstrains and external load. The use of the principle of the minimum potential energy led to analytical expres-sions for these coefficients and thus generated a closed-form solution for the elas-tic strain/stress fields. The resulting stress field in the inhomogeneity was exam-ined and verified by checking the continuity conditions for the normal and shear stresses on the interior boundary of the matrix.
Bemer, E.; Bouteca, M.; Vincke, O. [Institut Francais du Petrole (IFP), 92 - Rueil-Malmaison (France); Hoteit, N.; Ozanam, O. [Agence Nationale pour la Gestion des Dechets Radioactifs ANDRA, 92 - Chatenay Malabry (France)
2001-07-01
Due to the impact on productivity and oil an place estimates, reliable modeling of rock behavior is essential in reservoir engineering. This paper examines several aspects of rock poro-elastic behavior within the framework of Biot's mechanics of fluid saturated porous solids. Constitutive laws of linear and nonlinear poro-elasticity are first determined from a fundamental stress decomposition, which allows to clearly connect linear and nonlinear models. Concept of effective stress and rock compressibility are considered. Linear incremental stress-strain relations are derived from the proposed nonlinear constitutive law by defining tangent elastic properties. These characteristics are naturally functions of strains and pore pressure, but explicit expressions as functions of stresses and pore pressure are established herein. Experiments performed on a reservoir sandstone illustrate these points. A constitutive law of poro-visco-elasticity is finally presented and applied to experimental data obtained on clay. (authors)
2008-01-01
This paper presents an analytical solution for the elastic fields induced by non-elastic eigenstrains in a plane elliptical inhomogeneity embedded in the orthotropic matrix under tension at infinity and inclined at any angle. The conformal transformation and complex function method for the anisotropic elastic material were used to determine the strain energies in the inhomogeneity and matrix, which were expressed by four undetermined coefficients characterizing the equilibrium boundary of the inhomogeneity due to the acting eigenstrains and external load. The use of the principle of the minimum potential energy led to analytical expres-sions for these coefficients and thus generated a closed-form solution for the elas-tic strain/stress fields. The resulting stress field in the inhomogeneity was exam-ined and verified by checking the continuity conditions for the normal and shear stresses on the interior boundary of the matrix.
Moore, Talia Y; Rivera, Alberto M; Biewener, Andrew A
2017-01-01
Numerous historical descriptions of the Lesser Egyptian jerboa, Jaculus jaculus, a small bipedal mammal with elongate hindlimbs, make special note of their extraordinary leaping ability. We observed jerboa locomotion in a laboratory setting and performed inverse dynamics analysis to understand how this small rodent generates such impressive leaps. We combined kinematic data from video, kinetic data from a force platform, and morphometric data from dissections to calculate the relative contributions of each hindlimb muscle and tendon to the total movement. Jerboas leapt in excess of 10 times their hip height. At the maximum recorded leap height (not the maximum observed leap height), peak moments for metatarso-phalangeal, ankle, knee, and hip joints were 13.1, 58.4, 65.1, and 66.9 Nmm, respectively. Muscles acting at the ankle joint contributed the most work (mean 231.6 mJ / kg Body Mass) to produce the energy of vertical leaping, while muscles acting at the metatarso-phalangeal joint produced the most stress (peak 317.1 kPa). The plantaris, digital flexors, and gastrocnemius tendons encountered peak stresses of 25.6, 19.1, and 6.0 MPa, respectively, transmitting the forces of their corresponding muscles (peak force 3.3, 2.0, and 3.8 N, respectively). Notably, we found that the mean elastic energy recovered in the primary tendons of both hindlimbs comprised on average only 4.4% of the energy of the associated leap. The limited use of tendon elastic energy storage in the jerboa parallels the morphologically similar heteromyid kangaroo rat, Dipodomys spectabilis. When compared to larger saltatory kangaroos and wallabies that sustain hopping over longer periods of time, these small saltatory rodents store and recover less elastic strain energy in their tendons. The large contribution of muscle work, rather than elastic strain energy, to the vertical leap suggests that the fitness benefit of rapid acceleration for predator avoidance dominated over the need to enhance
Elastic filament velocimetry (EFV)
Fu, M. K.; Fan, Y.; Byers, C. P.; Chen, T.-H.; Arnold, C. B.; Hultmark, M.
2017-02-01
A novel method for velocity measurements in both gaseous and liquid flows is presented. The sensing element is comprised of a free-standing electrically conductive nanoscale ribbon suspended between silicon supports. Due to its minuscule size, the nanoribbon deflects in flow due to viscously dominated fluid forcing inducing an axial strain of the sensing element. The strain leads to a resistance change, which is measurable through a simple Wheatstone bridge circuit and can be related to the flow velocity through semi-analytic analysis. Two methods of characterization are employed to validate the sensor functionality. First, confocal microscopy was used to validate physical models and assumptions through imaging of the nanoribbon deformation under different fluid loads. Second, the resistance measurements of various nanoribbons under different flow conditions exhibited sensitivity to fluid flow consistent with lower order model predictions.
A nonlinear theory for elastic plates with application to characterizing paper properties
M. W. Johnson; Thomas J. Urbanik
1984-03-01
A theory of thin plates which is physically as well as kinematically nonlinear is, developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a...
Nonlinear elasticity in rocks: A comprehensive three-dimensional description
Lott, Martin; Remillieux, Marcel C.; Garnier, Vincent; Le Bas, Pierre-Yves; Ulrich, T. J.; Payan, Cédric
2017-07-01
We study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequency "pump" wave induces a strain field in the sample and modulates the propagation of a high-frequency "probe" wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined: the pump successively consists of the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) P and (shear) S waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dynamics and the three-dimensional effects resulting from the tensorial nature of elasticity.
The Einstein field equations for cylindrically symmetric elastic configurations
Brito, I; Vaz, E G L R [Departamento de Matematica e Aplicacoes, Universidade do Minho, 4800-058 Guimaraes (Portugal); Carot, J, E-mail: ireneb@math.uminho.pt, E-mail: jcarot@uib.cat, E-mail: evaz@math.uminho.pt [Departament de Fisica, Universitat de les Illes Balears, Cra Valdemossa pk 7.5, E-07122 Palma (Spain)
2011-09-22
In the context of relativistic elasticity it is interesting to study axially symmetric space-times due to their significance in modeling neutron stars and other astrophysical systems of interest. To approach this problem, here, a particular class of these space-times is considered. A cylindrically symmetric elastic space-time configuration is studied, where the material metric is taken to be flat. The components of the energy-momentum tensor for elastic matter are written in terms of the invariants of the strain tensor, here chosen to be the eigenvalues of the pulled-back material metric. The Einstein field equations are presented and a condition confirming the existence of a constitutive function is obtained. This condition leads to special cases, in one of which a new system for the metric functions and an expression for the constitutive function are deduced. The new system depends on a particular function, which builds up the constitutive equation.
The maximum force in a column under constant speed compression
Kuzkin, Vitaly A
2015-01-01
Dynamic buckling of an elastic column under compression at constant speed is investigated assuming the first-mode buckling. Two cases are considered: (i) an imperfect column (Hoff's statement), and (ii) a perfect column having an initial lateral deflection. The range of parameters, where the maximum load supported by a column exceeds Euler static force is determined. In this range, the maximum load is represented as a function of the compression rate, slenderness ratio, and imperfection/initial deflection. Considering the results we answer the following question: "How slowly the column should be compressed in order to measure static load-bearing capacity?" This question is important for the proper setup of laboratory experiments and computer simulations of buckling. Additionally, it is shown that the behavior of a perfect column having an initial deflection differ significantlys form the behavior of an imperfect column. In particular, the dependence of the maximum force on the compression rate is non-monotoni...
OECD Maximum Residue Limit Calculator
With the goal of harmonizing the calculation of maximum residue limits (MRLs) across the Organisation for Economic Cooperation and Development, the OECD has developed an MRL Calculator. View the calculator.
Finite-element formulations for problems of large elastic-plastic deformation
Mcmeeking, R. M.; Rice, J. R.
1975-01-01
An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is ideally suited to isotropically hardening Prandtl-Reuss materials. Further, the formulation is given in a manner which allows any conventional finite element program, for 'small strain' elastic-plastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. The paper closes with a unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures. Further, a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain, and the inadequacies of some of these are commented upon.
Schache, Anthony G.; Brown, Nicholas A. T.; Pandy, Marcus G.
2016-01-01
Tendon elastic strain energy is the dominant contributor to muscle–tendon work during steady-state running. Does this behaviour also occur for sprint accelerations? We used experimental data and computational modelling to quantify muscle fascicle work and tendon elastic strain energy for the human ankle plantar flexors (specifically soleus and medial gastrocnemius) for multiple foot contacts of a maximal sprint as well as for running at a steady-state speed. Positive work done by the soleus and medial gastrocnemius muscle fascicles decreased incrementally throughout the maximal sprint and both muscles performed more work for the first foot contact of the maximal sprint (FC1) compared with steady-state running at 5 m s−1 (SS5). However, the differences in tendon strain energy for both muscles were negligible throughout the maximal sprint and when comparing FC1 to SS5. Consequently, the contribution of muscle fascicle work to stored tendon elastic strain energy was greater for FC1 compared with subsequent foot contacts of the maximal sprint and compared with SS5. We conclude that tendon elastic strain energy in the ankle plantar flexors is just as vital at the start of a maximal sprint as it is at the end, and as it is for running at a constant speed. PMID:27581481
Flexural-slip during visco-elastic buckle folding
Damasceno, Davi R.; Eckert, Andreas; Liu, Xiaolong
2017-07-01
Flexural-slip is considered as an important mechanism during folding and a general conceptual and qualitative understanding has been provided by various field studies. However, quantitative evidence of the importance of the flexural-slip mechanism during fold evolution is sparse due to the lack of suitable strain markers. In this study, 2D finite element analysis is used to overcome these disadvantages and to simulate flexural-slip during visco-elastic buckle folding. Variations of single and multilayer layer fold configurations are investigated, showing that flexural-slip is most likely to occur in effective single layer buckle folds, where slip occurs between contacts of competent layers. Based on effective single layer buckle folds, the influence of the number of slip surfaces, the degree of mechanical coupling (based on the friction coefficient), and layer thickness, on the resulting slip distribution are investigated. The results are in agreement with the conceptual flexural-slip model and show that slip is initiated sequentially during the deformation history and is maximum along the central slip surface of the fold limb. The cumulative amount of slip increases as the number of slip surfaces is increased. For a lower degree of mechanical coupling increased slip results in different fold shapes, such as box folds, during buckling. In comparison with laboratory experiments, geometrical relationships and field observations, the numerical modeling results show similar slip magnitudes. It is concluded that flexural-slip should represent a significant contribution during buckle folding, affecting the resulting fold shape for increased amounts of slip.
Impedance of rigid bodies in one-dimensional elastic collisions
Santos, Janilo; Nelson, Osman Rosso
2012-01-01
In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance matching as a way to understand eficiency of energy transmission in elastic collisions, we find a solution which frames the problem in terms of this conception. We show that the mass of the ball can be seen as a measure of its impedance and verify that the problem of maximum energy transfer in elastic collisions can be thought of as a problem of impedance matching between different media. This approach extends the concept of impedance, usually associated with oscillatory systems, to system of rigid bodies.
吴志荣; 胡绪腾; 宋迎东
2013-01-01
工程中的大多构件承受着复杂的载荷形式,将单轴疲劳模型应用到多轴载荷情况已不能满足工程精度的要求,多轴载荷下的疲劳寿命计算日益引起人们的重视.基于临界平面的思想,结合Fatemi-Socie(FS)模型和Smith-Watson-Topper(SWT)参数各自的优点,提出一种新的多轴疲劳寿命预测模型.该模型以最大切应变幅与最大切应变幅平面上修正SWT参数的和作为多轴疲劳损伤控制参量,此参量可以同时考虑非比例附加循环硬化和平均应力对材料多轴疲劳寿命的影响,能同时适用于比例和非比例加载下的多轴疲劳问题.采用纯钛Ti、BT9钛合金、304不锈钢、S45C钢和1045HR钢5种材料多轴疲劳试验数据对提出的模型进行评估和验证,对几种材料比例和非比例加载下的多轴疲劳寿命预测结果大都分布在试验结果的2倍分散带之内,结果表明提出的多轴疲劳寿命模型具有较高的预测精度.%The most components of engineering structures are usually subjected to a complex loading. It is unable to meet the requirements of engineering precision if a uniaxial fatigue model is used under multi-axial loading. The calculation of fatigue life prediction under multiaxial loading causes people's attention more and more. A new multiaxial fatigue life prediction model is proposed based on the critical plane criteria. The model integrates the respective advantages of Fatemi-Socie(FS) model and Smith-Watson-Topper(SWT) parameter. The damage parameter in this model takes the sum of the maximum shear strain amplitude and the modified SWT parameter on the maximum shear strain amplitude plain. It can consider the effects of additional cyclic hardening due to non-proportional loading and mean stress on the multi-axial fatigue life of material. The proposed model can be applied to proportional and non-proportional loading. The model is evaluated by the multiaxial fatigue test data of pure titanium, BT9
COMPARISON OF ELASTIC OF POROUS CORDIERITE BY FLEXURE AND DYNAMIC TEST METHODS
Stafford, Randall [Cummins, Inc; Golovin, K. B. [Cummins, Inc; Dickinson, A. [Cummins, Inc; Watkins, Thomas R [ORNL; Shyam, Amit [ORNL; Lara-Curzio, Edgar [ORNL
2012-01-01
Previous work showed differences in apparent elastic modulus between mechanical flexure testing and resonance methods. Flexure tests have been conducted using non-contact optical systems to directly measure deflection for calculation of elastic modulus. Dynamic test methods for elastic modulus measurement were conducted on the same material for comparison. The results show significant difference in the apparent elastic modulus for static flexure versus dynamic methods. The significance of the difference in apparent elastic modulus on thermal stress and the hypotheses for these differences will be discussed. Dynamic measurement (resonance) and static measurement (mechanical) produce different values for elastic modulus of porous cordierite ceramic. The elastic modulus from resonance is a measure of the material response at very low strain which is different from the material response in a mechanical test with relatively large strain. The apparent elastic moduli for dynamic versus static test methods in this study are different by a factor of two. This result has significant impact on calculated stress and life in an aftertreatment component.
High Strain Rate Characterisation of Composite Materials
Eriksen, Rasmus Normann Wilken
The high strain rate characterisation of FRP materials present the experimenter with a new set of challenges in obtaining valid experimental data. These challenges were addressed in this work with basis in classic wave theory. The stress equilibrium process for linear elastic materials, as fibre...... a linear elastic specimen to reach a state of constant strain rate before fracture. This was in contrast to ductile materials, which are widely tested with for the High-speed servohydraulic test machine. The development of the analysis and the interpretation of the results, were based on the experience...
Nonlinear mechanics of hyper elastic polyurethane furniture foams
Jerzy Smardzewski
2008-07-01
Full Text Available Upholstered furniture intended to provide better sleep and rest, especially furniture for disabled persons, require careful design of elastic spring systems. In the majority of cases, when designing new articles, both furniture designers and manufacturers rely on long-term experience and craftsman’s intuition. On the other hand, the accumulated interdisciplinary knowledge of modern medical laboratories as well as furniture certification offices indicate that it is necessary to carry out investigations related to the mechanical properties of raw materials used to manufacture furniture and to conduct virtual modelling of the phenomena connected with the contact of the human body with the elastic base. The aim of this study was to determine the elastic properties of hyper-plastic polyurethane foams applied in furniture industry, to elaborate mathematical models of these materials on the basis of non-linear Mooney-Rivlin models and to conduct a non-linear numerical analysis of contact strains in a deformed seat made of polyurethane foam. The results of the experiments revealed that the mechanical properties of polyurethanefoams are described properly by the Mooney-Rivlin model. Knowing the mechanical properties of these foams, it is possible to create freely complex furniture elastic systems. The state of strains in the contact of the human body with foam depends on the friction between these bodies. Therefore, in practice, it is advisable to design seatsystems resulting in minimal frictions between the user’s clothes and the furniture seat.
An examination of the elastic structural response of the Advanced Neutron Source fuel plates
Swinson, W.F.; Luttrell, C.R.; Yahr, G.T.
