Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).
Hess, Peter; Lomonosov, Alexey M; Mayer, Andreas P
2014-01-01
The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented. Copyright © 2013 Elsevier B.V. All rights reserved.
Fu, Y. B.; Ogden, R. W.
2001-05-01
This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.
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...
Nonlinear Elasticity of Doped Semiconductors
2017-02-01
AFRL-RY-WP-TR-2016-0206 NONLINEAR ELASTICITY OF DOPED SEMICONDUCTORS Mark Dykman and Kirill Moskovtsev Michigan State University...2016 4. TITLE AND SUBTITLE NONLINEAR ELASTICITY OF DOPED SEMICONDUCTORS 5a. CONTRACT NUMBER FA8650-16-1-7600 5b. GRANT NUMBER 5c. PROGRAM...vibration amplitude. 15. SUBJECT TERMS semiconductors , microresonators, microelectromechanical 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF
Nonlinear theory of elastic shells
International Nuclear Information System (INIS)
Costa Junior, J.A.
1979-08-01
Nonlinear theory of elastic shells is developed which incorporates both geometric and physical nonlinearities and which does not make use of the well known Love-Kirchhoff hypothesis. The resulting equations are formulated in tensorial notation and are reduced to the ones of common use when simplifying assumptions encountered in the especific litterature are taken. (Author) [pt
Chong Li; Xiaoyong Hu; Hong Yang; Qihuang Gong
2017-01-01
We propose a scheme of unidirectional transmission in a 1D nonlinear topological photonic crystal based on the topological edge state and three order optical nonlinearity. The 1D photonic crystals consists of a nonlinear photonic crystal L and a linear photonic crystal R. In the backward direction, light is totally reflected for the photons transmission prohibited by the bandgap. While in the forward direction, light interacts with the nonlinear photonic crystal L by optical Kerr effect, brin...
Teaching nonlinear dynamics through elastic cords
International Nuclear Information System (INIS)
Chacon, R; Galan, C A; Sanchez-Bajo, F
2011-01-01
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.
Probing hysteretic elasticity in weakly nonlinear materials
Energy Technology Data Exchange (ETDEWEB)
Johnson, Paul A [Los Alamos National Laboratory; Haupert, Sylvain [UPMC UNIV PARIS; Renaud, Guillaume [UPMC UNIV PARIS; Riviere, Jacques [UPMC UNIV PARIS; Talmant, Maryline [UPMC UNIV PARIS; Laugier, Pascal [UPMC UNIV PARIS
2010-12-07
Our work is aimed at assessing the elastic and dissipative hysteretic nonlinear parameters' repeatability (precision) using several classes of materials with weak, intermediate and high nonlinear properties. In this contribution, we describe an optimized Nonlinear Resonant Ultrasound Spectroscopy (NRUS) measuring and data processing protocol applied to small samples. The protocol is used to eliminate the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic elastic nonlinearity. As an example, in our experiments, we identified external temperature fluctuation as a primary source of material resonance frequency and elastic modulus variation. A variation of 0.1 C produced a frequency variation of 0.01 %, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to eliminate environmental effects, the variation in f{sub 0} (the elastically linear resonance frequency proportional to modulus) is fit with the appropriate function, and that function is used to correct the NRUS calculation of nonlinear parameters. With our correction procedure, we measured relative resonant frequency shifts of 10{sup -5} , which are below 10{sup -4}, often considered the limit to NRUS sensitivity under common experimental conditions. Our results show that the procedure is an alternative to the stringent control of temperature often applied. Applying the approach, we report nonlinear parameters for several materials, some with very small nonclassical nonlinearity. The approach has broad application to NRUS and other Nonlinear Elastic Wave Spectroscopy approaches.
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.
Solitary waves on nonlinear elastic rods. I
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1984-01-01
Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction betwe...... nonlinearity. The balance between dispersion and nonlinearity in the equation is investigated.......Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...... the solitary waves numerically. It is demonstrated that the waves behave almost like solitons in agreement with the fact that the improved Boussinesq equations are nearly integrable. Thus three conservation theorems can be derived from the equations. A new subsonic quasibreather is found in the case of a cubic...
Dynamic nonlinear elasticity in geo materials
International Nuclear Information System (INIS)
Ostrovsky, L.A.; Johnson, P.A.
2001-01-01
The nonlinear elastic behaviour of earth materials is an extremely rich topic, one that has broad implications to earth and materials sciences, including strong ground motion, rock physics, nondestructive evaluation and materials science. The mechanical properties of rock appear to place it in a broader class of materials, it can be named the Structural nonlinear elasticity class (also Mesoscopic/nano scale elasticity, or MS/NSE class). These terms are in contrast to materials that display classical, Atomic Elasticity, such as most fluids and monocrystalline solids. The difference between these two categories of materials is both in intensity and origin of their nonlinear response. The nonlinearity of atomic elastic materials is due to the atomic/molecular lattice anharmonicity. The latter is relatively small because the intermolecular forces are extremely strong. In contrast, the materials considered below contain small soft features that it is called the bond system (cracks, grain contacts, dislocations, etc.) within a hard matrix and relaxation (slow dynamical effects) are characteristic, non of which appear in atomic elastic materials. The research begins with a brief historical background from nonlinear acoustics to the recent developments in rock nonlinearity. This is followed by an overview of some representative laboratory measurements which serve as primary indicators of nonlinear behaviour, followed by theoretical development, and finally, mention a variety of observations of nonlinearity under field conditions and applications to nondestructive testing of materials. The goal is not to survey all papers published in the are but to demonstrate some experimental and theoretical results and ideas that will the reader to become oriented in this broad and rapidly growing area bridging macro-, meso- and microscale (nano scale) phenomena in physics, materials science, and geophysics
Directory of Open Access Journals (Sweden)
Chong Li
2017-02-01
Full Text Available We propose a scheme of unidirectional transmission in a 1D nonlinear topological photonic crystal based on the topological edge state and three order optical nonlinearity. The 1D photonic crystals consists of a nonlinear photonic crystal L and a linear photonic crystal R. In the backward direction, light is totally reflected for the photons transmission prohibited by the bandgap. While in the forward direction, light interacts with the nonlinear photonic crystal L by optical Kerr effect, bringing a topological phase reversal and results the topological edge mode arising at the interface which could transmit photons through the bandgaps both of the photonic crystal L and R. When the signal power intensity larger than a moderate low threshold value of 10.0 MW/cm2, the transmission contrast ratio could remain at 30 steadily.
EDSPA, 1-D Mechanical Displacement for Elastic, Thermoelastic, Viscoelastic Behaviour
International Nuclear Information System (INIS)
Schlich, M.; Elsen, R.