1994-09-01
Procedures for evaluating the elastic structural response of the Advanced Neutron Source (ANS) fuel plates to coolant flow and to temperature variations are presented in this report. Calculations are made that predict the maximum deflection and the maximum stress for a representative plate from the upper and from the lower fuel elements.
Uniqueness theorems in linear elasticity
Knops, Robin John
1971-01-01
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...
Inverse problemfor an inhomogeneous elastic beam at a combined strength
Andreev Vladimir Igorevich
2014-01-01
Full Text Available In the article the authors describe a method of optimizing the stress state of an elastic beam, subject to the simultaneous action of the central concentrated force and bending moment. The optimization method is based on solving the inverse problem of the strength of materials, consisting in defining the law of changing in elasticity modulus with beam cross-section altitude. With this changing the stress state will be preset. Most problems of the elasticity theory of inhomogeneous bodies are solved in direct formulation, the essence of which is to determine the stress-strain state of a body at the known dependences of the material elastic characteristics from the coordinates. There are also some solutions of the inverse problems of the elasticity theory, in which the dependences of the mechanical characteristics from the coordinates, at which the stress state of a body is preset, are determined. In the paper the authors solve the problem of finding a dependence modulus of elasticity, where the stresses will be constant over the beam’s cross section. We will solve the problem of combined strength (in the case of the central stretching and bending. We will use an iterative method. As the initial solution, we take the solution for a homogeneous material. As the first approximation, we consider the stress state of a beam, when the modulus of elasticity varies linearly. According to the results, it can be stated that three approximations are sufficient in the considered problem. The obtained results allow us to use them in assessing the strength of a beam and its optimization.
Sivak, David Alexander
DNA bending elasticity on length scales of tens of basepairs is of critical importance in numerous biological contexts. Even the simplest models of DNA bending admit of few simple analytic results, thus there is a need for numerical methods to calculate experimental observables, such as distance distributions, forces, FRET efficiencies, and timescales of particular large-scale motions. We have implemented and helped develop a coarse-grained representation of DNA and various other covalently-linked groups that allows simple calculation of such observables for varied experimental systems. The simple freely-jointed chain (FJC) model and extremely coarse resolution proved useful in understanding DNA threading through nanopores, identifying steric occlusion by other parts of the chain as a prime culprit for slower capture as distance to the pore decreased. Enhanced sampling techniques of a finer resolution discrete wormlike chain (WLC) model permitted calculation of cyclization rates for small chains and identified the ramifications of a thermodynamically-sound treatment of thermal melts. Adding treatment of double-stranded DNA's helical nature and single-stranded DNA provided a model system that helped demonstrate the importance of statistical fluctuations in even highly-stressed DNA mini-loops, and allowed us to verify that even these constructs show no evidence of excitation-induced softening. Additional incorporation of salt-sensitivity to the model allowed us to calculate forces and FRET efficiencies for such mini-loops and their uncircularized precursors, thereby furthering the understanding of the nature of IHF binding and bending of its recognition sequence. Adding large volume-excluding spheres linked to the ends of the dsDNA permits calculation of distance distributions and thus small-angle X-ray scattering, whereby we demonstrated the validity of the WLC in describing bending fluctuations in DNA chains as short as 42 bp. We also make important connections
Electrodynamic forces in elastic matter
Antoci, S.; Mihich, L.
1999-01-01
A macroscopic theory for the dynamics of elastic, isotropic matter in presence of electromagnetic fields is proposed here. We avail of Gordon's general relativistic derivation of Abraham's electromagnetic energy tensor as starting point. The necessary description of the elastic and of the inertial behaviour of matter is provided through a four dimensional generalisation of Hooke's law, made possible by the introduction of a four dimensional ``displacement'' vector. As intimated by Nordstroem,...
Maximum margin Bayesian network classifiers.
Pernkopf, Franz; Wohlmayr, Michael; Tschiatschek, Sebastian
2012-03-01
We present a maximum margin parameter learning algorithm for Bayesian network classifiers using a conjugate gradient (CG) method for optimization. In contrast to previous approaches, we maintain the normalization constraints on the parameters of the Bayesian network during optimization, i.e., the probabilistic interpretation of the model is not lost. This enables us to handle missing features in discriminatively optimized Bayesian networks. In experiments, we compare the classification performance of maximum margin parameter learning to conditional likelihood and maximum likelihood learning approaches. Discriminative parameter learning significantly outperforms generative maximum likelihood estimation for naive Bayes and tree augmented naive Bayes structures on all considered data sets. Furthermore, maximizing the margin dominates the conditional likelihood approach in terms of classification performance in most cases. We provide results for a recently proposed maximum margin optimization approach based on convex relaxation. While the classification results are highly similar, our CG-based optimization is computationally up to orders of magnitude faster. Margin-optimized Bayesian network classifiers achieve classification performance comparable to support vector machines (SVMs) using fewer parameters. Moreover, we show that unanticipated missing feature values during classification can be easily processed by discriminatively optimized Bayesian network classifiers, a case where discriminative classifiers usually require mechanisms to complete unknown feature values in the data first.
Maximum Entropy in Drug Discovery
Chih-Yuan Tseng
2014-07-01
Full Text Available Drug discovery applies multidisciplinary approaches either experimentally, computationally or both ways to identify lead compounds to treat various diseases. While conventional approaches have yielded many US Food and Drug Administration (FDA-approved drugs, researchers continue investigating and designing better approaches to increase the success rate in the discovery process. In this article, we provide an overview of the current strategies and point out where and how the method of maximum entropy has been introduced in this area. The maximum entropy principle has its root in thermodynamics, yet since Jaynes’ pioneering work in the 1950s, the maximum entropy principle has not only been used as a physics law, but also as a reasoning tool that allows us to process information in hand with the least bias. Its applicability in various disciplines has been abundantly demonstrated. We give several examples of applications of maximum entropy in different stages of drug discovery. Finally, we discuss a promising new direction in drug discovery that is likely to hinge on the ways of utilizing maximum entropy.
Silver, Frederick H; Bradica, Gino; Tria, Alfred
2002-03-01
The viscoelastic mechanical properties of normal and osteoarthritic articular were analyzed based on data reported by Kempson [in: Adult Articular Cartilage (1973)] and Silver et al. (Connect. Tissue Res., 2001b). Results of the analysis of tensile elastic stress-strain curves suggest that the elastic modulus of cartilage from the superficial zone is approximately 7.0 GPa parallel and 2.21 GPa perpendicular to the cleavage line pattern. Collagen fibril lengths in the superficial zone were found to be approximately 1265 microm parallel and 668 microm perpendicular to the cleavage line direction. The values for the elastic modulus and fibril lengths decreased with increased extent of osteoarthritis. The elastic modulus of type II collagen parallel to the cleavage line pattern in the superficial zone approaches that of type I collagen in tendon, suggesting that elastic energy storage occurs in the superficial zone due to the tensile pre-tension that exists in this region. Decreases in the elastic modulus associated with osteoarthritis reflect decreased ability of cartilage to store elastic energy, which leads to cartilage fibrillation and fissure formation. We hypothesize that under normal physiological conditions, collagen fibrils in cartilage function to store elastic energy associated with weight bearing and locomotion. Enzymatic cleavage of cartilage proteoglycans and collagen observed in osteoarthritis may lead to fibrillation and fissure formation as a result of impaired energy storage capability of cartilage.
Algorithm of constructing hybrid effective modules for elastic isotropic composites
Svetashkov, A. A.; Miciński, J.; Kupriyanov, N. A.; Barashkov, V. N.; Lushnikov, A. V.
2017-02-01
The algorithm of constructing of new effective elastic characteristics of two-component composites based on the superposition of the models of Reiss and Voigt, Hashin and Strikman, as well as models of the geometric average for effective modules. These effective characteristics are inside forks Voigt and Reiss. Additionally, the calculations of the stress-strain state of composite structures with new effective characteristics give more accurate prediction than classical models do.
Bistable non-volatile elastic membrane memcapacitor exhibiting chaotic behavior
Martinez-Rincon, J.; Pershin, Y. V.
2011-01-01
We suggest a realization of a bistable non-volatile memory capacitor (memcapacitor). Its design utilizes a strained elastic membrane as a plate of a parallel-plate capacitor. The applied stress generates low and high capacitance configurations of the system. We demonstrate that a voltage pulse of an appropriate amplitude can be used to reliably switch the memcapacitor into the desired capacitance state. Moreover, charged-voltage and capacitance-voltage curves of such a system demonstrate hyst...
Highly Elastic and Conductive Human-Based Protein Hybrid Hydrogels.
Annabi, Nasim; Shin, Su Ryon; Tamayol, Ali; Miscuglio, Mario; Bakooshli, Mohsen Afshar; Assmann, Alexander; Mostafalu, Pooria; Sun, Jeong-Yun; Mithieux, Suzanne; Cheung, Louis; Tang, Xiaowu Shirley; Weiss, Anthony S; Khademhosseini, Ali
2016-01-01
A highly elastic hybrid hydrogel of methacryloyl-substituted recombinant human tropoelastin (MeTro) and graphene oxide (GO) nanoparticles are developed. The synergistic effect of these two materials significantly enhances both ultimate strain (250%), reversible rotation (9700°), and the fracture energy (38.8 ± 0.8 J m(-2) ) in the hybrid network. Furthermore, improved electrical signal propagation and subsequent contraction of the muscles connected by hybrid hydrogels are observed in ex vivo tests.
Elastic-plastic analysis of the SS-3 tensile specimen
Majumdar, S. [Argonne National Lab., IL (United States)
1998-09-01
Tensile tests of most irradiated specimens of vanadium alloys are conducted using the miniature SS-3 specimen which is not ASTM approved. Detailed elastic-plastic finite element analysis of the specimen was conducted to show that, as long as the ultimate to yield strength ratio is less than or equal to 1.25 (which is satisfied by many irradiated materials), the stress-plastic strain curve obtained by using such a specimen is representative of the true material behavior.
Elastic Behavior of Polymer Chains
Teng Lu; Tao Chen; Hao-jun Liang
2008-01-01
The elastic behavior of the polymer chain was investigated in a three-dimensional off-lattice model. We sample more than 109 conformations of each kind of polymer chain by using a Monte Carlo algorithm, then analyze them with the non-Gaussian theory of rubberlike elasticity, and end with a statistical study. Through observing the effect of the chain flexibility and the stretching ratio on the mean-square end-to-end distance,the average energy, the average Helmholtz free energy, the elastic force, the contribution of energy to the elastic force, and the entropy contribution to elastic force of the polymer chain, we find that a rigid polymer chain is much easier to stretch than a flexible polymer chain. Also, a rigid polymer chain will become difficult to stretch only at a quite high stretching ratio because of the effect of the entropy contribution.These results of our simulation calculation may explain some of the macroscopic phenomena of polymer and biomacromolecular elasticity.
Elastic bending modulus of monolayer graphene
Lu Qiang; Huang Rui [Department of Aerospace Engineering and Engineering Mechanics, University of Texas, Austin, TX 78712 (United States); Arroyo, Marino [Department of Applied Mathematics 3, LaCaN, Universitat Politecnica de Catalunya (UPC), Barcelona 08034 (Spain)
2009-05-21
An analytic formula is derived for the elastic bending modulus of monolayer graphene based on an empirical potential for solid-state carbon atoms. Two physical origins are identified for the non-vanishing bending stiffness of the atomically thin graphene sheet, one due to the bond-angle effect and the other resulting from the bond-order term associated with the dihedral angles. The analytical prediction compares closely with ab initio energy calculations. Pure bending of graphene monolayers into cylindrical tubes is simulated by a molecular mechanics approach, showing slight nonlinearity and anisotropy in the tangent bending modulus as the bending curvature increases. An intrinsic coupling between bending and in-plane strain is noted for graphene monolayers rolled into carbon nanotubes. (fast track communication)
Highly tunable elastic dielectric metasurface lenses
Kamali, Seyedeh Mahsa; Arbabi, Amir; Horie, Yu; Faraon, Andrei
2016-01-01
Dielectric metasurfaces are two-dimensional structures composed of nano-scatterers that manipulate phase and polarization of optical waves with subwavelength spatial resolution, enabling ultra-thin components for free-space optics. While high performance devices with various functionalities, including some that are difficult to achieve using conventional optical setups have been shown, most demonstrated components have a fixed functionality. Here we demonstrate highly tunable metasurface devices based on subwavelength thick silicon nano-posts encapsulated in a thin transparent elastic polymer. As proof of concept, we demonstrate a metasurface microlens operating at 915 nm, with focal distance tuning from 600 $\\mu$m to 1400 $\\mu$m through radial strain, while maintaining a diffraction limited focus and a focusing efficiency above 50$\\%$. The demonstrated tunable metasurface concept is highly versatile for developing ultra-slim, multi-functional and tunable optical devices with widespread applications ranging f...
Elastic properties of Thiel-embalmed human ankle tendon and ligament.
Liao, Xiaochun; Kemp, Sandy; Corner, George; Eisma, Roos; Huang, Zhihong
2015-10-01
Thiel embalming is recommended as an alternative to formalin-based embalming because it preserves tissue elasticity, color, and flexibility in the long term, with low infection and toxicity risk. The degree to which Thiel embalming preserves elasticity has so far been assessed mainly by subjective scoring, with little quantitative verification. The aim of this study is to quantify the effect of Thiel embalming on the elastic properties of human ankle tendons and ligament. Biomechanical tensile tests were carried out on six Thiel-embalmed samples each of the peroneus longus, peroneus brevis, and calcaneal tendons, and the calcaneofibular ligament, with strain rates of 0.25%s(-1), 2%s(-1), and 8%s(-1). The stress-strain relationship was calculated from the force-extension response with cross-sectional area and gauge length. Young's modulus was determined from the stress-strain curve. The results showed that the tendon and ligament elasticity were lower after Thiel embalming than the literature values for fresh nonembalmed tendons and ligament. The biomechanical tensile test showed that the measured elasticity of Thiel-embalmed tendons and ligaments increased with the strain rate. The Thiel embalming method is useful for preserving human ankle tendons and ligaments for anatomy and surgery teaching and research, but users need to be aware of its softening effects. The method retains the mechanical strain rate effect on tendons and ligament. © 2015 Wiley Periodicals, Inc.
Elastic Face, An Anatomy-Based Biometrics Beyond Visible Cue
Tsap, L V; Zhang, Y; Kundu, S J; Goldgof, D B; Sarkar, S
2004-03-29
This paper describes a face recognition method that is designed based on the consideration of anatomical and biomechanical characteristics of facial tissues. Elastic strain pattern inferred from face expression can reveal an individual's biometric signature associated with the underlying anatomical structure, and thus has the potential for face recognition. A method based on the continuum mechanics in finite element formulation is employed to compute the strain pattern. Experiments show very promising results. The proposed method is quite different from other face recognition methods and both its advantages and limitations, as well as future research for improvement are discussed.
SOLITARY WAVES IN FINITE DEFORMATION ELASTIC CIRCULAR ROD
LIU Zhi-fang; ZHANG Shan-yuan
2006-01-01
A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.
Stability boundaries for wrinkling in highly stretched elastic sheets
Li, Qingdu; Healey, Timothy J.
2016-12-01
We determine stability boundaries for the wrinkling of highly unidirectionally stretched, finely thin, rectangular elastic sheets. For a given fine thickness and length, a stability boundary here is a curve in the parameter plane, aspect ratio vs. the macroscopic strain; the values on one side of the boundary are associated with stable unwrinkled (flat) states, while stable wrinkled configurations correspond to all values on the other. In our recent work we demonstrated the importance of finite elasticity in the membrane part of such a model in order to capture the correct phenomena. Here we present and compare results for four distinct models: (i) the popular Föppl-von Kármán plate model (FvK), (ii) a correction of the latter, used in our earlier work, in which the approximate 2D Föppl strain tensor is replaced by the exact Green strain tensor, (iii) and (iv): effective 2D finite-elasticity membrane models based on 3D incompressible neo-Hookean and Mooney-Rivlin materials, respectively. In particular, (iii) and (iv) are superior models for elastomers. The 2D nonlinear, hyperelastic models (ii)-(iv) all incorporate the same quadratic bending energy used in FvK. Our results illuminate serious shortcomings of the latter in this problem, while also pointing to inaccuracies of model (ii) - in spite of yielding the correct qualitative phenomena in our earlier work. In each of these, the shortcoming is a due to a deficiency of the membrane part of the model.
An information-based machine learning approach to elasticity imaging.
Hoerig, Cameron; Ghaboussi, Jamshid; Insana, Michael F
2016-11-18
An information-based technique is described for applications in mechanical property imaging of soft biological media under quasi-static loads. We adapted the Autoprogressive method that was originally developed for civil engineering applications for this purpose. The Autoprogressive method is a computational technique that combines knowledge of object shape and a sparse distribution of force and displacement measurements with finite-element analyses and artificial neural networks to estimate a complete set of stress and strain vectors. Elasticity imaging parameters are then computed from estimated stresses and strains. We introduce the technique using ultrasonic pulse-echo measurements in simple gelatin imaging phantoms having linear-elastic properties so that conventional finite-element modeling can be used to validate results. The Autoprogressive algorithm does not require any assumptions about the material properties and can, in principle, be used to image media with arbitrary properties. We show that by selecting a few well-chosen force-displacement measurements that are appropriately applied during training and establish convergence, we can estimate all nontrivial stress and strain vectors throughout an object and accurately estimate an elastic modulus at high spatial resolution. This new method of modeling the mechanical properties of tissue-like materials introduces a unique method of solving the inverse problem and is the first technique for imaging stress without assuming the underlying constitutive model.
PLANE STRAIN PROBLEM OF PIEZOELECTRIC SOLID WITH ELLIPTIC INCLUSION
DAI Long-chao; GUO Wan-lin; SHE Chong-min
2005-01-01
By using the complex variables function theory, a plane strain electro-elastic analysis was performed on a transversely isotropic piezoelectric material containing an elliptic elastic inclusion, which is subjected to a uniform stress field and a uniform electric displacement loads at infinity. Based on the present finite element results and some related theoretical solutions, an acceptable conjecture was found that the stress field is constant inside the elastic inclusion. The stress field solutions in the piezoelectric matrix and the elastic inclusion were obtained in the form of complex potentials based on the impermeable electric boundary conditions.
APPLICABILITY OF DAMAGE DEFINITION BASED ON HYPOTHESIS OF STRAIN EQUIVALENCE
鞠杨; 谢和平
2000-01-01
The hypothesis of strain equivalence is used to measure damage in materials. The physical meaning of the elastic modulus of damaged materials defined in the hypothesis is discussed in this paper. The inapplicability of the hypothesis to be used to determine the damage and its evolution in elasto-plastic materials are analyzed. It is emphasized that the method in which the relaxed modulus is taken as the deformed modulus, i.e. the elastic modulus defined in the hypothesis, is only applicable for measuring the damage in elastic materials. A new damage variable is proposed, which is applicable for both elastic and elastoplastic materials.
Coherency in Neutrino-Nucleus Elastic Scattering
Kerman, S; Deniz, M; Wong, H T; Chen, J -W; Li, H B; Lin, S T; Liu, C -P; Yue, Q
2016-01-01
Neutrino-nucleus elastic scattering provides a unique laboratory to study the quantum mechanical coherency effects in electroweak interactions, towards which several experimental programs are being actively pursued. We report results of our quantitative studies on the transitions towards decoherency. A parameter ($\\alpha$) is identified to describe the degree of coherency, and its variations with incoming neutrino energy, detector threshold and target nucleus are studied. The ranges of $\\alpha$ which can be probed with realistic neutrino experiments are derived, indicating complementarity between projects with different sources and targets. Uncertainties in nuclear physics and in $\\alpha$ would constrain sensitivities in probing physics beyond the standard model. The maximum neutrino energies corresponding to $\\alpha$>0.95 are derived.
Elasticity of 3D networks with rigid filaments and compliant crosslinks
Heidemann, Knut M; Rehfeldt, Florian; Schmidt, Christoph F; Wardetzky, Max
2014-01-01
Disordered filamentous networks with compliant crosslinks exhibit a low linear elastic shear modulus at small strains, but stiffen dramatically at high strains. Experiments have shown that the elastic modulus can increase by up to three orders of magnitude while the networks withstand relatively large stresses without rupturing. Here, we perform an analytical and numerical study on model networks in three dimensions. Our model consists of a collection of randomly oriented rigid filaments connected by flexible crosslinks that are modeled as wormlike chains. Due to zero probability of filament intersection in three dimensions, our model networks are by construction prestressed in terms of initial tension in the crosslinks. We demonstrate how the linear elastic modulus can be related to the prestress in these network. Under the assumption of affine deformations in the limit of infinite crosslink density, we show analytically that the nonlinear elastic regime in 1- and 2-dimensional networks is characterized by p...
Elastic-plastic deformation of sandwich rod on elastic basis
GU Yu
2008-01-01
Sandwich composite material possesses advantages of both light weight and high strength.Although the mechanical behaviors of sandwich composite material with the influence of single external environment have been intensively studied,little work has been done in the study of mechanical property,in view of the nonlinear behavior of sandwich composites in the complicated external environments.In this paper,the problem about the bending of the three-layer elastic-plastic rod located on the elastic base,with a compressibly physical nonlinear core,has been studied.The mechanical response of the designed three-layer elements consisting of two bearing layers and a core has been examined.The complicated problem about curving of the three-layer rod located on the elastic base has been solved.The convergence of the proposed method of elastic solutions is examined to convince that the solution is acceptable.The calculated results indicate that the plasticity and physical nonlinearity of materials have a great influence on the deformation of the sandwich rod on the elastic basis.
Scaling Laws for the Response of Nonlinear Elastic Media with Implications for Cell Mechanics
Shokef, Yair; Safran, Samuel A.
2012-04-01
We show how strain stiffening affects the elastic response to internal forces, caused either by material defects and inhomogeneities or by active forces that molecular motors generate in living cells. For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that, even around a contractile inclusion or molecular motor, there is radial compression; it is only at a long distance that one recovers the linear response in which the medium is radially stretched. Scaling laws with irrational exponents relate the far-field renormalized strain to the near-field strain applied by the inclusion or active force.
Greenslade, Thomas B., Jr.
1985-01-01
Discusses a series of experiments performed by Thomas Hope in 1805 which show the temperature at which water has its maximum density. Early data cast into a modern form as well as guidelines and recent data collected from the author provide background for duplicating Hope's experiments in the classroom. (JN)
Abolishing the maximum tension principle
Dabrowski, Mariusz P
2015-01-01
We find the series of example theories for which the relativistic limit of maximum tension $F_{max} = c^2/4G$ represented by the entropic force can be abolished. Among them the varying constants theories, some generalized entropy models applied both for cosmological and black hole horizons as well as some generalized uncertainty principle models.
Abolishing the maximum tension principle
Mariusz P. Da̧browski
2015-09-01
Full Text Available We find the series of example theories for which the relativistic limit of maximum tension Fmax=c4/4G represented by the entropic force can be abolished. Among them the varying constants theories, some generalized entropy models applied both for cosmological and black hole horizons as well as some generalized uncertainty principle models.
A new paradigm for the molecular basis of rubber elasticity
Hanson, David E.; Barber, John L.
2015-07-01
The molecular basis for rubber elasticity is arguably the oldest and one of the most important questions in the field of polymer physics. The theoretical investigation of rubber elasticity began in earnest almost a century ago with the development of analytic thermodynamic models, based on simple, highly-symmetric configurations of so-called Gaussian chains, i.e. polymer chains that obey Markov statistics. Numerous theories have been proposed over the past 90 years based on the ansatz that the elastic force for individual network chains arises from the entropy change associated with the distribution of end-to-end distances of a free polymer chain. There are serious conceptual objections to this assumption and others, such as the assumption that all network nodes undergo a simple volume-preserving linear motion and that all of the network chains have the same length. Recently, a new paradigm for elasticity in rubber networks has been proposed that is based on mechanisms that originate at the molecular level. Using conventional statistical mechanics analyses, Quantum Chemistry, and Molecular Dynamics simulations, the fundamental entropic and enthalpic chain extension forces for polyisoprene (natural rubber) have been determined, along with estimates for the basic force constants. Concurrently, the complex morphology of natural rubber networks (the joint probability density distributions that relate the chain end-to-end distance to its contour length) has also been captured in a numerical model (EPnet). When molecular chain forces are merged with the network structure in this model, it is possible to study the mechanical response to tensile and compressive strains of a representative volume element of a polymer network. As strain is imposed on a network, pathways of connected taut chains, that completely span the network along strain axis, emerge. Although these chains represent only a few percent of the total, they account for nearly all of the elastic stress at high
ONE-DIMENSIONAL CONSOLIDATION OF LAYERED AND VISCO-ELASTIC SOILS UNDER ARBITRARY LOADING
蔡袁强; 徐长节; 袁海明
2001-01-01
Based on the layered visco-elastic soil model, according to the Terzaghi' s one dimensional consolidation theory, by the method of Laplace transform and matrix transfer technique, the problems about the consolidation of layered and saturated visco-elastic soils under arbitrary loading were solved. Through deductions, the general solution, in the terms of layer thickness, the modulus and the coefficients of permeability and Laplacian transform' s parameters was obtained. The strain and deformation of the layered and satu rated visco-elastic soils under arbitrary loading can be calculated by Laplace inversion. Ac cording to the results of several numerical examples, the consolidation of visco-elastic soils lags behind that of elastic soils. The development of effective stress and the displacement is vibrant process under cyclic loading. Finally, an engineering case is studied and the results prove that the methods are very effective.
High-pressure elastic properties of cubic Ir2P from ab initio calculations
Sun, Xiao-Wei; Bioud, Nadhira; Fu, Zhi-Jian; Wei, Xiao-Ping; Song, Ting; Li, Zheng-Wei
2016-10-01
A study of the high-pressure elastic properties of new synthetic Ir2P in the anti-fluorite structure is conducted using ab initio calculations based on density functional theory. The elastic constants C11, C12 and C44 for the cubic Ir2P are obtained by the stress-strain method and the elastic stability calculations under pressure indicate that it is stable at least 100 GPa. Additionally, the electronic density of states, the aggregate elastic moduli, that is bulk modulus, shear modulus, and Young's modulus along with the Debye temperature, Poisson's ratio, and elastic anisotropy factor are all successfully obtained. Moreover, the pressure dependence of the longitudinal and shear wave velocities in three different directions [100], [110], and [111] for Ir2P are also predicted for the first time.
俞家欢; 匡震邦
2001-01-01
The displacement and the stress states cased by single inclusion are achieved from the fundamental solutions such as nuclei of strain in bimaterals. The elastic field induced by multiple inclusions in dissimilar media could be found from the superstition of that of individual precipitate. In this paper, the effect of the planner interface with parameters of depth from the interface, both pairs of elastic moduli and also shapes of the inclusion are also given, which are of great significance in physical applications.
Studies on Dynamic Damage Evolution for Pp/pa Polymer Blends Under High Strain Rates
Sun, Zi-Jian; Wang, Li-Li
The dynamic damage evolution for PP/PA blends with different compatibilizers is studied in high strain rates from two different approaches, namely by determining the unloading elastic modulus of specimen experienced impact deformation and by combining the split Hopkinson pressure bar (SHPB) experimental technique with the back-propagation (BP) neural network. The results obtained by both approaches consistently show that a threshold strain ɛth exists for dynamic damage evolution, and both the damage evolution and ɛth are dependent on strain and strain rate. For non-linear visco-elastic materials, the damage evolution determined by the unloading elastic modulus provides an underestimation of real damage evolution.
Converging shocks in elastic-plastic solids.
Ortega, A López; Lombardini, M; Hill, D J
2011-11-01
We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy e=e(s)(I(1))+e(h)(ρ,ς), where e(s) accounts for shear through the first invariant of the Cauchy-Green tensor, and e(h) represents the hydrostatic contribution as a function of the density ρ and entropy ς. In the strong-shock limit, reached as the shock approaches the axis or origin r=0, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., e(h)=e(h)(ρ), with a power-law dependence e(h) is proportional to ρ(α), shock dynamics predicts that for a converging shock located at r=R(t) at time t, the Mach number increases as M is proportional to [log(1/R)](α), independently of the space index s, where s=2 in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with p(ρ) of the arctanh type, which enforces a finite density in the strong-shock limit, leads to M is proportional to R(-(s-1)) for strong shocks. A nonisothermal constitutive law, whose hydrostatic part e(h) is that of an ideal gas, is also tested, recovering the strong-shock limit M is proportional to R(-(s-1)/n(γ)) originally derived by Whitham for perfect gases, where γ is inherently related to the maximum compression ratio that the material can reach, (γ+1)/(γ-1). From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the
Converging shocks in elastic-plastic solids
López Ortega, A.; Lombardini, M.; Hill, D. J.
2011-11-01
We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy e=es(I1)+eh(ρ,ς), where es accounts for shear through the first invariant of the Cauchy-Green tensor, and eh represents the hydrostatic contribution as a function of the density ρ and entropy ς. In the strong-shock limit, reached as the shock approaches the axis or origin r=0, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., eh=eh(ρ), with a power-law dependence eh∝ρα, shock dynamics predicts that for a converging shock located at r=R(t) at time t, the Mach number increases as M∝[log(1/R)]α, independently of the space index s, where s=2 in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with p(ρ) of the arctanh type, which enforces a finite density in the strong-shock limit, leads to M∝R-(s-1) for strong shocks. A nonisothermal constitutive law, whose hydrostatic part eh is that of an ideal gas, is also tested, recovering the strong-shock limit M∝R-(s-1)/n(γ) originally derived by Whitham for perfect gases, where γ is inherently related to the maximum compression ratio that the material can reach, (γ+1)/(γ-1). From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the hydrostatic part of the energy essentially commands the strong-shock behavior, the shear
刘江伟; 黄炳香; 魏民涛
2012-01-01
In order to investigate the influence of cyclic loading on the coal-rock elastic-plastic properties and energy accumulation & dissipation, the cyclic loading test on uniaxial compression on Coal 22 was conducted in this study. Based on the analysis results, the first loading and unloading, and reloading are positively correlated with elasticity modulus. With the increase of cycle number, the elastic strain appears in an inverted U-shape change while the plastic strain exhibits a U-shape change. AH the elasticity modulus E, elastic energy index Wet and energy dissipating rate Wed caused by strain follows an inverted U-shape change. The first average variation rate n of elasticity modulus is 30%, and the energy dissipation φ>sd follows a U-shape change. When elastic energy index Wet reaches its maximum, a burst phenomenon will easily occur. With the increase of stress amplitude, the speed of production and propagation of micro-crack will increase, as well as the micro-plastic deformation speed will also increase. With the increase of loading level, the elastic energy index shows a tendency of increasing earlier and decreasing later during the compression and linear elasticity period, and reaches the maximum at "elastic-plastic critical point".%为了研究循环加载对煤岩弹塑性和能量积聚耗散的影响,对二2煤进行了单轴压缩循环加载实验,分析得出首次加载、卸载、再加载弹性模量呈正相关关系；随着循环数的增加,弹性应变会表现出倒“U”形变化,塑性应变表现出“U”形变化的规律,由应变引起的弹性模量E、弹性能量指数Wet和能量耗散率Wed都表现出倒“U”形变化的规律,首个平均弹性模量变化率η为30％,耗散的能量(ψ)sd呈“U”形变化,当弹性能量指数Wet达到最大值时,冲击现象最容易发生；分析出微裂纹的萌生传播速度随应力振幅的增加而增加,微塑性变形速度也随之增加,弹性能量指数在压密
Khanafer, Khalil; Duprey, Ambroise; Schlicht, Marty; Berguer, Ramon
2009-04-01
Tensile tests on Polydimethylsiloxane (PDMS) materials were conducted to illustrate the effects of mixing ratio, definition of the stress-strain curve, and the strain rate on the elastic modulus and stress-strain curve. PDMS specimens were prepared according to the ASTM standards for elastic materials. Our results indicate that the physiological elastic modulus depends strongly on the definition of the stress-strain curve, mixing ratio, and the strain rate. For various mixing ratios and strain rates, true stress-strain definition results in higher stress and elastic modulus compared with engineering stress-strain and true stress-engineering strain definitions. The elastic modulus increases as the mixing ratio increases up-to 9:1 ratio after which the elastic modulus begins to decrease even as the mixing ratio continues to increase. The results presented in this study will be helpful to assist the design of in vitro experiments to mimic blood flow in arteries and to understand the complex interaction between blood flow and the walls of arteries using PDMS elastomer.