1995-01-01
1 - Description of program or function: EDSPA solves the one dimensional mechanical displacement equation in radial (sphere) axisymmetric cylindrical (infinite cylinder, slab) coordinates. The constitutive laws for the material to be considered can comprise the - elastic and/or - thermoelastic and/or - viscoplastic behaviour. The boundary conditions allow to prescribe displacement and/or stress values. The delivered version of EDSPA is especially suitable for the calculation of borehole problems in rock salt (heater boreholes or free converging boreholes or caverns) where convergence rates and/or contact pressures are of interest. 2 - Method of solution: The coarse-mesh method is used to transform the displacement differential equation (quasi-stationary case: second order ordinary differential equation as a two point boundary value problem) into a system of algebraic equations. This three-diagonal system is solved with the Thomas algorithm (direct solver). 3 - Restrictions on the complexity of the problem: Because of EDSPA's simple one-dimensional formulation there are no restrictions for storage allocation and argument ranges
Nonlinear elasticity in resonance experiments
Li, Xun; Sens-Schönfelder, Christoph; Snieder, Roel
2018-04-01
Resonant bar experiments have revealed that dynamic deformation induces nonlinearity in rocks. These experiments produce resonance curves that represent the response amplitude as a function of the driving frequency. We propose a model to reproduce the resonance curves with observed features that include (a) the log-time recovery of the resonant frequency after the deformation ends (slow dynamics), (b) the asymmetry in the direction of the driving frequency, (c) the difference between resonance curves with the driving frequency that is swept upward and downward, and (d) the presence of a "cliff" segment to the left of the resonant peak under the condition of strong nonlinearity. The model is based on a feedback cycle where the effect of softening (nonlinearity) feeds back to the deformation. This model provides a unified interpretation of both the nonlinearity and slow dynamics in resonance experiments. We further show that the asymmetry of the resonance curve is caused by the softening, which is documented by the decrease of the resonant frequency during the deformation; the cliff segment of the resonance curve is linked to a bifurcation that involves a steep change of the response amplitude when the driving frequency is changed. With weak nonlinearity, the difference between the upward- and downward-sweeping curves depends on slow dynamics; a sufficiently slow frequency sweep eliminates this up-down difference. With strong nonlinearity, the up-down difference results from both the slow dynamics and bifurcation; however, the presence of the bifurcation maintains the respective part of the up-down difference, regardless of the sweep rate.
Solitary waves on nonlinear elastic rods. II
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1987-01-01
In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results ar...... are compared with predictions of conservation theorems for energy and momentum....
Nonlinear surface elastic modes in crystals
Gorentsveig, V. I.; Kivshar, Yu. S.; Kosevich, A. M.; Syrkin, E. S.
1990-03-01
The influence of nonlinearity on shear horizontal surface elastic waves in crystals is described on the basis of the effective nonlinear Schrödinger equation. It is shown that the corresponding solutions form a set of surface modes and the simplest mode coincides with the solution proposed by Mozhaev. The higher order modes have internal frequencies caused by the nonlinearity. All these modes decay in the crystal as uoexp(- z/ zo) atz≫ zo- u o-1 ( z is the distance from the crystal surface, uo the wave amplitude at the surface). The creation of the modes from a localized surface excitation has a threshold. The stability of the modes is discussed.
Beams on nonlinear elastic foundation
International Nuclear Information System (INIS)
Lukkassen, Dag; Meidell, Annette
2014-01-01
In order to determination vertical deflections and rail bending moments the Winkler model (1867) is often used. This linear model neglects several conditions. For example, by using experimental results, it has been observed that there is a substantial increase in the maximum rail deflection and rail bending moment when considering the nonlinearity of the track support system. A deeper mathematical analysis of the models is necessary in order to obtain better methods for more accurate numerical solutions in the determination of deflections and rail bending moments. This paper is intended to be a small step in this direction
Nonlinear constitutive relations for anisotropic elastic materials
Sokolova, Marina; Khristich, Dmitrii
2018-03-01
A general approach to constructing of nonlinear variants of connection between stresses and strains in anisotropic materials with different types of symmetry of properties is considered. This approach is based on the concept of elastic proper subspaces of anisotropic materials introduced in the mechanics of solids by J. Rychlewski and on the particular postulate of isotropy proposed by A. A. Il’yushin. The generalization of the particular postulate on the case of nonlinear anisotropic materials is formulated. Systems of invariants of deformations as lengths of projections of the strain vector into proper subspaces are developed. Some variants of nonlinear constitutive relations for anisotropic materials are offered. The analysis of these relations from the point of view of their satisfaction to general and limit forms of generalization of partial isotropy postulate on anisotropic materials is performed. The relations for particular cases of anisotropy are written.
Special discontinuities in nonlinearly elastic media
Chugainova, A. P.
2017-06-01
Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.
Nonlinear transverse vibrations of elastic beams under tension
International Nuclear Information System (INIS)
Ichikawa, Y.H.; Konno, Kimiaki; Wadati, Miki.
1980-02-01
Nonlinear transverse vibrations of elastic beams under end-thrust have been examined with full account of the rigorous nonlinear relation of curvature and deformation of elastic beams. When the beams are subject to tension, the derived equation is shown to be reduced to one of the new integrable evolution equations discovered by us. (author)
Manipulating acoustic wave reflection by a nonlinear elastic metasurface
Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent
2018-03-01
The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.
Nonlinear elastic inclusions in isotropic solids
Yavari, A.
2013-10-16
We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construction. The problem of residual stress calculation is then reduced to finding a mapping from the Riemannian material manifold to the ambient Euclidean space. Using this construction, we find the residual stress fields of three model systems with spherical and cylindrical symmetries in both incompressible and compressible isotropic elastic solids. In particular, we consider a finite spherical ball with a spherical inclusion with uniform pure dilatational eigenstrain and we show that the stress in the inclusion is uniform and hydrostatic. We also show how singularities in the stress distribution emerge as a consequence of a mismatch between radial and circumferential eigenstrains at the centre of a sphere or the axis of a cylinder.
Sapphire: A kinking nonlinear elastic solid
Basu, S.; Barsoum, M. W.; Kalidindi, S. R.
2006-03-01
Kinking nonlinear elastic (KNE) solids are a recently identified large class of solids that deform fully reversibly by the formation of dislocation-based kink bands [Barsoum et al. Phys. Rev. Lett. 92, 255508 (2004)]. We further conjectured that a high c/a ratio-that ensures that only basal slip is operative-is a sufficient condition for a solid to be KNE. The c/a ratio of sapphire is 2.73 and thus, if our conjecture is correct, it should be a KNE solid. Herein by repeatedly loading-up to 30 times-the same location of sapphire single crystals of two orientations-A and C-with a 1 μm radius spherical nanoindenter, followed by atomic force microscopy, we showed that sapphire is indeed a KNE solid. After pop-ins of the order of 100 nm, the repeated loadings give rise to fully reversible, reproducible hysteresis loops wherein the energy dissipated per unit volume per cycle Wd is of the order of 0.5 GJ/m3. Wd is due to the back and fro motion of the dislocations making up the incipient kink bands that are fully reversible. The results presented here strongly suggest that-like in graphite and mica-kink bands play a more critical role in the room temperature constrained deformation of sapphire than had hitherto been appreciated. Our interpretation is also in agreement with, and can explain most, recent nanoindentation results on sapphire.
On Maximally Dissipative Shock Waves in Nonlinear Elasticity
Knowles, James K.
2010-01-01
Shock waves in nonlinearly elastic solids are, in general, dissipative. We study the following question: among all plane shock waves that can propagate with a given speed in a given one-dimensional nonlinearly elastic bar, which one—if any—maximizes the rate of dissipation? We find that the answer to this question depends strongly on the qualitative nature of the stress-strain relation characteristic of the given material. When maximally dissipative shocks do occur, they propagate according t...
Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks
Sebastian, Resmi; Sitharam, T. G.