Strain index: a new visualizing parameter for US elastography
Sosa-Cabrera, Dario; de Luis-García, R.; Tristán-Vega, A.; Alberola-López, Carlos; Ruiz-Alzola, Juan
2008-03-01
Elastography, an ultrasound modality based on the relation between tissue strain and its mechanical properties, has a strong potential in the diagnosis and prognosis of tumors. For instance, tissue affected by breast and prostate cancer undergoes a change in its elastic properties. These changes can be measured using ultrasound signals. The standard way to visualize the elastic properties of tissues in elastography is the representation of the axial strain. Other approaches investigate the information contained in shear strain elastograms, vorticity or the representation of the full strain tensor. In this paper, we propose to represent the elastic behaviour of tissues through the visualization of the Strain Index, related with the trace of the strain tensor. Based on the mathematical interpretation of the strain tensor, this novel parameter is equivalent to the sum of the eigenvalues of the strain tensor, and constitutes a measure of the total amount of strain of the soft tissue. In order to show the potential of this visualization approach, a tissue-mimicking phantom was modeled as a 10x10x5 cm region containing a centered 10mm cylindrical inclusion three times stiffer than the surrounding material, and its elastic behavior was simulated using finite elements software. Synthetic pre- and post-compression (1.25%) B-mode images were computer-generated with ultrasound simulator. Results show that the visualization of the tensor trace significantly improves the representation and detection of inclusions, and can help add insight in the detection of different types of tumors.
Buckling modes of elastic thin films on elastic substrates
Mei, Haixia; Huang, Rui; Chung, Jun Young; Stafford, Christopher M.; Yu, Hong-Hui
2007-04-01
Two buckling modes have been observed in thin films: buckle delamination and wrinkling. This letter identifies the conditions for selecting the favored buckling modes for elastic films on elastic substrates. Transition from one buckling mode to another is predicted as the stiffness ratio between the substrate and the film or is predicted for variation of the stiffness ratio between the substrate and the film or variation of theinterfacial defect size. The theoretical results are demonstrated experimentally by observing the coexistence of both buckling modes and mode transition in one film-substrate system.
STUDY OF THE EQUIVALENT THEOREM OF GENERALIZED VARIATIONAL PRINCIPLES IN ELASTICITY
张国清; 余建星
2004-01-01
The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.
Elastic properties of two dimensional hard discs in the close packing limit
Wojciechowski, K W; Kowalik, M; Tretiakov, K V
2003-01-01
Elastic constants and the Poisson ratio of defect-free hard disc solid are determined by two independent methods: (1) analysis of the box side fluctuations in the NpT ensemble with variable box +shape and (2) numerical differentiation (with respect to strain components) of the free energy computed in the NVT ensemble. It is shown that reasonable estimates of the elastic properties can be obtained by studying small systems and that the singular behavior of the elastic constants near close packing is well described by the free volume approximation; the coefficients of the leading singularities are estimated.
GAO Ning; LAI Wen-Sheng
2006-01-01
@@ The calculation of elastic constants of Ag/Pd superlattice thin films by molecular dynamics simulations with many-body potentials is presented. It reveals that the elastic constants C11 and C55 increase with decreasing modulation wavelength A of the films, which is consistent with experiments. However, the change of C11 and C55 with A is found to be around the values determined by a rule of mixture using bulk elastic constants of metals.No supermodulus effect is observed and it is due to cancellation between enhanced and reduced contributions to elastic constants from Ag and Pd layers subjected to compressive and tensile strains, respectively.
Perfect elastic-viscoplastic field at mode Ⅰ dynamic propagating crack-tip
WANG Zhen-qing; LIANG Wen-yan; ZHOU Bo; SU Juan
2007-01-01
The viscosity of material is considered at propagating crack-tip. Under the assumption that the artificial viscosity coefficient is in inverse proportion to power law of the plastic strain rate, an elastic-viscoplastic asymptotic analysis is carried out for moving crack-tip fields in power-hardening materials under plane-strain condition. A continuous solution is obtained containing no discontinuities. The variations of numerical solution are discussed for mode Ⅰ crack according to each parameter. It is shown that stress and strain both possess exponential singularity. The elasticity, plasticity and viscosity of material at crack-tip only can be matched reasonably under linear-hardening condition. And the tip field contains no elastic unloading zone for mode Ⅰ crack. It approaches the limiting case, crack-tip is under ultra-viscose situation and energy accumulates, crack-tip begins to propagate under different compression situations.
Chen, Zi; Srolovitz, David J; Haataja, Mikko
2012-01-01
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is developed to analytically predict the equilibrium deformed helical shape of an initially flat, straight ribbon, with prescribed magnitudes and orientations of the principal curvatures when subjected to arbitrary surface stress and/or internal residual strain distribution. The helix angle, radius, axis and chirality of the deformed helical ribbons are predicted with a comprehensive, three-dimensional model that incorporates elasticity, differential geometry, and variational principles. In general, the mechanical anisotropy (e.g., in surface/external stress, residual strain or elastic modulus) will lead to spontaneous, three-dimensional helical deformations. Ring shapes are formed when the principle axes of deformation coincide with the geometric axes of the ribbon. The transition f...
A non-linear elastic constitutive framework for replicating plastic deformation in solids.
Roberts, Scott Alan; Schunk, Peter Randall
2014-02-01
Ductile metals and other materials typically deform plastically under large applied loads; a behavior most often modeled using plastic deformation constitutive models. However, it is possible to capture some of the key behaviors of plastic deformation using only the framework for nonlinear elastic mechanics. In this paper, we develop a phenomenological, hysteretic, nonlinear elastic constitutive model that captures many of the features expected of a plastic deformation model. This model is based on calculating a secant modulus directly from a materials stress-strain curve. Scalar stress and strain values are obtained in three dimensions by using the von Mises invariants. Hysteresis is incorporated by tracking an additional history variable and assuming an elastic unloading response. This model is demonstrated in both single- and multi-element simulations under varying strain conditions.
Maximum Genus of Strong Embeddings
Er-ling Wei; Yan-pei Liu; Han Ren
2003-01-01
The strong embedding conjecture states that any 2-connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2-connected graph has a circuit double cover.Conversely, it is not true. But for a 3-regular graph, the two conjectures are equivalent. In this paper, a characterization of graphs having a strong embedding with exactly 3 faces, which is the strong embedding of maximum genus, is given. In addition, some graphs with the property are provided. More generally, an upper bound of the maximum genus of strong embeddings of a graph is presented too. Lastly, it is shown that the interpolation theorem is true to planar Halin graph.
Effects of nonlinear muscle elasticity on pelvic floor mechanics during vaginal childbirth.
Li, Xinshan; Kruger, Jennifer A; Nash, Martyn P; Nielsen, Poul M F
2010-11-01
The role of the pelvic floor soft tissues during the second stage of labor, particularly the levator ani muscle, has attracted much interest recently. It has been postulated that the passage of the fetal head through the pelvis may cause excessive stretching of the levator ani muscle, which may lead to pelvic floor dysfunction and pelvic organ prolapse later in life. In order to study the complex biomechanical interactions between the levator ani muscle and the fetal head during the second stage of labor, finite element models have been developed for quantitative analysis of this process. In this study we have simulated vaginal delivery using individual-specific anatomical computer models of the pelvic floor interacting with a fetal head model with minimal restrictions placed upon its motion. Two constitutive relations were considered for the levator ani muscle (of exponential and neo-Hookean forms). For comparison purposes, the exponential relation was chosen to exhibit much greater stiffening at higher strains beyond the range of the experimental data. We demonstrated that increased nonlinearity in the elastic response of the tissues leads to considerably higher (56%) estimated force required for delivery, accompanied by a more homogeneous spatial distribution of maximum principal stretch ratio across the muscle. These results indicate that the form of constitutive relation beyond the presently available experimental data markedly affects the estimated function of the levator ani muscle during vaginal delivery, due to the large strains that occur. Further experimental data at higher strains are necessary in order to more reliably characterize the constitutive behavior required for modeling vaginal childbirth.
Remizov, Ivan D
2009-01-01
In this note, we represent a subdifferential of a maximum functional defined on the space of all real-valued continuous functions on a given metric compact set. For a given argument, $f$ it coincides with the set of all probability measures on the set of points maximizing $f$ on the initial compact set. This complete characterization lies in the heart of several important identities in microeconomics, such as Roy's identity, Sheppard's lemma, as well as duality theory in production and linear programming.
Photoacoustic elastic oscillation and characterization.
Gao, Fei; Feng, Xiaohua; Zheng, Yuanjin
2015-08-10
Photoacoustic imaging and sensing have been studied extensively to probe the optical absorption of biological tissue in multiple scales ranging from large organs to small molecules. However, its elastic oscillation characterization is rarely studied and has been an untapped area to be explored. In literature, photoacoustic signal induced by pulsed laser is commonly modelled as a bipolar "N-shape" pulse from an optical absorber. In this paper, the photoacoustic damped oscillation is predicted and modelled by an equivalent mass-spring system by treating the optical absorber as an elastic oscillator. The photoacoustic simulation incorporating the proposed oscillation model shows better agreement with the measured signal from an elastic phantom, than conventional photoacoustic simulation model. More interestingly, the photoacoustic damping oscillation effect could potentially be a useful characterization approach to evaluate biological tissue's mechanical properties in terms of relaxation time, peak number and ratio beyond optical absorption only, which is experimentally demonstrated in this paper.
Elastic actuation for legged locomotion
Cao, Chongjing; Conn, Andrew
2017-04-01
The inherent elasticity of dielectric elastomer actuators (DEAs) gives this technology great potential in energy efficient locomotion applications. In this work, a modular double cone DEA is developed with reduced manufacturing and maintenance time costs. This actuator can lift 45 g of mass (5 times its own weight) while producing a stroke of 10.4 mm (23.6% its height). The contribution of the elastic energy stored in antagonistic DEA membranes to the mechanical work output is experimentally investigated by adding delay into the DEA driving voltage. Increasing the delay time in actuation voltage and hence reducing the duty cycle is found to increase the amount of elastic energy being recovered but an upper limit is also noticed. The DEA is then applied to a three-segment leg that is able to move up and down by 17.9 mm (9% its initial height), which demonstrates the feasibility of utilizing this DEA design in legged locomotion.
Photoacoustic elastic oscillation and characterization
Gao, Fei; Zheng, Yuanjin
2014-01-01
Photoacoustic imaging and sensing have been studied extensively to probe the optical absorption of biological tissue in multiple scales ranging from large organs to small molecules. However, its elastic oscillation characterization is rarely studied and has been an untapped area to be explored. In literature, photoacoustic signal induced by pulsed laser is commonly modelled as a bipolar "N-shape" pulse from an optical absorber. In this paper, the photoacoustic damped oscillation is predicted and modelled by an equivalent mass-spring system by treating the optical absorber as an elastic oscillator. The photoacoustic simulation incorporating the proposed oscillation model shows better agreement with the measured signal from an elastic phantom, than conventional photoacoustic simulation model. More interestingly, the photoacoustic damping oscillation effect could potentially be a useful characterization approach to evaluate biological tissue's mechanical properties in terms of relaxation time, peak number and ra...
Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness
Berger, J. B.; Wadley, H. N. G.; McMeeking, R. M.
2017-02-01
A wide variety of high-performance applications require materials for which shape control is maintained under substantial stress, and that have minimal density. Bio-inspired hexagonal and square honeycomb structures and lattice materials based on repeating unit cells composed of webs or trusses, when made from materials of high elastic stiffness and low density, represent some of the lightest, stiffest and strongest materials available today. Recent advances in 3D printing and automated assembly have enabled such complicated material geometries to be fabricated at low (and declining) cost. These mechanical metamaterials have properties that are a function of their mesoscale geometry as well as their constituents, leading to combinations of properties that are unobtainable in solid materials; however, a material geometry that achieves the theoretical upper bounds for isotropic elasticity and strain energy storage (the Hashin–Shtrikman upper bounds) has yet to be identified. Here we evaluate the manner in which strain energy distributes under load in a representative selection of material geometries, to identify the morphological features associated with high elastic performance. Using finite-element models, supported by analytical methods, and a heuristic optimization scheme, we identify a material geometry that achieves the Hashin–Shtrikman upper bounds on isotropic elastic stiffness. Previous work has focused on truss networks and anisotropic honeycombs, neither of which can achieve this theoretical limit. We find that stiff but well distributed networks of plates are required to transfer loads efficiently between neighbouring members. The resulting low-density mechanical metamaterials have many advantageous properties: their mesoscale geometry can facilitate large crushing strains with high energy absorption, optical bandgaps and mechanically tunable acoustic bandgaps, high thermal insulation, buoyancy, and fluid storage and transport. Our relatively simple
Magnetization dynamics and spin pumping induced by standing elastic waves
Azovtsev, A. V.; Pertsev, N. A.
2016-11-01
The magnetization dynamics induced by standing elastic waves excited in a thin ferromagnetic film is described with the aid of micromagnetic simulations taking into account the magnetoelastic coupling between spins and lattice strains. Our calculations are based on the numerical solution of the Landau-Lifshitz-Gilbert equation comprising the damping term and the effective magnetic field with all relevant contributions. The simulations have been performed for 2-nm-thick F e81G a19 film dynamically strained by longitudinal and transverse standing waves with various frequencies, which span a wide range around the resonance frequency νres of coherent magnetization precession in unstrained F e81G a19 film. It is found that standing elastic waves give rise to complex local magnetization dynamics and spatially inhomogeneous dynamic patterns in the form of standing spin waves with the same wavelength. Remarkably, the amplitude of magnetization precession does not go to zero at nodes of these spin waves, which cannot be precisely described by simple analytical formulae. In the steady-state regime, magnetization oscillates with the frequency of the elastic wave, except in the case of longitudinal waves with frequencies well below νres, where the magnetization precesses with variable frequency strongly exceeding the wave frequency. The results obtained for the magnetization dynamics driven by elastic waves are used to calculate the spin current pumped from the dynamically strained ferromagnet into adjacent paramagnetic metal. Numerical calculations demonstrate that the transverse charge current in the paramagnetic layer, which is created by the spin current via inverse spin Hall effect, is high enough to be measured experimentally.
The Testability of Maximum Magnitude
Clements, R.; Schorlemmer, D.; Gonzalez, A.; Zoeller, G.; Schneider, M.
2012-12-01
Recent disasters caused by earthquakes of unexpectedly large magnitude (such as Tohoku) illustrate the need for reliable assessments of the seismic hazard. Estimates of the maximum possible magnitude M at a given fault or in a particular zone are essential parameters in probabilistic seismic hazard assessment (PSHA), but their accuracy remains untested. In this study, we discuss the testability of long-term and short-term M estimates and the limitations that arise from testing such rare events. Of considerable importance is whether or not those limitations imply a lack of testability of a useful maximum magnitude estimate, and whether this should have any influence on current PSHA methodology. We use a simple extreme value theory approach to derive a probability distribution for the expected maximum magnitude in a future time interval, and we perform a sensitivity analysis on this distribution to determine if there is a reasonable avenue available for testing M estimates as they are commonly reported today: devoid of an appropriate probability distribution of their own and estimated only for infinite time (or relatively large untestable periods). Our results imply that any attempt at testing such estimates is futile, and that the distribution is highly sensitive to M estimates only under certain optimal conditions that are rarely observed in practice. In the future we suggest that PSHA modelers be brutally honest about the uncertainty of M estimates, or must find a way to decrease its influence on the estimated hazard.
Alternative Multiview Maximum Entropy Discrimination.
Chao, Guoqing; Sun, Shiliang
2016-07-01
Maximum entropy discrimination (MED) is a general framework for discriminative estimation based on maximum entropy and maximum margin principles, and can produce hard-margin support vector machines under some assumptions. Recently, the multiview version of MED multiview MED (MVMED) was proposed. In this paper, we try to explore a more natural MVMED framework by assuming two separate distributions p1( Θ1) over the first-view classifier parameter Θ1 and p2( Θ2) over the second-view classifier parameter Θ2 . We name the new MVMED framework as alternative MVMED (AMVMED), which enforces the posteriors of two view margins to be equal. The proposed AMVMED is more flexible than the existing MVMED, because compared with MVMED, which optimizes one relative entropy, AMVMED assigns one relative entropy term to each of the two views, thus incorporating a tradeoff between the two views. We give the detailed solving procedure, which can be divided into two steps. The first step is solving our optimization problem without considering the equal margin posteriors from two views, and then, in the second step, we consider the equal posteriors. Experimental results on multiple real-world data sets verify the effectiveness of the AMVMED, and comparisons with MVMED are also reported.