2018-01-01
Rocks are generally regarded as linearly elastic even though the manifestations of nonlinearity are prominent. The variations of elastic constants with varying strain levels and stress conditions, disagreement between static and dynamic moduli, etc., are some of the examples of nonlinear elasticity in rocks. The grain-to-grain contact, presence of pores and joints along with other compliant features induce the nonlinear behavior in rocks. The nonlinear elastic behavior of rocks is demonstrated through resonant column tests and numerical simulations in this paper. Resonant column tests on intact and jointed gypsum samples across varying strain levels have been performed in laboratory and using numerical simulations. The paper shows the application of resonant column apparatus to obtain the wave velocities of stiff samples at various strain levels under long wavelength condition, after performing checks and incorporating corrections to the obtained resonant frequencies. The numerical simulation and validation of the resonant column tests using distinct element method are presented. The stiffness reductions of testing samples under torsional and flexural vibrations with increasing strain levels have been analyzed. The nonlinear elastic behavior of rocks is reflected in the results, which is enhanced by the presence of joints. The significance of joint orientation and influence of joint spacing during wave propagation have also been assessed and presented using the numerical simulations. It has been found that rock joints also exhibit nonlinear behavior within the elastic limit.
Non-linear theory of elasticity and optimal design
Ratner, LW
2003-01-01
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it
Alastruey, Jordi; Khir, Ashraf W; Matthys, Koen S; Segers, Patrick; Sherwin, Spencer J; Verdonck, Pascal R; Parker, Kim H; Peiró, Joaquim
2011-08-11
The accuracy of the nonlinear one-dimensional (1-D) equations of pressure and flow wave propagation in Voigt-type visco-elastic arteries was tested against measurements in a well-defined experimental 1:1 replica of the 37 largest conduit arteries in the human systemic circulation. The parameters required by the numerical algorithm were directly measured in the in vitro setup and no data fitting was involved. The inclusion of wall visco-elasticity in the numerical model reduced the underdamped high-frequency oscillations obtained using a purely elastic tube law, especially in peripheral vessels, which was previously reported in this paper [Matthys et al., 2007. Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements. J. Biomech. 40, 3476-3486]. In comparison to the purely elastic model, visco-elasticity significantly reduced the average relative root-mean-square errors between numerical and experimental waveforms over the 70 locations measured in the in vitro model: from 3.0% to 2.5% (p<0.012) for pressure and from 15.7% to 10.8% (p<0.002) for the flow rate. In the frequency domain, average relative errors between numerical and experimental amplitudes from the 5th to the 20th harmonic decreased from 0.7% to 0.5% (p<0.107) for pressure and from 7.0% to 3.3% (p<10(-6)) for the flow rate. These results provide additional support for the use of 1-D reduced modelling to accurately simulate clinically relevant problems at a reasonable computational cost. Copyright © 2011 Elsevier Ltd. All rights reserved.
Non-linear theory of elasticity
Lurie, AI
2012-01-01
This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.
Correlation between ultrasonic nonlinearity and elastic nonlinearity in heat-treated aluminum alloy
Energy Technology Data Exchange (ETDEWEB)
Kim, Jong Beom; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)
2017-04-15
The nonlinear ultrasonic technique is a potential nondestructive method to evaluate material degradation, in which the ultrasonic nonlinearity parameter is usually measured. The ultrasonic nonlinearity parameter is defined by the elastic nonlinearity coefficients of the nonlinear Hooke’s equation. Therefore, even though the ultrasonic nonlinearity parameter is not equal to the elastic nonlinearity parameter, they have a close relationship. However, there has been no experimental verification of the relationship between the ultrasonic and elastic nonlinearity parameters. In this study, the relationship is experimentally verified for a heat-treated aluminum alloy. Specimens of the aluminum alloy were heat-treated at 300°C for different periods of time (0, 1, 2, 5, 10, 20, and 50 h). The relative ultrasonic nonlinearity parameter of each specimen was then measured, and the elastic nonlinearity parameter was determined by fitting the stress-strain curve obtained from a tensile test to the 5th-order-polynomial nonlinear Hooke’s equation. The results showed that the variations in these parameters were in good agreement with each other.
NONLINEAR SPECTRAL IMAGING OF ELASTIC CARTILAGE IN RABBIT EARS
Directory of Open Access Journals (Sweden)
JING CHEN
2013-07-01
Full Text Available Elastic cartilage in the rabbit external ear is an important animal model with attractive potential value for researching the physiological and pathological states of cartilages especially during wound healing. In this work, nonlinear optical microscopy based on two-photon excited fluorescence and second harmonic generation were employed for imaging and quantifying the intact elastic cartilage. The morphology and distribution of main components in elastic cartilage including cartilage cells, collagen and elastic fibers were clearly observed from the high-resolution two-dimensional nonlinear optical images. The areas of cell nuclei, a parameter related to the pathological changes of normal or abnormal elastic cartilage, can be easily quantified. Moreover, the three-dimensional structure of chondrocytes and matrix were displayed by constructing three-dimensional image of cartilage tissue. At last, the emission spectra from cartilage were obtained and analyzed. We found that the different ratio of collagen over elastic fibers can be used to locate the observed position in the elastic cartilage. The redox ratio based on the ratio of nicotinamide adenine dinucleotide (NADH over flavin adenine dinucleotide (FAD fluorescence can also be calculated to analyze the metabolic state of chondrocytes in different regions. Our results demonstrated that this technique has the potential to provide more accurate and comprehensive information for the physiological states of elastic cartilage.
Nonlinear elastic inclusions in isotropic solids
Yavari, A.; Goriely, A.
2013-01-01
We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
International Nuclear Information System (INIS)
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-01-01
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.
Nonlinear analysis of flexible plates lying on elastic foundation
Directory of Open Access Journals (Sweden)
Trushin Sergey
2017-01-01
Full Text Available This article describes numerical procedures for analysis of flexible rectangular plates lying on elastic foundation. Computing models are based on the theory of plates with account of transverse shear deformations. The finite difference energy method of discretization is used for reducing the initial continuum problem to finite dimensional problem. Solution procedures for nonlinear problem are based on Newton-Raphson method. This theory of plates and numerical methods have been used for investigation of nonlinear behavior of flexible plates on elastic foundation with different properties.
Dynamic nonlinear interaction of elastic plates on discrete supports
International Nuclear Information System (INIS)
Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.
1984-01-01
A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt
Power laws and elastic nonlinearity in materials with complex microstructure
Energy Technology Data Exchange (ETDEWEB)
Scalerandi, M., E-mail: marco.scalerandi@infm.polito.it
2016-01-28
Nonlinear ultrasonic methods have been widely used to characterize the microstructure of damaged solids and consolidated granular media. Besides distinguishing between materials exhibiting classical nonlinear behaviors from those exhibiting hysteresis, it could be of importance the discrimination between ultrasonic indications from different physical sources (scatterers). Elastic hysteresis could indeed be due to dislocations, grain boundaries, stick-slip at interfaces, etc. Analyzing data obtained on various concrete samples, we show that the power law behavior of the nonlinear indicator vs. the energy of excitation could be used to classify different microscopic features. In particular, the power law exponent ranges between 1 and 3, depending on the nature of nonlinearity. We also provide a theoretical interpretation of the collected data using models for clapping and hysteretic nonlinearities. - Highlights: • Several materials exhibit a nontrivial nonlinear elastic behavior which can be ascribed to different physical sources. • The quantitative nonlinear response is dependent on the type of microstructure present in the material. • A nonlinear indicator could be defined which depends on the excitation energy of the sample. • Assuming a power law dependence, the exponent depends on the microstructure of the material and could evolve in time. • Experimental results on concrete are discussed and a theoretical description is proposed.
Geometrically Nonlinear Transient Response of Laminated Plates with Nonlinear Elastic Restraints
Directory of Open Access Journals (Sweden)
Shaochong Yang
2017-01-01
Full Text Available To investigate the dynamic behavior of laminated plates with nonlinear elastic restraints, a varied constraint force model and a systematic numerical procedure are presented in this work. Several kinds of typical relationships of force-displacement for spring are established to simulate the nonlinear elastic restraints. In addition, considering the restraining moments of flexible pads, the pads are modeled by translational and rotational springs. The displacement- dependent constraint forces are added to the right-hand side of equations of motion and treated as additional applied loads. These loads can be explicitly defined, via an independent set of nonlinear load functions. The time histories of transverse displacements at typical points of the laminated plate are obtained through the transient analysis. Numerical examples show that the present method can effectively treat the geometrically nonlinear transient response of plates with nonlinear elastic restraints.
On the dynamic buckling of a weakly damped nonlinear elastic ...
African Journals Online (AJOL)
In this paper we determine the dynamic buckling load of a strictly nonlinear but weakly damped elastic oscillatory model structure subjected to small perturbations The loading history is explicitly time dependent and varies slowly with time over a natural period of oscillation of the structure. A multiple timing regular ...
Elastic reflection based waveform inversion with a nonlinear approach
Guo, Qiang; Alkhalifah, Tariq Ali
2017-01-01
Full waveform inversion (FWI) is a highly nonlinear problem due to the complex reflectivity of the Earth, and this nonlinearity only increases under the more expensive elastic assumption. In elastic media, we need a good initial P-wave velocity and even a better initial S-wave velocity models with accurate representation of the low model wavenumbers for FWI to converge. However, inverting for the low wavenumber components of P- and S-wave velocities using reflection waveform inversion (RWI) with an objective to fit the reflection shape, rather than produce reflections, may mitigate the limitations of FWI. Because FWI, performing as a migration operator, is in preference of the high wavenumber updates along reflectors. We propose a nonlinear elastic RWI that inverts for both the low wavenumber and perturbation components of the P- and S-wave velocities. To generate the full elastic reflection wavefields, we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields. We update both the perturbation and propagation parts of the velocity models in a nested fashion. Applications on synthetic isotropic models and field data show that our method can efficiently update the low and high wavenumber parts of the models.
Elastic reflection based waveform inversion with a nonlinear approach
Guo, Qiang
2017-08-16
Full waveform inversion (FWI) is a highly nonlinear problem due to the complex reflectivity of the Earth, and this nonlinearity only increases under the more expensive elastic assumption. In elastic media, we need a good initial P-wave velocity and even a better initial S-wave velocity models with accurate representation of the low model wavenumbers for FWI to converge. However, inverting for the low wavenumber components of P- and S-wave velocities using reflection waveform inversion (RWI) with an objective to fit the reflection shape, rather than produce reflections, may mitigate the limitations of FWI. Because FWI, performing as a migration operator, is in preference of the high wavenumber updates along reflectors. We propose a nonlinear elastic RWI that inverts for both the low wavenumber and perturbation components of the P- and S-wave velocities. To generate the full elastic reflection wavefields, we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields. We update both the perturbation and propagation parts of the velocity models in a nested fashion. Applications on synthetic isotropic models and field data show that our method can efficiently update the low and high wavenumber parts of the models.
Unraveling complex nonlinear elastic behaviors in rocks using dynamic acousto-elasticity
Riviere, J.; Guyer, R.; Renaud, G.; TenCate, J. A.; Johnson, P. A.
2012-12-01
In comparison with standard nonlinear ultrasonic methods like frequency mixing or resonance based measurements that allow one to extract average, bulk variations of modulus and attenuation versus strain level, dynamic acousto-elasticity (DAE) allows to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. This method consists of exciting a sample in Bulk-mode resonance at strains of 10-7 to 10-5 and simultaneously probing with a sequence of high frequency, low amplitude pulses. Time of flight and amplitudes of these pulses, respectively related to nonlinear elastic and dissipative parameters, can be plotted versus vibration strain level. Despite complex nonlinear signatures obtained for most rocks, it can be shown that for low strain amplitude (Pasqualini et al., JGR 2007), but not with the extreme detail of elasticity provided by DAE. Previous quasi-static measurements made in Berea sandstone (Claytor et al, GRL 2009), show that the hysteretic behavior disappears when the protocol is performed at a very low strain-rate (static limit). Therefore, future work will aim at linking quasi-static and dynamic observations, i.e. the frequency or strain-rate dependence, in order to understand underlying physical phenomena.
A nonlinear approach of elastic reflection waveform inversion
Guo, Qiang
2016-09-06
Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.
A nonlinear approach of elastic reflection waveform inversion
Guo, Qiang; Alkhalifah, Tariq Ali
2016-01-01
Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.
16-channel DWDM based on 1D defect mode nonlinear photonic crystal
Kalhan, Abhishek; Sharma, Sanjeev; Kumar, Arun
2018-05-01
We propose a sixteen-channel Dense Wavelength Division Multiplexer (DWDM), using the 1-D defect mode nonlinear photonic crystal which is a function of intensity as well as wavelength. Here, we consider an alternate layer of two semiconductor materials in which we found the bandgap of materials when defect layer is introduced then 16-channel dense wavelength division multiplexer is obtained within bandgap. From the theoretical analysis, we can achieve average quality factor of 7800.4, the uniform spectral line-width of 0.2 nm, crosstalk of -31.4 dB, central wavelength changes 0.07 nm/(1GW/cm2) and 100% transmission efficiency. Thus, Sixteen-channel DWDM has very high quality factor, low crosstalk, near 100% power transmission efficiency and small channel spacing (1.44 nm).
A REMARK ON FORMAL MODELS FOR NONLINEARLY ELASTIC MEMBRANE SHELLS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the “classical” linear limiting membrane model, whose juetification has already been established by a convergence theorem.
Non-linear elastic thermal stress analysis with phase changes
International Nuclear Information System (INIS)
Amada, S.; Yang, W.H.
1978-01-01
The non-linear elastic, thermal stress analysis with temperature induced phase changes in the materials is presented. An infinite plate (or body) with a circular hole (or tunnel) is subjected to a thermal loading on its inner surface. The peak temperature around the hole reaches beyond the melting point of the material. The non-linear diffusion equation is solved numerically using the finite difference method. The material properties change rapidly at temperatures where the change of crystal structures and solid-liquid transition occur. The elastic stresses induced by the transient non-homogeneous temperature distribution are calculated. The stresses change remarkably when the phase changes occur and there are residual stresses remaining in the plate after one cycle of thermal loading. (Auth.)