Measurement of Elastic Modulus of Collagen Type I Single Fiber.
Pavel Dutov
Full Text Available Collagen fibers are the main components of the extra cellular matrix and the primary contributors to the mechanical properties of tissues. Here we report a novel approach to measure the longitudinal component of the elastic moduli of biological fibers under conditions close to those found in vivo and apply it to type I collagen from rat tail tendon. This approach combines optical tweezers, atomic force microscopy, and exploits Euler-Bernoulli elasticity theory for data analysis. This approach also avoids drying for measurements or visualization, since samples are freshly extracted. Importantly, strains are kept below 0.5%, which appear consistent with the linear elastic regime. We find, surprisingly, that the longitudinal elastic modulus of type I collagen cannot be represented by a single quantity but rather is a distribution that is broader than the uncertainty of our experimental technique. The longitudinal component of the single-fiber elastic modulus is between 100 MPa and 360 MPa for samples extracted from different rats and/or different parts of a single tail. Variations are also observed in the fibril-bundle/fibril diameter with an average of 325±40 nm. Since bending forces depend on the diameter to the fourth power, this variation in diameter is important for estimating the range of elastic moduli. The remaining variations in the modulus may be due to differences in composition of the fibril-bundles, or the extent of the proteoglycans constituting fibril-bundles, or that some single fibrils may be of fibril-bundle size.
Wu, Shuying; Ladani, Raj B; Zhang, Jin; Ghorbani, Kamran; Zhang, Xuehua; Mouritz, Adrian P; Kinloch, Anthony J; Wang, Chun H
2016-09-21
Strain sensors with high elastic limit and high sensitivity are required to meet the rising demand for wearable electronics. Here, we present the fabrication of highly sensitive strain sensors based on nanocomposites consisting of graphene aerogel (GA) and polydimethylsiloxane (PDMS), with the primary focus being to tune the sensitivity of the sensors by tailoring the cellular microstructure through controlling the manufacturing processes. The resultant nanocomposite sensors exhibit a high sensitivity with a gauge factor of up to approximately 61.3. Of significant importance is that the sensitivity of the strain sensors can be readily altered by changing the concentration of the precursor (i.e., an aqueous dispersion of graphene oxide) and the freezing temperature used to process the GA. The results reveal that these two parameters control the cell size and cell-wall thickness of the resultant GA, which may be correlated to the observed variations in the sensitivities of the strain sensors. The higher is the concentration of graphene oxide, then the lower is the sensitivity of the resultant nanocomposite strain sensor. Upon increasing the freezing temperature from -196 to -20 °C, the sensitivity increases and reaches a maximum value of 61.3 at -50 °C and then decreases with a further increase in freezing temperature to -20 °C. Furthermore, the strain sensors offer excellent durability and stability, with their piezoresistivities remaining virtually unchanged even after 10 000 cycles of high-strain loading-unloading. These novel findings pave the way to custom design strain sensors with a desirable piezoresistive behavior.
Equilibrium theory for braided elastic filaments
van der Heijden, Gert
Motivated by supercoiling of DNA and other filamentous structures, we formulate a theory for equilibria of 2-braids, i.e., structures formed by two elastic rods winding around each other in continuous contact and subject to a local interstrand interaction. Unlike in previous work no assumption is made on the shape of the contact curve. Rather, this shape is found as part of the solution. The theory is developed in terms of a moving frame of directors attached to one of the strands with one of the directors pointing to the position of the other strand. The constant-distance constraint is automatically satisfied by the introduction of what we call braid strains. The price we pay is that the potential energy involves arclength derivatives of these strains, thus giving rise to a second-order variational problem. The Euler-Lagrange equations for this problem give balance equations for the overall braid force and moment referred to the moving frame as well as differential equations that can be interpreted as effective constitutive relations encoding the effect that the second strand has on the first as the braid deforms under the action of end loads. Simple analytical cases are discussed first and used as starting solutions in parameter continuation studies to compute classes of both open and closed (linked or knotted) braid solutions.
Nematic order by elastic interactions and rigidity sensing of living cells
Friedrich, Benjamin M
2010-01-01
We predict spontaneous nematic order in an ensemble of active force generators with elastic interactions as a minimal model for early cytoskeletal self-polarization. Mean-field theory is formally equivalent to Maier-Saupe theory for a nematic liquid. However, the elastic interactions are long-ranged (and thus depend on cell shape and matrix elasticity) and originate in cell activity. Depending on the density of force generators, we find two regimes of cellular rigidity sensing for which nematic order depends on matrix rigidity either in a step-like manner or with a maximum at an optimal rigidity.
Revisit of the relationship between the elastic properties and sound velocities at high pressures
Wang, Chenju; Xiang, Shikai; Gu, Jianbing; Kuang, Xiaoyu; Yu, Yin; Yan, Xiaozhen; Chen, Haiyan
2014-09-01
The second-order elastic constants and stress-strain coefficients are defined, respectively, as the second derivatives of the total energy and the first derivative of the stress with respect to strain. Since the Lagrangian and infinitesimal strain are commonly used in the two definitions above, the second-order elastic constants and stress-strain coefficients are separated into two categories, respectively. In general, any of the four physical quantities is employed to characterize the elastic properties of materials without differentiation. Nevertheless, differences may exist among them at non-zero pressures, especially high pressures. Having explored the confusing issue systemically in the present work, we find that the four quantities are indeed different from each other at high pressures and these differences depend on the initial stress applied on materials. Moreover, the various relations between the four quantities depicting elastic properties of materials and high-pressure sound velocities are also derived from the elastic wave equations. As examples, we calculated the high-pressure sound velocities of cubic tantalum and hexagonal rhenium using these nexus. The excellent agreement of our results with available experimental data suggests the general applicability of the relations.
High-pressure elasticity of stishovite and the P42/mnm ⇌ Pnnm phase transition
Carpenter, Michael A.; Hemley, Russell J.; Mao, Ho-Kwang
2000-05-01
A Landau free energy expansion has been developed to describe the elastic constant variations of stishovite (SiO2) associated with the P42/mnm (rutile-type) ⇌ Pnnm (CaCl2-type) phase transition as a function of pressure. The transition appears to display classical second-order character, with an equilibrium transition pressure which is renormalized by coupling of the soft optic mode with spontaneous strain. Lattice parameter data from the literature show that the symmetry breaking strain is large, while the nonsymmetry breaking strains are small. These have been used to constrain the numerical values of the strain/order parameter coupling coefficients, which in turn have been used to constrain values for the Landau coefficients. When substituted into expressions for all the individual elastic constants, taking values for experimental and calculated values of the bare elastic constants from the literature, a clear view of the pattern of elastic constant variations is produced. Variations of P and S wave velocities derived from the calculated elastic constants for a second-order transition show a dip as the transition point is approached from high pressure and from low pressure but do not show a discontinuity. The velocity anomaly provides a signature for the presence of free silica in the lower mantle.
Dynamics of Elastic Excitable Media
Cartwright, J H E; Hernández-García, E; Piro, O; Cartwright, Julyan H. E.; Eguiluz, Victor M.; Hernandez-Garcia, Emilio; Piro, Oreste
1999-01-01
The Burridge-Knopoff model of earthquake faults with viscous friction is equivalent to a van der Pol-FitzHugh-Nagumo model for excitable media with elastic coupling. The lubricated creep-slip friction law we use in the Burridge-Knopoff model describes the frictional sliding dynamics of a range of real materials. Low-dimensional structures including synchronized oscillations and propagating fronts are dominant, in agreement with the results of laboratory friction experiments. Here we explore the dynamics of fronts in elastic excitable media.
Dynamics of elastic interactions in soft and biological matter
Yuval, Janni; Safran, Samuel A.
2013-04-01
Cells probe their mechanical environment and can change the organization of their cytoskeletons when the elastic and viscous properties of their environment are modified. We use a model in which the forces exerted by small, contractile acto-myosin filaments (e.g., nascent stress fibers in stem cells) on the extracellular matrix are modeled as local force dipoles. In some cases, the strain field caused by these force dipoles propagates quickly enough so that only static elastic interactions need be considered. On the other hand, in the case of significant energy dissipation, strain propagation is slower and may be eliminated completely by the relaxation of the cellular cytoskeleton (e.g., by cross-link dissociation). Here, we consider several dissipative mechanisms that affect the propagation of the strain field in adhered cells and consider these effects on the interaction between force dipoles and their resulting mutual orientations. This is a first step in understanding the development of orientational (nematic) or layering (smectic) order in the cytoskeleton. We use the theory to estimate the propagation time of the strain fields over a cellular distance for different mechanisms and find that in some cases it can be of the order of seconds, thus competing with the cytoskeletal relaxation time. Furthermore, for a simple system of two force dipoles, we predict that in some cases the orientation of force dipoles might change significantly with time, e.g., for short times the dipoles exhibit parallel alignment while for later times they align perpendicularly.
The role of beneficial bacteria wall elasticity in regulating innate immune response.
Мokrozub, Viktoria V; Lazarenko, Liudmyla M; Sichel, Liubov M; Babenko, Lidia P; Lytvyn, Petro M; Demchenko, Olga M; Melnichenko, Yulia O; Boyko, Nadiya V; Biavati, Bruno; DiGioia, Diana; Bubnov, Rostyslav V; Spivak, Mykola Ya
2015-01-01
Probiotics have great potential to contribute to development of healthy dietary regimes, preventive care, and an integrated approach to immunity-related disease management. The bacterial wall is a dynamic entity, depending on many components and playing an essential role in modulating immune response. The impact of cell wall elasticity on the beneficial effects of probiotic strains has not been sufficiently studied. The aim was to investigate the effect of lactic acid bacteria (LAB) and bifidobacteria strains on phagocytic system cells (macrophages) as related to bacterial wall elasticity, estimated using atomic force microscopy (AFM). We conducted studies on Balb/c line mice 18-20 g in weight using lyophilized strains of LAB-Lactobacillus acidophilus IMV B-7279, Lactobacillus casei IMV B-7280, Lactobacillus delbrueckii subsp. bulgaricus IMV B-7281, and bifidobacteria-Bifidobacterium animalis VKL and Bifidobacterium animalis VKB. We cultivated the macrophages obtained from the peritoneal cavity of mice individually with the strains of LAB and bifidobacteria and evaluated their effect on macrophages, oxygen-dependent bactericidal activity, nitric oxide production, and immunoregulatory cytokines. We used AFM scanning to estimate bacterial cell wall elasticity. All strains had a stimulating effect on the functional activity of macrophages and ability to produce NO/NO2 in vitro. Lactobacilli strains increased the production of IL-12 and IFN-γ in vitro. The AFM demonstrated different cell wall elasticity levels in various strains of LAB and bifidobacteria. The rigidity of the cell walls among lactobacilli was distributed as follows: Lactobacillus acidophilus IMV B-7279 > Lactobacillus casei IMV B-7280 > Lactobacillus delbrueckii subsp. bulgaricus IMV B-7281; among the strains of bifidobacteria: B. animalis VKB > B. animalis VKL. Probiotic strain survival in the macrophages depended on the bacterial cell wall elasticity and on the time of their joint cultivation. LAB
Extension of elastic stiffness formula for leaf type holddown spring assembly
Song, Kee Nam; Kang, Heung Seok; Yoon, Kyung Ho; Kim, Hyung Kyu [Korea Atomic Energy Research Institute, Taejon (Korea)
1998-09-01
Based on the Euler beam theory and the strain energy method, an elastic stiffness formula of the holddown spring assembly consisting of several leaves was previously derived. The formula was known to be useful to estimate the elastic stiffness of the holddown spring assembly only with the geometric data and the material properties of the leaf. Recently, it was reported that the elastic stiffness from the formula deviated much from the test results as the number of leaves was increased. In this study, in order to resolve such an increasing deviation as the increasing number of leaves, the formula has been extended to be able to consider normal forces and friction forces acting on interfaces between the leaves. The elastic stiffness analysis on specimens of leaf type holddown springs has been carried out using the extended formula and the analysis results are compared with the test results. As a result of comparisons, it is found that the extended formula is able to evaluate the elastic stiffness of the holddown spring assembly within an error range of 10%, irrespective of the number of leaves. In addition, it is found that the effect of shear forces and axial forces on the elastic stiffness of the holddown spring assembly is only below 0.2% of the elastic stiffness, and therefore the greatest portion of the elastic stiffness of the holddown spring assembly is attributed to the bending moment. (author). 13 refs., 10 figs., 12 tabs.
Martin, S.E.; Newman, J.B.
1980-11-01
A thermomechanical theory of large deformation elastic-inelastic material behavior is developed which is based on a multiplicative decomposition of the strain. Very general assumptions are made for the elastic and inelastic constitutive relations and effects such as thermally-activated creep, fast-neutron-flux-induced creep and growth, annealing, and strain recovery are compatible with the theory. Reduced forms of the constitutive equations are derived by use of the second law of thermodynamics in the form of the Clausius-Duhem inequality. Observer invariant equations are derived by use of an invariance principle which is a generalization of the principle of material frame indifference.
Reches, Z.; Dieterich, J.H.
1983-01-01
The dependence of the number of sets of faults and their orientation on the intermediate strain axis is investigated through polyaxial tests, reported here, and theoretical analysis, reported in an accompanying paper. In the experiments, cubic samples of Berea sandstone, Sierra-White and Westerly granites, and Candoro and Solnhofen limestones were loaded on their three pairs of faces by three independent, mutually perpendicular presses at room temperature. Two of the presses were servo-controlled and applied constant displacement rates throughout the experiment. Most samples display three or four sets of faults in orthorhombic symmetry. These faults form in several yielding events that follow a stage of elastic deformation. In many experiments, the maximum and the intermediate compressive stresses interchange orientations during the yielding events, where the corresponding strains are constant. The final stage of most experiments is characterized by slip along the faults. ?? 1983.
Cacti with maximum Kirchhoff index
Wang, Wen-Rui; Pan, Xiang-Feng
2015-01-01
The concept of resistance distance was first proposed by Klein and Randi\\'c. The Kirchhoff index $Kf(G)$ of a graph $G$ is the sum of resistance distance between all pairs of vertices in $G$. A connected graph $G$ is called a cactus if each block of $G$ is either an edge or a cycle. Let $Cat(n;t)$ be the set of connected cacti possessing $n$ vertices and $t$ cycles, where $0\\leq t \\leq \\lfloor\\frac{n-1}{2}\\rfloor$. In this paper, the maximum kirchhoff index of cacti are characterized, as well...
Generic maximum likely scale selection
Pedersen, Kim Steenstrup; Loog, Marco; Markussen, Bo
2007-01-01
The fundamental problem of local scale selection is addressed by means of a novel principle, which is based on maximum likelihood estimation. The principle is generally applicable to a broad variety of image models and descriptors, and provides a generic scale estimation methodology. The focus...... on second order moments of multiple measurements outputs at a fixed location. These measurements, which reflect local image structure, consist in the cases considered here of Gaussian derivatives taken at several scales and/or having different derivative orders....
Detachable endoloop vs. elastic band ligation for bleeding esophageal varices.
Naga, Mazen Ibrahim; Okasha, Hussein Hassan; Foda, Ayman Ragaei; Gomaa, Mohamed Saeed; Fouad, Ayman Mohamed; Masoud, Amgad Gerges; El-din, Hazem Hossam
2004-06-01
Variceal bleeding is a serious complication with a mortality rate that ranges from 20% to 50%. Patients who have variceal hemorrhage usually are treated by endoscopic injection sclerotherapy or elastic band ligation to eradicate the varices. Endoloop ligation is a newly developed technique for achieving hemostasis and variceal eradication. This study compared endoloop ligation with elastic band ligation in patients with acute esophageal variceal bleeding. Fifty patients with acute esophageal variceal bleeding were recruited: 25 were treated by elastic band ligation and 25 by endoloop ligation. Although the number of patients in whom bleeding recurred during a follow-up period of 6 months was smaller in the endoloop group (12%) vs. the band group (28%), this difference was not statistically significant. Furthermore, no statistically significant difference was found between the two groups with respect to the number of patients in whom variceal eradication was achieved, the number of treatment sessions required for variceal eradication, or the frequency of variceal recurrence. The total cost for variceal obliteration by endoloop ligation was 342 dollars per patient, whereas, the total cost of variceal eradication by elastic band ligation was 356 dollars per patient. The endoloop had certain technical advantages over band application: a better field of vision, tighter application, good results with junctional varices, and a lack of strain exerted by the device on the endoscope. Endoloop ligation is a promising new technique for management of patients with bleeding esophageal varices.