DYNAMICS OF VIBRATION FEEDERS WITH A NONLINEAR ELASTIC CHARACTERISTIC
Directory of Open Access Journals (Sweden)
V. I. Dyrda
2017-04-01
Full Text Available Purpose. Subject to the smooth and efficient operation of each production line, is the use of vehicles transporting high specification. It worked well in practice for transporting construction machines, which are used during the vibration. The use of vibration machines requires optimization of their operation modes. In the form of elastic link in them are increasingly using rubber-metallic elements, which are characterized by nonlinear damping properties. So it is necessary to search for new, more modern, methods of calculation of dynamic characteristics of the vibration machines on the properties of rubber as a cushioning material. Methodology. The dynamics of vibration machine that is as elastic rubber block units and buffer shock absorbers limiting the amplitude of the vibrations of the working body. The method of determining amplitude-frequency characteristics of the vibrating feeder is based on the principle of Voltaire, who in the calculations of the damping properties of the dampers will allow for elastic-hereditary properties of rubber. When adjusting the basic dynamic stiffness of the elastic ties and vibratory buffers, using the principle of heredity rubber properties, determine the dependence of the amplitude of the working body of the machine vibrations. This method is called integro-operator using the fractional-exponential kernels of relaxation. Findings. Using the derived formula for determining the amplitude of the resonance curve is constructed one-mass nonlinear system. It is established that the use of the proposed method of calculation will provide a sufficiently complete description of the damping parameters of rubber-metallic elements and at the same time be an effective means of calculating the amplitude-frequency characteristics of nonlinear vibration systems. Originality. The authors improved method of determining damping characteristics of rubber-metallic elements and the amplitude-frequency characteristics of nonlinear
Ojo, A. O.; Xie, Jun; Olorunfemi, M. O.
2018-01-01
To reduce ambiguity related to nonlinearities in the resistivity model-data relationships, an efficient direct-search scheme employing the Neighbourhood Algorithm (NA) was implemented to solve the 1-D resistivity problem. In addition to finding a range of best-fit models which are more likely to be global minimums, this method investigates the entire multi-dimensional model space and provides additional information about the posterior model covariance matrix, marginal probability density function and an ensemble of acceptable models. This provides new insights into how well the model parameters are constrained and make assessing trade-offs between them possible, thus avoiding some common interpretation pitfalls. The efficacy of the newly developed program is tested by inverting both synthetic (noisy and noise-free) data and field data from other authors employing different inversion methods so as to provide a good base for comparative performance. In all cases, the inverted model parameters were in good agreement with the true and recovered model parameters from other methods and remarkably correlate with the available borehole litho-log and known geology for the field dataset. The NA method has proven to be useful whilst a good starting model is not available and the reduced number of unknowns in the 1-D resistivity inverse problem makes it an attractive alternative to the linearized methods. Hence, it is concluded that the newly developed program offers an excellent complementary tool for the global inversion of the layered resistivity structure.
Directory of Open Access Journals (Sweden)
Nicolae Tudoroiu
2017-09-01
Full Text Available The objective of this paper is to investigate the use of the 1-D wavelet analysis to extract several patterns from signals data sets collected from healthy and faulty input-output signals of control systems as a preliminary step in real-time implementation of fault detection diagnosis and isolation strategies. The 1-D wavelet analysis proved that is an useful tool for signals processing, design and analysis based on wavelet transforms found in a wide range of control systems industrial applications. Based on the fact that in the real life there is a great similitude between the phenomena, we are motivated to extend the applicability of these techniques to solve similar applications from control systems field, such is done in our research work. Their efficiency will be demonstrated on a case study mainly chosen to evaluate the impact of the uncertainties and the nonlinearities of the sensors and actuators on the overall performance of the control systems. The proposed techniques are able to extract in frequency domain some pattern features (signatures of interest directly from the signals data set collected by data acquisition equipment from the control system.
Geometric Structure-Preserving Discretization Schemes for Nonlinear Elasticity
2015-08-13
sufficient conditions for the compatibility of displacement gradient and the existence of stress functions on non-contractible bodies. The main...conditions. 15. SUBJECT TERMS geometric theory for nonlinear elasticity, discrete exterior calculus 16. SECURITY CLASSIFICATION OF: 17. LIMITATION...complex allows one to readily derive the necessary and sufficient conditions for the compatibility of displacement gradient and the existence of stress
A Lagrangian meshfree method applied to linear and nonlinear elasticity.
Walker, Wade A
2017-01-01
The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.
Nonlinear reflection of shock shear waves in soft elastic media.
Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël
2010-02-01
For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.
Free-vibration acoustic resonance of a nonlinear elastic bar
Tarumi, Ryuichi; Oshita, Yoshihito
2011-02-01
Free-vibration acoustic resonance of a one-dimensional nonlinear elastic bar was investigated by direct analysis in the calculus of variations. The Lagrangian density of the bar includes a cubic term of the deformation gradient, which is responsible for both geometric and constitutive nonlinearities. By expanding the deformation function into a complex Fourier series, we derived the action integral in an analytic form and evaluated its stationary conditions numerically with the Ritz method for the first three resonant vibration modes. This revealed that the bar shows the following prominent nonlinear features: (i) amplitude dependence of the resonance frequency; (ii) symmetry breaking in the vibration pattern; and (iii) excitation of the high-frequency mode around nodal-like points. Stability of the resonant vibrations was also addressed in terms of a convex condition on the strain energy density.
Nonlinear modulation of torsional waves in elastic rod. [Instability
Energy Technology Data Exchange (ETDEWEB)
Hirao, M; Sugimoto, N [Osaka Univ., Toyonaka (Japan). Faculty of Engineering Science
1977-06-01
Nonlinear Schroedinger equation, which describes the nonlinear modulation of dispersive torsional waves in an elastic rod of circular cross-section, is derived by the derivative expansion method. It is found, for the lowest dispersive mode, that the modulational instability occurs except in the range of the carrier wavenumber, 2.799
Elastic Nonlinear Response in Granular Media Under Resonance Conditions
Jia, X.; Johnson, P. A.
2004-12-01
We are studying the elastic linear and nonlinear behavior of granular media using dynamic wave methods. In the work presented here, our goal is to quantify the elastic nonlinear response by applying wave resonance. Resonance studies are desirable because they provide the means to easily study amplitude dependencies of elastic nonlinear behavior and thus to characterize the physical nature of the elastic nonlinearity. This work has implications for a variety of topics, in particular, the in situ nonlinear response of surface sediments. For this work we constructed an experimental cell in which high sensitivity dynamic resonance studies were conducted using granular media under controlled effective pressure. We limit our studies here to bulk modes but have the capability to employ shear waves as well. The granular media are composed of glass beads held under pressure by a piston, while applying resonance waves from transducers as both the excitation and the material probe. The container is closed with two fitted pistons and a normal load is applied to the granular sample across the top piston. Force and displacement are measured directly. Resonant frequency sweeps with frequencies corresponding to the fundamental bulk mode are applied to the longitudinal source transducer. The pore pressure in the system is 1 atm. The glass beads used in our experiments are of diameter 0.5 mm, randomly deposited in a duralumin cylinder of diameter 30 mm and height of 15 mm. This corresponds to a granular skeleton acoustic wave velocity of v ª 750m/s under 50 N of force [0.07 Mpa]. The loaded system gives fundamental mode resonances in the audio frequency band at half a wavelength where resonance frequency is effective-pressure dependent. The volume fraction of glass beads thus obtained is found to be 0.63 ± 0.01. Plane-wave generating and detecting transducers of diameter 30 mm are placed on axis at the top and bottom of the cylindrical container in direct contact with the glass
IMPAC-2, Dynamic Impact Analysis for 1-D Nonlinear Spring Shipping Container Model
International Nuclear Information System (INIS)
Payne, J. B.; Counts, J.