Elastic Sag Property of Low Carbon Martensite Spring Steel
LI Ye-sheng; CHEN Mi-song; WU Zi-ping; ZHU Yin-lu; DUO Tie-yun
2004-01-01
This paper studies the elastic sag resistance of new low-carbon martensite spring steel 35Si2CrVB developed recently and points out that the cause of elastic sag is attributed to cyclic softening of spring steel engendered during its serving,also considers that elastic sag property should be evaluated by dynamic mechanical properties of spring material such as dynamic yield strength σ'0.2, ratio of dynamic yield strength σ'0.2 vs. tensile strength σb (σ'0.2/σb) and ratio of dynamic yield strength σ' 0.2vs. static yield strengthσ0.2 (σ'0.2/σ0. 2 )etc. , which are measured by the cyclic stress-strain curve test. Compared with conventional spring steel 60Si2MnA, 35Si2CrVB has good advantages in both dynamic and static properties, which show it possesses higher elastic sag resistance than 60Si2MnA because of its lath-martensite structure tempering in low temperature different from 60Si2MnA steel's plate martensite structure tempering inmedium temperature. So it can be demonstrated that low carbon martensite spring steel is more appropriate for the demands of spring.
Characterisation of elastic turbulence in a serpentine micro-channel
Souliès, Antoine; Aubril, Julien; Castelain, Cathy; Burghelea, Teodor
2017-08-01
A systematic experimental investigation of the onset, development, and statistical and scaling properties of elastic turbulence in a curvilinear micro-channel of a dilute solution of a high molecular weight polymer is presented. By measurements of time series of high spatial resolution flow fields performed over a time 320 times longer than the average relaxation, we show that the transition to elastic turbulence occurs via an imperfect bifurcation. Slightly above the onset of the primary elastic instability, rare events manifested through a local deceleration of the flow are observed. By measurements of the spatial distributions and statistics of the second invariant of the rate of strain tensor, we show that the main prediction of the theory regarding the saturation of root mean square of fluctuations of the velocity gradients is qualitatively verified though a quantitative agreement could not be found. A systematic analysis of the statistics of the fluctuations of flow fields in terms of spatial and temporal correlations, power spectra, and probability distributions is presented. The scaling properties of structure functions of the increments of the velocity gradients are discussed. Our experimental findings call for further developments of the theory of elastic turbulence in bounded flow channels.
Intergranular strains in textured steel
Daymond, M.R. [Los Alamos Neutron Science Center (LANSCE), Los Alamos, NM (United States); Tome, C.N. [Los Alamos National Lab., NM (United States). Materials Science and Technology Div.; Bourke, M.A.M. [Los Alamos Neutron Science Center (LANSCE), Los Alamos, NM (United States); Los Alamos National Lab., NM (United States). Materials Science and Technology Div.
2000-07-01
Tensile specimens were machined from heat treated austenitic stainless steel plate prior to and after 70% reduction by uni-directional rolling. In addition to a specimen from the as-received plate, two specimens were cut from the rolled plate, with axes parallel and perpendicular to the rolling direction respectively. In situ measurements of the strain response of multiple hkl lattice planes to an applied uniaxial tensile load were made using neutron diffraction. The experimental results are compared with predictions from a self-consistent Hill-Hutchinson model. The measured texture in the plate was approximately 3 times random, however its effect on the hkl response was small compared to the residual strains left by rolling. The apparent elastic modulus and Poisson's ratios of the planes is affected by the residual strains, which is attributed to the effect of micro-plasticity. Interpretation of residual stress measurements is considered in light of these results. (orig.)
Elastically stretchable thin film conductors on an elastomeric substrate
Jones Harris, Joyelle Elizabeth
Imagine a large, flat screen television that can be rolled into a small cylinder after purchase in the store and then unrolled and mounted onto the wall of a home. The electronic devices within the television must be able to withstand large deformation and tensile strain. Consider a robot that is covered with an electronic skin that simulates human skin. The skin would enable the machine to lift an elderly person with care and sensitivity. The skin will endure repeated deformation with the highest tensile strains being experienced at the robot's joints. These applications and many others will benefit from stretchable electronic circuitry. While several different methods have been employed to create stretchable electronics, all methods use a common tool -- stretchable conductors. Therefore, the goal of this thesis work was to fabricate elastically stretchable conductors that can be used in stretchable electronics. We deposited Au thin films on an elastomeric substrate, and the resulting conductors remained electrically continuous when stretched by 30% and more. We developed photolithographic processes that can be used to pattern elastically stretchable conductors with a 10 mum resolution. We fabricated bi-level stretchable conductors that are separated by an elastomeric insulator and are electrically connected through via holes in the insulator. We applied our bi-level conductors to create a stretchable resistor-inductor-capacitor (RLC) circuit with a tunable resonant frequency. We also used stretchable conductors to measure action potentials in biological samples. This thesis describes the fabrication and application of our elastically stretchable conductors.
Pilot Study of Debt Elasticity
Greiner, Keith; Girardi, Tony
2006-01-01
This report examines the relationship between student loan debt and the manner in which that debt is described. It focuses on three forms of description: (1) monthly payments, (2) total debt, and (3) income after graduation. The authors used the term elasticity to describe the relationship between consumers' college choices and the retention…
Mechanistic Constitutive Models for Rubber Elasticity and Viscoelasticity
Puso, M
2003-01-21
Physically based models which describe the finite strain behavior of vulcanized rubber are developed. Constitutive laws for elasticity and viscoelasticity are derived by integrating over orientation space the forces due to each individual polymer chain. A novel scheme is presented which effectively approximates these integrals in terms of strain and strain invariants. In addition, the details involving the implementation of such models into a quasi-static large strain finite element formulation are provided. In order to account for the finite extensibility of a molecular chain, Langevin statistics is used to model the chain response. The classical statistical model of rubber assumes that polymer chains interact only at the chemical crosslinks. It is shown that such model when fitted for uniaxial tension data cannot fit compression or equibiaxial data. A model which incorporates the entanglement interactions of surrounding chains, in addition to the finite extensibility of the chains, is shown to give better predictions than the classical model. The technique used for approximating the orientation space integral was applied to both the classical and entanglement models. A viscoelasticity model based on the force equilibration process as described by Doi and Edwards is developed. An assumed form for the transient force in the chain is postulated. The resulting stress tensor is composed of an elastic and a viscoelastic portion with the elastic stress given by the proposed entanglement model. In order to improve the simulation of experimental data, it was found necessary to include the effect of unattached or dangling polymer chains in the viscoelasticity model. The viscoelastic effect of such chains is the manifestation of a disengagement process. This disengagement model for unattached polymer chains motivated an empirical model which was very successful in simulating the experimental results considered.
Economics and Maximum Entropy Production
Lorenz, R. D.
2003-04-01
Price differentials, sales volume and profit can be seen as analogues of temperature difference, heat flow and work or entropy production in the climate system. One aspect in which economic systems exhibit more clarity than the climate is that the empirical and/or statistical mechanical tendency for systems to seek a maximum in production is very evident in economics, in that the profit motive is very clear. Noting the common link between 1/f noise, power laws and Self-Organized Criticality with Maximum Entropy Production, the power law fluctuations in security and commodity prices is not inconsistent with the analogy. There is an additional thermodynamic analogy, in that scarcity is valued. A commodity concentrated among a few traders is valued highly by the many who do not have it. The market therefore encourages via prices the spreading of those goods among a wider group, just as heat tends to diffuse, increasing entropy. I explore some empirical price-volume relationships of metals and meteorites in this context.
Sulcus formation in a compressed elastic half space
Biggins, John; Mahadevan, L.
2012-02-01
When a block of rubber, biological tissue or other soft material is subject to substantial compression, its surfaces undergo a folding instability. Rather than having a smooth profile, these folds contain cusps and hence have been called creases or sulcii rather than wrinkles. The stability of a compressed surface was first investigated by Biot (1965), assuming the strains associated with the instability were small. However, the compression threshold predicted with this approach is substantially too high. I will introduce a family of analytic area preserving maps that contain cusps (and hence points of infinite strain) that save energy before the linear stability threshold even at vanishing amplitude. This establishes that there is a region before the linear stability threshold is reached where the system is unstable to infinitesimal perturbations, but that this instability is quintessentially non-linear and cannot be found with linear strain elasticity.
Schweizer, Kenneth S.; Sussman, Daniel M.
2016-12-01
We employ a first-principles-based, force-level approach to construct the anharmonic tube confinement field for entangled fluids of rigid needles, and also for chains described at the primitive-path (PP) level in two limiting situations where chain stretch is assumed to either be completely equilibrated or unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a self-consistent analysis of transverse polymer harmonic dynamical fluctuations predicts that deformation-induced orientation leads to tube weakening or widening. In contrast, for deformed polymers in which chain stretch does not relax, we find tube strengthening or compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear elastic limit, and the possibility of a "microscopic absolute yielding" event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance occurs at a stress of order the equilibrium shear modulus and a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from elastic to irreversible viscous response requires chain retraction to initiate disentanglement. We qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments.
Spin and elastic contributions to isothermal entropy change
Mukherjee, T.; Skomski, R.; Michalski, S.; Sellmyer, D. J.; Binek, Ch.
2012-04-01
Statistical considerations of ensembles of localized magnetic moments reveal an upper bound of the isothermal entropy change when only the magnetic degrees of freedom are considered. In this case, the maximum molar isothermal entropy change is determined by the spin multiplicity and is equal to Rln(2J + 1), where J is the angular momentum of an individual atom. However, in materials with giant magnetocaloric effect, the isothermal field-induced entropy change goes beyond the spin-multiplicity limit due to field-activated elastic degrees of freedom. Recently, we investigated a model of pairs of exchange-coupled Ising spins with variable real-space positions. We showed, within a classical approximation for the elastic degree of freedom, that a vibrational entropy contribution can be activated via applied magnetic fields. Here we quantify the impact of quantum corrections in the low-temperature limit. We compare calculations that include elastic interaction with the rigid exchange model in the high-temperature limit. We find that quantum effects provide quantitative corrections in the low-temperature limit. In addition we show that the elastic contributions to the isothermal entropy change can be additive but, remarkably, it can also give rise to reduced isothermal entropy change in certain temperature regions.
Elastic modulus of posts and the risk of root fracture.
Meira, Josete B C; Espósito, Camila O M; Quitero, Mayra F Z; Poiate, Isis A V P; Pfeifer, Carmem Silvia C; Tanaka, Carina B; Ballester, Rafael Y
2009-08-01
The definition of an optimal elastic modulus for a post is controversial. This work hypothesized that the influence of the posts' elastic modulus on dentin stress concentration is dependent on the load direction. The objective was to evaluate, using finite element analysis, the maximum principal stress (sigma(max)) on the root, using posts with different elastic modulus submitted to different loading directions. Nine 3D models were built, representing the dentin root, gutta-percha, a conical post and the cortical bone. The softwares used were: MSC.PATRAN2005r2 (preprocessing) and MSC.Marc2005r2 (processing). Load of 100 N was applied, varying the directions (0 degrees, 45 degrees and 90 degrees) in relation to the post's long axis. The magnitude and direction of the sigma(max) were recorded. At the 45 degrees and 90 degrees loading, the highest values of sigma(max) were recorded for the lowest modulus posts, on the cervical region, with a direction that suggests debonding of the post. For the 0 degrees loading, the highest values of sigma(max) were recorded for higher modulus posts, on the apical region, and the circumferential direction suggests vertical root fracture. The hypothesis was accepted: the effect of the elastic modulus on the magnitude and direction of the sigma(max) generated on the root was dependent on the loading direction.
Eulerian Formulation of Spatially Constrained Elastic Rods
Huynen, Alexandre
by means of either its relative position with respect to the constraint axis (contact-free segments) or its angular position on the constraint surface (continuous contacts.) This formulation circumvents both drawbacks that afflict the conventional Lagrangian approach associated with the segmentation strategy. As the a priori unknown domain, viz. the rod length, is substituted for the known constraint axis, the free boundary problem and the associated isoperimetric constraints are converted into a classical two-point boundary value problem. Additionally, the description of the rod deflection by means of its eccentricity with respect to the constraint axis trivializes the assessment of the unilateral contact condition. Along continuous contacts, this formulation expresses the strain variables, measuring the rod change of shape, in terms of the geometric invariants of the constraint surface, and emphasizes the influence of the constraint local geometry on the reaction pressure. Formalizing the segmentation strategy, a computational model that exploits the Eulerian formulation of the rod governing equations is devised. To solve the quasi-static deflection of elastic rods constrained inside or around a tube-like surface, this computational model identifies the number of contacts, their nature (either discrete or continuous), and the rod configuration at the connections that satisfies the unilateral contact condition and preserves the rod integrity along the sequence of elementary problems.
Heart transplantation and arterial elasticity
Colvin-Adams M
2013-12-01
Full Text Available Monica Colvin-Adams,1 Nonyelum Harcourt,1 Robert LeDuc,2 Ganesh Raveendran,1 Yassir Sonbol,3 Robert Wilson,1 Daniel Duprez11Cardiovascular Division, University of Minnesota, Minneapolis, MN, USA; 2Division of Biostatistics University of Minnesota, Minneapolis, MN, USA; 3Cardiovascular Division, St Luke's Hospital System, Sugar Land, TX, USAObjective: Arterial elasticity is a functional biomarker that has predictive value for cardiovascular morbidity and mortality in nontransplant populations. There is little information regarding arterial elasticity in heart transplant recipients. This study aimed to characterize small (SAE and large (LAE artery elasticity in heart transplant recipients in comparison with an asymptomatic population free of overt cardiovascular disease. A second goal was to identify demographic and clinical factors associated with arterial elasticity in this unique population.Methods: Arterial pulse waveform was registered noninvasively at the radial artery in 71 heart transplant recipients between 2008 and 2010. SAEs and LAEs were derived from diastolic pulse contour analysis. Comparisons were made to a healthy cohort of 1,808 participants selected from our prevention clinic database. Multiple regression analyses were performed to evaluate associations between risk factors and SAE and LAE within the heart transplant recipients.Results: LAE and SAE were significantly lower in heart transplant recipients than in the normal cohort (P <0.01 and P < 0.0001, respectively. Female sex and history of ischemic cardiomyopathy were significantly associated with reduced LAE and SAE. Older age and the presence of moderate cardiac allograft vasculopathy were also significantly associated with reduced SAE. Transplant duration was associated with increased SAE.Conclusion: Heart transplants are associated with peripheral endothelial dysfunction and arterial stiffness, as demonstrated by a significant reduction in SAE and LAE when compared with a
Strain solitons in solids and how to construct them
Samsonov, Alexander M
2001-01-01
Although the theory behind solitary waves of strain shows that they hold significant promise in nondestructive testing and a variety of other applications, an enigma has long persisted-the absence of observable elastic solitary waves in practice. Inspired by this apparent contradiction, Strain Solitons in Solids and How to Construct Them refines the existing theory, explores how to construct a powerful deformation pulse in a waveguide without plastic flow or fracture, and proposes a direct method of strain soliton generation, detection, and observation.The author focuses on the theory, simulation, generation, and propagation of strain solitary waves in a nonlinearly elastic, straight cylindrical rod under finite deformations. He introduces the general theory of wave propagation in nonlinearly elastic solids and shows, from first principles, how its main ideas can lead to successful experiments. In doing so, he develops a new approach to solving the corresponding doubly dispersive equation (DDE) with dissipati...
Thermodynamic parameters of elasticity and electrical conductivity ...
Thermodynamic parameters of elasticity and electrical conductivity of reinforced natural rubber (nr) vulca nizates. ... Bulletin of the Chemical Society of Ethiopia ... The thermodynamic parameters (change in free energy of elasticity, DGe; ...
Elasticity imaging for regularly spaced structures utilizing WT matched filtering method
无
2002-01-01
Based on wavelet transform of time-scale domain, a new strain estimation method is presented to position the regular scatterers, calculate the local scatterer spacing and its change, and estimate the internal strain distribution of tissue mimicking phantom. Simulation and experiment results for uniform and nonuniform phantoms show the internal strain of regularly spaced structures can be estimated accurately using this method and the influence of global boundary condition on the estimated strain distribution can be eliminated by reconstructing the real elasticity distribution. This approach has the potentials to become a valuable tool for the regularly spaced structures.
The role of elasticity in the wetting and adhesion of soft materials
Webber, Rebecca Elisabeth
In this work, the effect of elasticity on the adhesive behavior of soft materials is investigated by studying three model systems: an elastic gel, a viscoelastic hydrogel, and nonelastic liquid interfaces. These systems span the elastic spectrum and represent a wide range of matter in the increasingly important category of soft materials. The first system is a thermally reversible gel made from a triblock copolymer, wherein physical gelation occurs upon dissolution in a selective solvent for the midblock. The triblock copolymer gel is perfectly elastic at room temperature, with debonding behavior affected by the degree of geometric confinement. The effect of confinement on the mechanical and adhesive response of the triblock gels is investigated and quantified using an axisymmetric probe tack test and a compliance-based analysis method. It is found that as confinement increases, the debonding morphology of elastic gels changes, with finger-like interfacial instabilities appearing at very high confinement. Additionally, four dimensionless ratios that predict the tensile detachment behavior of soft materials have been defined as a result of this work. The viscoelastic material is an ionically-crosslinked alginate hydrogel with a strain-dependent mechanical response. These soft hydrogels exhibit elastic behavior at small strains, but possess dissipative ability that allows toughness at higher strains. The stress relaxation and strain hardening behavior of alginate hydrogels has been investigated and quantified using an axisymmetric probe tack apparatus. It was found that stress relaxation serves to regain an elastic response in the hydrogels at strains as high as 4.4 and that permanent deformation is induced above strains of 0.23. A study of the strain-dependent rheological response revealed time-dependent adhesion in these materials. To complete the elastic spectrum, the adhesive interactions created by wetting a polymer surface with various liquids were explored. A
Objects of maximum electromagnetic chirality
Fernandez-Corbaton, Ivan
2015-01-01
We introduce a definition of the electromagnetic chirality of an object and show that it has an upper bound. The upper bound is attained if and only if the object is transparent for fields of one handedness (helicity). Additionally, electromagnetic duality symmetry, i.e. helicity preservation upon scattering, turns out to be a necessary condition for reciprocal scatterers to attain the upper bound. We use these results to provide requirements for the design of such extremal scatterers. The requirements can be formulated as constraints on the polarizability tensors for dipolar scatterers or as material constitutive relations. We also outline two applications for objects of maximum electromagnetic chirality: A twofold resonantly enhanced and background free circular dichroism measurement setup, and angle independent helicity filtering glasses.
Maximum mutual information regularized classification
Wang, Jim Jing-Yan
2014-09-07
In this paper, a novel pattern classification approach is proposed by regularizing the classifier learning to maximize mutual information between the classification response and the true class label. We argue that, with the learned classifier, the uncertainty of the true class label of a data sample should be reduced by knowing its classification response as much as possible. The reduced uncertainty is measured by the mutual information between the classification response and the true class label. To this end, when learning a linear classifier, we propose to maximize the mutual information between classification responses and true class labels of training samples, besides minimizing the classification error and reducing the classifier complexity. An objective function is constructed by modeling mutual information with entropy estimation, and it is optimized by a gradient descend method in an iterative algorithm. Experiments on two real world pattern classification problems show the significant improvements achieved by maximum mutual information regularization.
The strong maximum principle revisited
Pucci, Patrizia; Serrin, James
In this paper we first present the classical maximum principle due to E. Hopf, together with an extended commentary and discussion of Hopf's paper. We emphasize the comparison technique invented by Hopf to prove this principle, which has since become a main mathematical tool for the study of second order elliptic partial differential equations and has generated an enormous number of important applications. While Hopf's principle is generally understood to apply to linear equations, it is in fact also crucial in nonlinear theories, such as those under consideration here. In particular, we shall treat and discuss recent generalizations of the strong maximum principle, and also the compact support principle, for the case of singular quasilinear elliptic differential inequalities, under generally weak assumptions on the quasilinear operators and the nonlinearities involved. Our principal interest is in necessary and sufficient conditions for the validity of both principles; in exposing and simplifying earlier proofs of corresponding results; and in extending the conclusions to wider classes of singular operators than previously considered. The results have unexpected ramifications for other problems, as will develop from the exposition, e.g. two point boundary value problems for singular quasilinear ordinary differential equations (Sections 3 and 4); the exterior Dirichlet boundary value problem (Section 5); the existence of dead cores and compact support solutions, i.e. dead cores at infinity (Section 7); Euler-Lagrange inequalities on a Riemannian manifold (Section 9); comparison and uniqueness theorems for solutions of singular quasilinear differential inequalities (Section 10). The case of p-regular elliptic inequalities is briefly considered in Section 11.
Stress and fold localization in thin elastic membranes
Pocivavsek, Luka; Dellsy, Robert; Kern, Andrew; Johnson, Sebastián; Lin, Binhua; Lee, Ka Yee C.; Cerda, Enrique (Universidad de Santiago); (UC)
2010-11-08
Thin elastic membranes supported on a much softer elastic solid or a fluid deviate from their flat geometries upon compression. We demonstrate that periodic wrinkling is only one possible solution for such strained membranes. Folds, which involve highly localized curvature, appear whenever the membrane is compressed beyond a third of its initial wrinkle wavelength. Eventually the surface transforms into a symmetry-broken state with flat regions of membrane coexisting with locally folded points, reminiscent of a crumpled, unsupported membrane. We provide general scaling laws for the wrinkled and folded states and proved the transition with numerical and experimental supported membranes. Our work provides insight into the interfacial stability of such diverse systems as biological membranes such as lung surfactant and nanoparticle thin films.
Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types
Remillieux, Marcel C.; Guyer, Robert A.; Payan, Cédric; Ulrich, T. J.
2016-03-01
In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. This result could lead to further understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.
Eigen theory of elastic mechanics for anisotropic solids
无
2000-01-01
Eigen characters of the fundamental equations, equilibrium equation of stress and harmony equation of deformation, of the traditional elastic mechanics under geometrical space were testified by means of the concept of standardspace, and the modal equilihrium equation and the modal harmony equation under mechanical space were obtained. Basedon them and the modal Hooke' s law, a new system of the fundamental equation of elastic mechanics is given. The advan-tages of the theory given here are as following: the form of the fundamental equation is in common for both isotropy andanisotropy, both force method and displacement method, both force boundary and displacement boundary; the number ofstress functions is equal to that of the anisotropic subspaces, which avoids the man-made mistakes; the solution of stressfield or strain field is given in form of the modal superimposition, which makes calculation simplified greatly; no matterhow complicated the anisotropy of solids may be, the complete solutions can be obtained.
Structural mechanics and helical geometry of thin elastic composites.
Wada, Hirofumi
2016-09-21
Helices are ubiquitous in nature, and helical shape transition is often observed in residually stressed bodies, such as composites, wherein materials with different mechanical properties are glued firmly together to form a whole body. Inspired by a variety of biological examples, the basic physical mechanism responsible for the emergence of twisting and bending in such thin composite structures has been extensively studied. Here, we propose a simplified analytical model wherein a slender membrane tube undergoes a helical transition driven by the contraction of an elastic ribbon bound to the membrane surface. We analytically predict the curvature and twist of an emergent helix as functions of differential strains and elastic moduli, which are confirmed by our numerical simulations. Our results may help understand shapes observed in different biological systems, such as spiral bacteria, and could be applied to novel designs of soft machines and robots.
Mapping the Strain Distributions in Deformed Bulk Metallic Glasses Using Hard X-Ray Diffraction
Bednarcik, J.; Chen, L. Y.; Wang, X. D.; Jiang, J. Z.; Franz, H.
2012-05-01
The deformation behavior of Cu45 Zr46.5 Al7Ti1.5 bulk metallic glass (BMG) under bending was investigated in-situ using high-energy X-ray synchrotron diffraction. Samples were bent using two different benders with radii of 10 and 20 mm. The components of the strain tensor were determined from the change of positions of the first maximum of the diffracted intensity in reciprocal space. The procedure of data treatment was improved by the introduction of direct beam off-center correction. Comparing results for the two different bending radii, we found that the zero stress region does not necessarily lay within the central part of the specimen. Bending with smaller radius resulted in symmetric strain distribution, whereas a larger bending radius revealed strong asymmetry. Furthermore, bending with a smaller radius (10 mm) shows steeper strain gradients as compared with the situation in which the larger bending radius (20 mm) was used. Using a smaller bending radius implies reaching higher tensile/compressive stresses and reveals the signs of the plastic deformation, which are demonstrated as a saturation of elastic strains.
On Elasticity Measurement in Cloud Computing
Wei Ai
2016-01-01
Full Text Available Elasticity is the foundation of cloud performance and can be considered as a great advantage and a key benefit of cloud computing. However, there is no clear, concise, and formal definition of elasticity measurement, and thus no effective approach to elasticity quantification has been developed so far. Existing work on elasticity lack of solid and technical way of defining elasticity measurement and definitions of elasticity metrics have not been accurate enough to capture the essence of elasticity measurement. In this paper, we present a new definition of elasticity measurement and propose a quantifying and measuring method using a continuous-time Markov chain (CTMC model, which is easy to use for precise calculation of elasticity value of a cloud computing platform. Our numerical results demonstrate the basic parameters affecting elasticity as measured by the proposed measurement approach. Furthermore, our simulation and experimental results validate that the proposed measurement approach is not only correct but also robust and is effective in computing and comparing the elasticity of cloud platforms. Our research in this paper makes significant contribution to quantitative measurement of elasticity in cloud computing.
Some Measurements of Elasticities of Substitution
J. Tinbergen (Jan)
1946-01-01
textabstractSo far, when measuring elasticities of demand, most econometricians have concentrated upon the plain elasticity of total demand for a given commodity. For many important problems we should, in addition, like to know something of "partial elasticities," as I might provisionally call them.
Complementary energy principle for large elastic deformation
GAO; Yuchen
2006-01-01
Using the "base forces" as the fundamental unknowns to determine the state of an elastic system, the complementary energy principle for large elastic deformation is constructed for the conjugate quantities being displacement gradients, which possesses exactly the same form as that of classical linear elasticity. It is revealed that the complementary energy contains deformation part and rotation part.
Role of Elastic Compatibility and Disorder in Texture Evolution in Martensitic Materials.
Kerr, W. C.; Shenoy, S. R.; Saxena, A.; Swart, P. J.; Bishop, A. R.; Killough, M. G.
1997-03-01
Based on a k-space analysis of the 2D elastic compatibility condition, we derive an anisotropic long-range elastic interaction that is responsible for twinning in martensitic materials. This 2D condition is operational only for textures that have nonzero "elastic quadrupole" moment such as twins impinging on a martensite-austenite interface or tweed intersections. The long-range interaction, previously obtained (G.R. Barsch, B. Horovitz, and J.A. Krumhansl, PRL 59, 1251 (1987); PR B 43, 1021 (1991).) by integrating out the elastic fringing field energy contribution in the austenite, is thus shown as a direct consequence of elastic compatibility. Using both annealed and quenched averaging over compositional disorder, we derive an effective cross-gradient elastic energy contribution that is fourth-order in gradient and second-order in strain. The coefficient of this term is negative in a limited temperature range, indicating the presence of tweed texture and its coarsening with cooling. These results are borne out by integration of the equations of motion for rectangular and shear strains, obtained from the Ginzburg-Landau functional with the compatibility condition.
Pseudo-elastic Hysteresis Damping Characteristics of SMA Hybrid Composite Lamina
SUN Shuangshuang; JIANG Xiance; SUN Guojun
2008-01-01
The longitudinal mechanical behavior of shape memory alloy (SMA) composite lamina subjected to longitudinally strain or stress controlled cyclic loading is investigated. The SMA is under pseudo-elastic condition and the fibers are embedded (bonded) to the host material. The influences of temperature, volume fraction of SMA and longitudinal modulus of the host material on the stress-strain relation and energy dissipation of the SMA hybrid composite lamina are discussed. The results indicate that the stress-strain curve of the lamina per cycle shows a hysteresis loop. The hysteresis damping decreases with increasing temperature and with decreasing volume fractions of SMA. In addition, the hysteresis damping is nearly independent of the longitudinal modulus of the host material under strain controlled loading. However, it depends dramatically on the longitudinal modulus of the host material under stress controlled loading, which shows the SMA composite lamina has high pseudo-elastic hysteresis damping when the longitudinal modulus of the host material is low.
Finite element formulations for problems of large elastic-plastic deformation
Mcmeeking, R. M.; Rice, J. R.
1974-01-01
An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is suited to isotropically hardening Prandtl-Reuss materials. The formulation is given in a manner which allows any conventional finite element program, for "small strain" elasticplastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. A unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures, and a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain.
In-situ neutron diffraction of LaCoO3 perovskite under uniaxial compression. II. Elastic properties
Lugovy, Mykola; Aman, Amjad; Chen, Yan; Orlovskaya, Nina; Kuebler, Jakob; Graule, Thomas; Reece, Michael J.; Ma, Dong; Stoica, Alexandru D.; An, Ke
2014-07-01
Calculations of elastic constants and development of elastic anisotropy under uniaxial compression in originally isotropic polycrystalline LaCoO3 perovskite are reported. The lattice strains in individual (hkl) planes as well as average lattice strain were determined both for planes oriented perpendicular and parallel to the loading direction using in-situ neutron diffraction. Utilizing average lattice strains as well as lattice strains along the a and c crystallographic directions, an attempt was made to determine Poisson's ratio of LaCoO3, which was then compared with that measured using an impulse excitation technique. The elastic constants were calculated and Young's moduli of LaCoO3 single crystal in different crystallographic directions were estimated.
Lugovy, Mykola [Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, Florida 32816 (United States); Institute for Problems of Materials Science, Kiev 03142 (Ukraine); Aman, Amjad; Orlovskaya, Nina, E-mail: Nina.Orlovskaya@ucf.edu [Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, Florida 32816 (United States); Chen, Yan [Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, Florida 32816 (United States); Chemical and Engineering Materials Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States); Kuebler, Jakob; Graule, Thomas [Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for High Performance Ceramics, Ueberlandstrasse 129, 8600 Duebendorf (Switzerland); Reece, Michael J. [The School of Engineering and Materials Science, Queen Mary, University of London, London E1 4NS (United Kingdom); Ma, Dong; Stoica, Alexandru D.; An, Ke [Chemical and Engineering Materials Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)
2014-07-07
Calculations of elastic constants and development of elastic anisotropy under uniaxial compression in originally isotropic polycrystalline LaCoO{sub 3} perovskite are reported. The lattice strains in individual (hkl) planes as well as average lattice strain were determined both for planes oriented perpendicular and parallel to the loading direction using in-situ neutron diffraction. Utilizing average lattice strains as well as lattice strains along the a and c crystallographic directions, an attempt was made to determine Poisson's ratio of LaCoO{sub 3}, which was then compared with that measured using an impulse excitation technique. The elastic constants were calculated and Young's moduli of LaCoO{sub 3} single crystal in different crystallographic directions were estimated.
Nonlinear effect of elastic vortexlike motion on the dynamic stress state of solids
Shilko, Evgeny V.; Grinyaev, Yurii V.; Popov, Mikhail V.; Popov, Valentin L.; Psakhie, Sergey G.