1980-01-01
1 - Description of problem or function: IMPAC2 solves the equations of motion for a one-dimensional, lumped-mass, nonlinear spring mathematical container model. The program was designed to analyze the dynamic response of metallic shipping containers impacting an unyielding surface. The container may consist of several hollow concentric cylinders, each of a different material and length. 2 - Method of solution: An iteration technique (Newmark-Beta) is used to solve the equations of motion for displacement, velocity, and acceleration of the masses at each time-step. 3 - Restrictions on the complexity of the problem: The maximum number of masses is 100. The program is written for a maximum of 10 different materials. The first seven have been given the following designations: 1 steel, 2 clad lead, 3 uranium, 4 pine, 5 lead, 6 balsa, 7 marine plywood. Stress-strain characteristics for materials 1, 3, 4, and 6 are approximated by a bilinear curve fit which requires as input the modulus of elasticity, the stress at the intersection of the two lines and the slope of the second line
Phononic Crystal Waveguide Transducers for Nonlinear Elastic Wave Sensing.
Ciampa, Francesco; Mankar, Akash; Marini, Andrea
2017-11-07
Second harmonic generation is one of the most sensitive and reliable nonlinear elastic signatures for micro-damage assessment. However, its detection requires powerful amplification systems generating fictitious harmonics that are difficult to discern from pure nonlinear elastic effects. Current state-of-the-art nonlinear ultrasonic methods still involve impractical solutions such as cumbersome signal calibration processes and substantial modifications of the test component in order to create material-based tunable harmonic filters. Here we propose and demonstrate a valid and sensible alternative strategy involving the development of an ultrasonic phononic crystal waveguide transducer that exhibits both single and multiple frequency stop-bands filtering out fictitious second harmonic frequencies. Remarkably, such a sensing device can be easily fabricated and integrated on the surface of the test structure without altering its mechanical and geometrical properties. The design of the phononic crystal structure is supported by a perturbative theoretical model predicting the frequency band-gaps of periodic plates with sinusoidal corrugation. We find our theoretical findings in excellent agreement with experimental testing revealing that the proposed phononic crystal waveguide transducer successfully attenuates second harmonics caused by the ultrasonic equipment, thus demonstrating its wide range of potential applications for acousto/ultrasonic material damage inspection.
Rayleigh scattering and nonlinear inversion of elastic waves
Energy Technology Data Exchange (ETDEWEB)
Gritto, Roland [Univ. of California, Berkeley, CA (United States)
1995-12-01
Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of -100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to k_{p}R = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.
Karavashkin, S B
2002-01-01
We analyse the exact analytical solutions for 1D elastic lumped lines under action of an external force inclined to the line axis. We show that in this case an inclined wave being described by an implicit function propagates along the line. We extend this conclusion both to free vibrations and to distributed lines. We prove that the presented solution in the form of implicit function is a generalizing for the wave equation. When taken into consideration exactly, the dynamical processes pattern leads to the conclusion that the divergence of a vector in dynamical fields is not zero but proportional to the scalar product of the partial derivative of the given vector with respect to time into the wave propagation direction vector.
A new type of surface acoustic waves in solids due to nonlinear elasticity
International Nuclear Information System (INIS)
Mozhaev, V.G.
1988-12-01
It is shown that in nonlinear elastic semi-infinite medium possessing a property of self focusing of shear waves, besides bulk non-linear shear waves, new surface acoustic waves exist, localization of which near the boundary is entirely due to nonlinear effects. (author). 8 refs
Nonlinear Subincremental Method for Determination of Elastic-Plastic-Creep Behaviour
DEFF Research Database (Denmark)
Ottosen, N. Saabye; Gunneskov, O.
1985-01-01
to general elastic-plastic-creep behaviour including problems with a highly nonlinear total strain path caused by the occurrence of creep hardening. This nonlinear method degenerates to the linear approach for elastic-plastic behaviour and when secondary creep is present. It is also linear during step......The frequently used subincremental method has so far been used on a linear interpolation of the total strain path within each main step. This method has proven successful when elastic-plastic behaviour and secondary creep is involved. The authors propose a nonlinear subincremental method applicable...
Pepi, John W.
2017-08-01
Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.
International Nuclear Information System (INIS)
Zhao Dun; Zhang Yujuan; Lou Weiwei; Luo Honggang
2011-01-01
By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLS systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.
International Nuclear Information System (INIS)
Mehdian, H.; Mohammadzahery, Z.; Hasanbeigi, A.
2014-01-01
In this work, we study the defect mode and bistability behavior of 1-D photonic band gap structure with magnetized plasma and coupled nonlinear defects. The transfer matrix method has been employed to investigate the magnetic field effect on defect mode frequency and bistability threshold. The obtained results show that the frequency of defect mode and bistability threshold can be altered, without changing the structure of the photonic multilayer. Therefore, the bistability behavior of the subjected structure in the presence of magnetized plasma can be utilized in manufacturing wide frequency range devices
Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems
International Nuclear Information System (INIS)
Mikhlin, Yu V; Perepelkin, N V; Klimenko, A A; Harutyunyan, E
2012-01-01
Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.
Bulk nonlinear elastic strain waves in a bar with nanosize inclusions
DEFF Research Database (Denmark)
Gula, Igor A.; Samsonov (†), Alexander M.
2018-01-01
We propose a mathematical model for propagation of the long nonlinearly elastic longitudinal strain waves in a bar, which contains nanoscale structural inclusions. The model is governed by a nonlinear doubly dispersive equation (DDE) with respect to the one unknown longitudinal strain function. We...
On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation
Zarubinskaya, M.A.; Van Horssen, W.T.
2003-01-01
In this paper an initial-boundary value problem for a weakly nonlinear plate equation with a quadratic nonlinearity will be studied. This initial-boundary value problem can be regarded as a simple model describing free oscillations of a simply supported square plate on an elastic foundation. It is
Variational problems arising in classical mechanics and nonlinear elasticity
International Nuclear Information System (INIS)
Spencer, P.
1999-01-01
In this thesis we consider two different classes of variational problems. First, one-dimensional problems arising from classical mechanics where the problem is to determine whether there is a unique function η 0 (x) which minimises the energy functional of the form I(η) = ∫ a b L(x,η(x), η'(x)) dx. We will investigate uniqueness by making a change of dependent and independent variables and showing that for a class of integrands L with a particular kind of scaling invariance the resulting integrand is completely convex. The change of variables arises by applying results from Lie group theory as applied in the study of differential equations and this work is motivated by [60] and [68]. Second, the problem of minimising energy functionals of the form E(u) = ∫ A W(∇u(x)) dx in the case of a nonlinear elastic body occupying an annular region A contains R 2 with u : A-bar → A-bar. This work is motivated by [57] (in particular the example of paragraph 4). We will consider rotationally symmetric deformations satisfying prescribed boundary conditions. We will show the existence of minimisers for stored energy functions of the form W(F) = g-tilde(vertical bar-F-vertical bar, det(F)) in a class of general rotationally symmetric deformations of a compressible annulus and for stored energy functions of the form W(F) = g-bar(vertical bar-F-vertical bar) in a class of rotationally symmetric deformations of an incompressible annulus. We will also show that in each case the minimisers are solutions of the full equilibrium equations. A model problem will be considered where the energy functional is the Dirichlet integral and it will be shown that the rotationally symmetric solution obtained is a minimiser among admissible non-rotationally symmetric deformations. In the case of an incompressible annulus, we will consider the Dirichlet integral as the energy functional and show that the rotationally symmetric equilibrium solutions in this case are weak local minimisers in
An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures
DEFF Research Database (Denmark)
Christensen, Claus Dencker; Byskov, Esben
2010-01-01
A new, enhanced asymptotic expansion applicable to stability of structures made of nonlinear elastic materials is established. The method utilizes “hyperbolic” terms instead of the conventional polynomial terms, covers full kinematic nonlinearity and is applied to nonlinear elastic Euler columns...... with two different types of cross-section. Comparison with numerical results show that our expansion provides more accurate predictions of the behavior than usual expansions. The method is based on an extended version of the principle of virtual displacements that covers cases with auxiliary conditions...
Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A
2003-06-01
Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.
Nonlinear elasticity in wurtzite GaN/AlN planar superlattices and quantum dots
International Nuclear Information System (INIS)
Lepkowski, S.P.; Majewski, J.A.; Jurczak, G.
2005-01-01
The elastic stiffness tensor for wurtzite GaN and AlN show a significant hydrostatic pressure dependence, which id the evidence of nonlinear elasticity of these compounds. We have examined how the pressure dependence of elastic constants for wurtzite nitrides influences elastic and piezoelectric properties of GaN/AlN planar superlattices and quantum dots. Particularly we show that built-in hydrostatic pressure, present in both quantum wells of the GaN/AlN superlattices and GaN/AlN quantum dots, increases significantly by 0.3-0.7 GPa when nonlinear elasticity is used. Consequently, the compressive volumetric strain in quantum wells and quantum dots decreases in comparison to the case of the linear elastic theory, However, the-component of the built-in electric field in the quantum wells and quantum dots increases considerably when nonlinear elasticity is taken into account. Both effects, i.e., a decrease in the compressive volumetric strain as well as an increase in the built-in electric field, decrease the band-to-band transition energies in the quantum wells and quantum dots. (author)
Non-linear buckling of an FGM truncated conical shell surrounded by an elastic medium
International Nuclear Information System (INIS)
Sofiyev, A.H.; Kuruoglu, N.
2013-01-01
In this paper, the non-linear buckling of the truncated conical shell made of functionally graded materials (FGMs) surrounded by an elastic medium has been studied using the large deformation theory with von Karman–Donnell-type of kinematic non-linearity. A two-parameter foundation model (Pasternak-type) is used to describe the shell–foundation interaction. The FGM properties are assumed to vary continuously through the thickness direction. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of the FGM truncated conical shell resting on the Pasternak-type elastic foundation are derived. By using the Superposition and Galerkin methods, the non-linear stability equations for the FGM truncated conical shell is solved. Finally, influences of variations of Winkler foundation stiffness and shear subgrade modulus of the foundation, compositional profiles and shell characteristics on the dimensionless critical non-linear axial load are investigated. The present results are compared with the available data for a special case. -- Highlights: • Nonlinear buckling of FGM conical shell surrounded by elastic medium is studied. • Pasternak foundation model is used to describe the shell–foundation interaction. • Nonlinear basic equations are derived. • Problem is solved by using Superposition and Galerkin methods. • Influences of various parameters on the nonlinear critical load are investigated
Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.
2015-10-01
An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit
Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates
International Nuclear Information System (INIS)
Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young
2010-01-01
Since the acoustic nonlinearity is sensitive to the minute variation of material properties, the nonlinear ultrasonic technique(NUT) has been considered as a promising method to evaluate the material degradation or fatigue. However, there are certain limitations to apply the conventional NUT using the bulk wave to thin plates. In case of plates, the use of Lamb wave can be considered, however, the propagation characteristics of Lamb wave are completely different with the bulk wave, and thus the separate study for the nonlinearity of Lamb wave is required. For this work, this paper analyzed first the conditions of mode pair suitable for the practical application as well as for the cumulative propagation of quadratic harmonic frequency and summarized the result in for conditions: phase matching, non-zero power flux, group velocity matching, and non-zero out-of-plane displacement. Experimental results in aluminum plates showed that the amplitude of the secondary Lamb wave and nonlinear parameter grew up with increasing propagation distance at the mode pair satisfying the above all conditions and that the ration of nonlinear parameters measured in Al6061-T6 and Al1100-H15 was closed to the ratio of the absolute nonlinear parameters
Non-linear waves in heterogeneous elastic rods via homogenization
Quezada de Luna, Manuel
2012-03-01
We consider the propagation of a planar loop on a heterogeneous elastic rod with a periodic microstructure consisting of two alternating homogeneous regions with different material properties. The analysis is carried out using a second-order homogenization theory based on a multiple scale asymptotic expansion. © 2011 Elsevier Ltd. All rights reserved.
Contribution to the study of heavy-ion induced quasi-elastic processes in the 2s-1d shell
International Nuclear Information System (INIS)
Greiner, A.
1982-06-01
In the first part of this thesis, we present a study of the charge exchange reaction 28 Si( 18 O, 18 F) 28 Al at 56 MeV. This reaction can be easily understood in terms of a one-step direct charge exchange mechanism. With a very simple shell model, it can be interpreted that a neutron of the 18 O in the Jsup(π)=0 + , T=1 state interacts with a proton in the dsub(5/2) shell of 28 Si and they exchange their spin and charge forming Jsup(π)=1 + , T=0 18 F, and Jsup(π)=3 + or 2 + , T=1 28 Al. In the present analysis of data, we have first performed the direct charge exchange DWBA calculations. These results are compared with the exact-finite-range (EFR) second order DWBA calculations which take into account the successive one-nucleon stripping and pickup, and pickup and stripping process. In the second part, we wish to report results and analysis concerning the 24 Mg+ 12 C system. The 180 0 c.m. angle scattering excitation functions were measured between 12- and 27-MeV c.m. corresponding to a range in the compound 36 Ar excitation energy of 28.3 to 43.3 MeV. Several angular distributions for the elastic and inelastic scattering have been measured on the top of the bumps of the elastic scattering excitation function. These elastic scattering angular distributions cannot be fitted by a single squared Legendre polynomial of order L. A complete phase shift analysis is presented. We discuss also the shapes of the first 24 Mg 2 + inelastic scattering angular distributions with respect to the shape of the elastic scattering differential cross section [fr
The propagation of nonlinear rayleigh waves in layered elastic half-space
International Nuclear Information System (INIS)
Ahmetolan, S.