2016-05-01
We present a theoretical analysis of the dynamic stress-strain state of regions in a solid body that are involved in a collective elastic vortexlike motion. It is shown that the initiation of elastic vortexlike motion in the material is accompanied by the appearance of dilatancy and equivalent strain, the magnitudes of which are proportional to the square of the ratio of linear velocity on the periphery of the elastic vortex to the velocity of longitudinal elastic waves (P wave). Under conditions of dynamic loading the described dynamic effects are able to initiate inelastic deformation or destruction of the material at loading speeds of a few percent of the P -wave speed. The obtained analytical estimates suggest that dynamic nonlinear strains can make a significant contribution in a number of widely studied nonlinear dynamic phenomena in solids. Among them are the effect of acoustic (dynamic) dilatancy in solids and granular media, which leads to the generation of longitudinal elastic waves by transverse waves [V. Tournat et al., Phys. Rev. Lett. 92, 085502 (2004), 10.1103/PhysRevLett.92.085502] and the formation of an array of intense "hot spots" (reminiscent of shear-induced hydrodynamic instabilities in fluids) in adiabatic shear bands [P. R. Guduru et al., Phys. Rev. E 64, 036128 (2001), 10.1103/PhysRevE.64.036128].
Da-Guang Zhang
2015-10-01
Full Text Available For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications.
Zhang, Da-Guang; Li, Meng-Han; Zhou, Hao-Miao, E-mail: zhouhm@cjlu.edu.cn [College of Information Engineering, China Jiliang University, 310018, Hangzhou (China)
2015-10-15
For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications.
贾鹏飞; 孔令伟; 王勇; 杨爱武
2013-01-01
strain amplitude are two important stiffness and damping parameters. It is found through resonant column test study that the shear modulus G of soil due to vibrations must be determined by the strain amplitude and the confining pressure, even though under small-strain (shear strain amplitude 10-6
Electrodynamic forces in elastic matter
Antoci, S
2000-01-01
A macroscopic theory for the dynamics of elastic, isotropic matter in presence of electromagnetic fields is proposed here. We avail of Gordon's general relativistic derivation of Abraham's electromagnetic energy tensor as starting point. The necessary description of the elastic and of the inertial behaviour of matter is provided through a four dimensional generalisation of Hooke's law, made possible by the introduction of a four dimensional ``displacement'' vector. As intimated by Nordstroem, the physical origin of electrostriction and of magnetostriction is attributed to the change in the constitutive equation of electromagnetism caused by the deformation of matter. The part of the electromagnetic Lagrangian that depends on that deformation is given explicitly for the case of an isotropic medium and the resulting expression of the electrostrictive force is derived, thus showing how more realistic equations of motion for matter subjected to electromagnetic fields can be constructed.
Elastic deformations of compact stars
Andersson, Lars; Schmidt, Bernd G
2014-01-01
We prove existence of solutions for an elastic body interacting with itself through its Newtonian gravitational field. Our construction works for configurations near one given by a self-gravitating ball of perfect fluid. We use an implicit function argument. In so doing we have to revisit some classical work in the astrophysical literature concerning linear stability of perfect fluid stars. The results presented here extend previous work by the authors, which was restricted to the astrophysically insignificant situation of configurations near one of vanishing stress. In particular, "mountains on neutron stars", which are made possible by the presence of an elastic crust in neutron stars, can be treated using the techniques developed here.
Elastic modulus of viral nanotubes
Zhao, Yue; Ge, Zhibin; Fang, Jiyu
2008-09-01
We report an experimental and theoretical study of the radial elasticity of tobacco mosaic virus (TMV) nanotubes. An atomic force microscope tip is used to apply small radial indentations to deform TMV nanotubes. The initial elastic response of TMV nanotubes can be described by finite-element analysis in 5nm indentation depths and Hertz theory in 1.5nm indentation depths. The derived radial Young’s modulus of TMV nanotubes is 0.92±0.15GPa from finite-element analysis and 1.0±0.2GPa from the Hertz model, which are comparable with the reported axial Young’s modulus of 1.1GPa [Falvo , Biophys. J. 72, 1396 (1997)].
Elastic cone for Chinese calligraphy
Cai, Fenglei; Li, Haisheng
2014-01-01
The brush plays an important role in creating Chinese calligraphy. We regard a single bristle of a writing brush as an elastic rod and the brush tuft absorbing ink as an elastic cone, which naturally deforms according to the force exerted on it when painting on a paper, and the brush footprint is formed by the intersection region between the deformed tuft and the paper plane. To efficiently generate brush strokes, this paper introduces interpolation and texture mapping approach between two adjacent footprints, and automatically applies bristle-splitting texture to the stroke after long-time painting. Experimental results demonstrate that our method is effective and reliable. Users can create realistic calligraphy in real time.
Elastic scattering in geometrical model
Plebaniak, Zbigniew; Wibig, Tadeusz
2016-10-01
The experimental data on proton-proton elastic and inelastic scattering emerging from the measurements at the Large Hadron Collider, calls for an efficient model to fit the data. We have examined the optical, geometrical picture and we have found the simplest, linear dependence of this model parameters on the logarithm of the interaction energy with the significant change of the respective slopes at one point corresponding to the energy of about 300 GeV. The logarithmic dependence observed at high energies allows one to extrapolate the proton-proton elastic, total (and inelastic) cross sections to ultra high energies seen in cosmic rays events which makes a solid justification of the extrapolation to very high energy domain of cosmic rays and could help us to interpret the data from an astrophysical and a high energy physics point of view.
Variants of lumbosacral elastic band.
Carlos Cesar Santín Alfaro
2011-06-01
Full Text Available It is made an intervention research, qualitative and quantitative of two variants of lumbosacral elastic bands used in Provincial Laboratory of Technical Orthopedics in Sancti Spiritus Province, taking into account the high demand for this device and that the laboratory do not often count with the raw material needed for the original lumbosacral belt made by denim cloth which is the conventional belt. The main goal of this research is to explain the technological process and to compare the cost of production of both elastic variants with lumbosacral belt made by cloth which are offer to patients who look for this service , giving them a rapid solution so that they can feel comfortable.
Elasticity of Long Distance Travelling
Knudsen, Mette Aagaard
2011-01-01
With data from the Danish expenditure survey for 12 years 1996 through 2007, this study analyses household expenditures for long distance travelling. Household expenditures are examined at two levels of aggregation having the general expenditures on transportation and leisure relative to five other...... aggregated commodities at the highest level, and the specific expenditures on plane tickets and travel packages at the lowest level. The Almost Ideal Demand System is applied to determine the relationship between expenditures on transportation and leisure and all other purchased non-durables within...... packages has higher income elasticity of demand than plane tickets but also higher than transportation and leisure in general. The findings within price sensitiveness are not as sufficient estimated, but the model results indicate that travel packages is far more price elastic than plane tickets which...
An Implicit Elastic Theory for Lung Parenchyma☆,☆☆
Freed, Alan D.; Einstein, Daniel R.
2012-01-01
The airways and parenchyma of lung experience large deformations during normal respiration. Spatially accurate predictions of airflow patterns and aerosol transport therefore require respiration to be modeled as a fluid-structure interaction problem. Such computational models in turn require constitutive models for the parencyhma that are both accurate and efficient. Herein, an implicit theory of elasticity is derived from thermodynamics to meet this need, leading to a generic template for strain-energy that is shown to be an exact analogue for the well-known Fung model that is the root of modern constitutive theory of tissues. To support this theory, we also propose a novel definition of Lagrangian strain rate. Unlike the classic definition of Lagrangian strain rate, this new definition is separable into volumetric and deviatoric terms, a separation that is both mathematically and physically justified. Within this framework, a novel material model capable of describing the elastic contribution of the nonlinear response of parenchyma is constructed and characterized against published data. PMID:23144500
1992-12-16
12 = (K,, + )- (29) K 2 (see [3]). The parameter KM represents the amplitude of the periodic curva - ture function and sm denotes the value at which K...Additamentum De curvis elasticis. Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes, Ser. 1., Vol. 24, Lausanne 1744. 17 [10...Mathematical Theory of Elasticity. 4th. ed., Cambridge University Press, 1927. [12] G. Nielson. Bernstein/ Bezier Curves and Splines on Spheres based upon
Impact of Thresholds and Load Patterns when Executing HPC Applications with Cloud Elasticity
Vinicius Facco Rodrigues
2016-04-01
Full Text Available Elasticity is one of the most known capabilities related to cloud computing, being largely deployed reactively using thresholds. In this way, maximum and minimum limits are used to drive resource allocation and deallocation actions, leading to the following problem statements: How can cloud users set the threshold values to enable elasticity in their cloud applications? And what is the impact of the application’s load pattern in the elasticity? This article tries to answer these questions for iterative high performance computing applications, showing the impact of both thresholds and load patterns on application performance and resource consumption. To accomplish this, we developed a reactive and PaaS-based elasticity model called AutoElastic and employed it over a private cloud to execute a numerical integration application. Here, we are presenting an analysis of best practices and possible optimizations regarding the elasticity and HPC pair. Considering the results, we observed that the maximum threshold influences the application time more than the minimum one. We concluded that threshold values close to 100% of CPU load are directly related to a weaker reactivity, postponing resource reconfiguration when its activation in advance could be pertinent for reducing the application runtime.
Teaching nonlinear dynamics through elastic cords
Chacon, R; Galan, C A; Sanchez-Bajo, F, E-mail: rchacon@unex.e [Departamento de Fisica Aplicada, Escuela de IngenierIas Industriales, Universidad de Extremadura, Apartado Postal 382, E-06071 Badajoz (Spain)
2011-01-15
We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.
Transient waves in visco-elastic media
Ricker, Norman
1977-01-01
Developments in Solid Earth Geophysics 10: Transient Waves in Visco-Elastic Media deals with the propagation of transient elastic disturbances in visco-elastic media. More specifically, it explores the visco-elastic behavior of a medium, whether gaseous, liquid, or solid, for very-small-amplitude disturbances. This volume provides a historical overview of the theory of the propagation of elastic waves in solid bodies, along with seismic prospecting and the nature of seismograms. It also discusses the seismic experiments, the behavior of waves propagated in accordance with the Stokes wave
Phase diagram of elastic spheres.
Athanasopoulou, L; Ziherl, P
2017-02-15
Experiments show that polymeric nanoparticles often self-assemble into several non-close-packed lattices in addition to the face-centered cubic lattice. Here, we explore theoretically the possibility that the observed phase sequences may be associated with the softness of the particles, which are modeled as elastic spheres interacting upon contact. The spheres are described by two finite-deformation theories of elasticity, the modified Saint-Venant-Kirchhoff model and the neo-Hookean model. We determine the range of indentations where the repulsion between the spheres is pairwise additive and agrees with the Hertz theory. By computing the elastic energies of nine trial crystal lattices at densities far beyond the Hertzian range, we construct the phase diagram and find the face- and body-centered cubic lattices as well as the A15 lattice and the simple hexagonal lattice, with the last two being stable at large densities where the spheres are completely faceted. These results are qualitatively consistent with observations, suggesting that deformability may indeed be viewed as a generic property that determines the phase behavior in nanocolloidal suspensions.
Maximum entropy production in daisyworld
Maunu, Haley A.; Knuth, Kevin H.
2012-05-01
Daisyworld was first introduced in 1983 by Watson and Lovelock as a model that illustrates how life can influence a planet's climate. These models typically involve modeling a planetary surface on which black and white daisies can grow thus influencing the local surface albedo and therefore also the temperature distribution. Since then, variations of daisyworld have been applied to study problems ranging from ecological systems to global climate. Much of the interest in daisyworld models is due to the fact that they enable one to study self-regulating systems. These models are nonlinear, and as such they exhibit sensitive dependence on initial conditions, and depending on the specifics of the model they can also exhibit feedback loops, oscillations, and chaotic behavior. Many daisyworld models are thermodynamic in nature in that they rely on heat flux and temperature gradients. However, what is not well-known is whether, or even why, a daisyworld model might settle into a maximum entropy production (MEP) state. With the aim to better understand these systems, this paper will discuss what is known about the role of MEP in daisyworld models.
Maximum stellar iron core mass
F W Giacobbe
2003-03-01
An analytical method of estimating the mass of a stellar iron core, just prior to core collapse, is described in this paper. The method employed depends, in part, upon an estimate of the true relativistic mass increase experienced by electrons within a highly compressed iron core, just prior to core collapse, and is signiﬁcantly different from a more typical Chandrasekhar mass limit approach. This technique produced a maximum stellar iron core mass value of 2.69 × 1030 kg (1.35 solar masses). This mass value is very near to the typical mass values found for neutron stars in a recent survey of actual neutron star masses. Although slightly lower and higher neutron star masses may also be found, lower mass neutron stars are believed to be formed as a result of enhanced iron core compression due to the weight of non-ferrous matter overlying the iron cores within large stars. And, higher mass neutron stars are likely to be formed as a result of fallback or accretion of additional matter after an initial collapse event involving an iron core having a mass no greater than 2.69 × 1030 kg.
Maximum Matchings via Glauber Dynamics
Jindal, Anant; Pal, Manjish
2011-01-01
In this paper we study the classic problem of computing a maximum cardinality matching in general graphs $G = (V, E)$. The best known algorithm for this problem till date runs in $O(m \\sqrt{n})$ time due to Micali and Vazirani \\cite{MV80}. Even for general bipartite graphs this is the best known running time (the algorithm of Karp and Hopcroft \\cite{HK73} also achieves this bound). For regular bipartite graphs one can achieve an $O(m)$ time algorithm which, following a series of papers, has been recently improved to $O(n \\log n)$ by Goel, Kapralov and Khanna (STOC 2010) \\cite{GKK10}. In this paper we present a randomized algorithm based on the Markov Chain Monte Carlo paradigm which runs in $O(m \\log^2 n)$ time, thereby obtaining a significant improvement over \\cite{MV80}. We use a Markov chain similar to the \\emph{hard-core model} for Glauber Dynamics with \\emph{fugacity} parameter $\\lambda$, which is used to sample independent sets in a graph from the Gibbs Distribution \\cite{V99}, to design a faster algori...
Influence of structural parameters of the masonry on effective elastic properties and strength
А.I. Grishchenko
2014-08-01
Full Text Available Two phase masonry model, which contains elastic mortar and elastic bricks, is analyzed numerically in order to evaluate sensitivity of effective elastic moduli and strength properties to a deviation in the masonry structural parameters. Different methods of masonry homogenization are studied. Effective elastic moduli of the masonry representative volume element are obtained by means of direct finite element simulation and homogenization procedure. Influence of variation in the heterogeneous material microstructure characteristics (influence of brick aspect ratio and orientation angle on the local stress-strain state and mechanical properties of the representative volume element of the composite considered is analyzed. Mechanical properties obtained by direct finite element modeling and other methods in various literary sources are compared. These studies are relevant for the design of composite materials with a structure similar to masonry.
Spring or string: does tendon elastic action influence wing muscle mechanics in bat flight?
Konow, Nicolai; Cheney, Jorn A; Roberts, Thomas J; Waldman, J Rhea S; Swartz, Sharon M
2015-10-07
Tendon springs influence locomotor movements in many terrestrial animals, but their roles in locomotion through fluids as well as in small-bodied mammals are less clear. We measured muscle, tendon and joint mechanics in an elbow extensor of a small fruit bat during ascending flight. At the end of downstroke, the tendon was stretched by elbow flexion as the wing was folded. At the end of upstroke, elastic energy was recovered via tendon recoil and extended the elbow, contributing to unfurling the wing for downstroke. Compared with a hypothetical 'string-like' system lacking series elastic compliance, the tendon spring conferred a 22.5% decrease in muscle fascicle strain magnitude. Our findings demonstrate tendon elastic action in a small flying mammal and expand our understanding of the occurrence and action of series elastic actuator mechanisms in fluid-based locomotion.
A theoretical study of the elastic and thermal properties of ScRu compound under pressure
Huang, Shuo; Li, Rui-Zi; Qi, San-Tao; Chen, Bao; Shen, Jiang
2014-06-01
The elastic and thermal properties of ScRu under pressure are studied using a first-principles pseudopotential method within the generalized gradient approximation. The calculated lattice parameter and formation enthalpy are in good agreement with the previous experimental and theoretical results. From the static finite strain technique, we obtained three independent elastic constants (C 11, C 12 and C 44) and various secondary elasticity parameters such as shear modulus, Young’s modulus and elastic anisotropy, as functions of pressure. This study also provided the pressure and temperature variations of the bulk modulus, Debye temperature, thermal expansion coefficient and heat capacity in wide pressure (0-60 GPa) and temperature (0-1800 K) ranges.