2004-01-01
In this work, the propagation of small but finite amplitude generalized Rayleigh waves in an elastic half-space covered by a different elastic layer of uniform and finite thickness is considered. The constituent materials are assumed to be homogeneous, isotropic, compressible hyperelastic. Excluding the harmonic resonance phenomena, it is shown that the nonlinear self modulation of generalized Rayleigh waves is governed asymptotically by a nonlinear Schrodinger (NLS) equation. The stability of the solutions and the existence of solitary wave-type solutions a NLS are strongly depend on the sign of the product of the coefficients of the nonlinear and dipersion terms of the equation.Therefore the analysis continues with the examination of dependence of these coefficients on the nonlinear material parameters. Three different models have been considered which are nonlinear layer-nonlinear half space, linear layer-nonlinear half space and nonlinear layer-linear half space. The behavior of the coefficients of the NLS equation was also analyzed the limit as h(thickness of the layer) goes to zero and k(the wave number) is constant. Then conclusions are drawn about the effect of nonlinear material parameters on the wave modulation. In the numerical investigations both hypothetical and real material models are used
International Nuclear Information System (INIS)
Zhang, Da-Guang; Li, Meng-Han; Zhou, Hao-Miao
2015-01-01
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
Analysis of nonlinear elastic behavior in miniature pneumatic artificial muscles
Hocking, Erica G.; Wereley, Norman M.
2013-01-01
Pneumatic artificial muscles (PAMs) are well known for their excellent actuator characteristics, including high specific work, specific power, and power density. Recent research has focused on miniaturizing this pneumatic actuator technology in order to develop PAMs for use in small-scale mechanical systems, such as those found in robotic or aerospace applications. The first step in implementing these miniature PAMs was to design and characterize the actuator. To that end, this study presents the manufacturing process, experimental characterization, and analytical modeling of PAMs with millimeter-scale diameters. A fabrication method was developed to consistently produce low-cost, high performance, miniature PAMs using commercially available materials. The quasi-static behavior of these PAMs was determined through experimentation on a single actuator with an active length of 39.16 mm (1.54 in) and a diameter of 4.13 mm (0.1625 in). Testing revealed the PAM’s full evolution of force with displacement for operating pressures ranging from 207 to 552 kPa (30-80 psi in 10 psi increments), as well as the blocked force and free contraction at each pressure. Three key nonlinear phenomena were observed: nonlinear PAM stiffness, hysteresis of the force versus displacement response for a given pressure, and a pressure deadband. To address the analysis of the nonlinear response of these miniature PAMs, a nonlinear stress versus strain model, a hysteresis model, and a pressure bias are introduced into a previously developed force balance analysis. Parameters of these nonlinear model refinements are identified from the measured force versus displacement data. This improved nonlinear force balance model is shown to capture the full actuation behavior of the miniature PAMs at each operating pressure and reconstruct miniature PAM response with much more accuracy than previously possible.
Analysis of nonlinear elastic behavior in miniature pneumatic artificial muscles
International Nuclear Information System (INIS)
Hocking, Erica G; Wereley, Norman M
2013-01-01
Pneumatic artificial muscles (PAMs) are well known for their excellent actuator characteristics, including high specific work, specific power, and power density. Recent research has focused on miniaturizing this pneumatic actuator technology in order to develop PAMs for use in small-scale mechanical systems, such as those found in robotic or aerospace applications. The first step in implementing these miniature PAMs was to design and characterize the actuator. To that end, this study presents the manufacturing process, experimental characterization, and analytical modeling of PAMs with millimeter-scale diameters. A fabrication method was developed to consistently produce low-cost, high performance, miniature PAMs using commercially available materials. The quasi-static behavior of these PAMs was determined through experimentation on a single actuator with an active length of 39.16 mm (1.54 in) and a diameter of 4.13 mm (0.1625 in). Testing revealed the PAM’s full evolution of force with displacement for operating pressures ranging from 207 to 552 kPa (30–80 psi in 10 psi increments), as well as the blocked force and free contraction at each pressure. Three key nonlinear phenomena were observed: nonlinear PAM stiffness, hysteresis of the force versus displacement response for a given pressure, and a pressure deadband. To address the analysis of the nonlinear response of these miniature PAMs, a nonlinear stress versus strain model, a hysteresis model, and a pressure bias are introduced into a previously developed force balance analysis. Parameters of these nonlinear model refinements are identified from the measured force versus displacement data. This improved nonlinear force balance model is shown to capture the full actuation behavior of the miniature PAMs at each operating pressure and reconstruct miniature PAM response with much more accuracy than previously possible. (paper)
Energy Technology Data Exchange (ETDEWEB)
Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr. [Los Alamos National Lab., NM (United States)
1993-11-01
Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime.
International Nuclear Information System (INIS)
Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr.
1993-01-01
Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime
Equations of motion for anisotropic nonlinear elastic continuum in gravitational field
International Nuclear Information System (INIS)
Sokolov, S.N.
1994-01-01
Equations of motion for anisotropic nonlinear elastic continuum in the gravitational field are written in the form convenient for numerical calculations. The energy-stress tensor is expressed through scalar and tensor products of three vectors frozen in the continuum. Examples of expansion of the energy-stress tensor into scalar and tensor invariants corresponding to some crystal classes are given. 47 refs
Directory of Open Access Journals (Sweden)
Alain Mignot
2005-09-01
Full Text Available This paper shows the existence of a solution of the quasi-static unilateral contact problem with nonlocal friction law for nonlinear elastic materials. We set up a variational incremental problem which admits a solution, when the friction coefficient is small enough, and then by passing to the limit with respect to time we obtain a solution.
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Thomsen, Jon Juel; Snaeland, Sveinn Orri
2008-01-01
The aim of this article is to investigate how highfrequency (HF) excitation, combined with strong nonlinear elastic material behavior, influences the effective material or structural properties for low-frequency excitation and wave propagation. The HF effects are demonstrated on discrete linear s...
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...
Ultrasound Shear Wave Simulation of Breast Tumor Using Nonlinear Tissue Elasticity
Directory of Open Access Journals (Sweden)
Dae Woo Park
2016-01-01
Full Text Available Shear wave elasticity imaging (SWEI can assess the elasticity of tissues, but the shear modulus estimated in SWEI is often less sensitive to a subtle change of the stiffness that produces only small mechanical contrast to the background tissues. Because most soft tissues exhibit mechanical nonlinearity that differs in tissue types, mechanical contrast can be enhanced if the tissues are compressed. In this study, a finite element- (FE- based simulation was performed for a breast tissue model, which consists of a circular (D: 10 mm, hard tumor and surrounding tissue (soft. The SWEI was performed with 0% to 30% compression of the breast tissue model. The shear modulus of the tumor exhibited noticeably high nonlinearity compared to soft background tissue above 10% overall applied compression. As a result, the elastic modulus contrast of the tumor to the surrounding tissue was increased from 0.46 at 0% compression to 1.45 at 30% compression.
A non-linear elastic constitutive framework for replicating plastic deformation in solids.
Energy Technology Data Exchange (ETDEWEB)
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.
Ultrasound Shear Wave Simulation of Breast Tumor Using Nonlinear Tissue Elasticity.
Park, Dae Woo
2015-01-01
Shear wave elasticity imaging (SWEI) can assess the elasticity of tissues, but the shear modulus estimated in SWEI is often less sensitive to a subtle change of the stiffness that produces only small mechanical contrast to the background tissues. Because most soft tissues exhibit mechanical nonlinearity that differs in tissue types, mechanical contrast can be enhanced if the tissues are compressed. In this study, a finite element- (FE-) based simulation was performed for a breast tissue model, which consists of a circular (D: 10 mm, hard) tumor and surrounding tissue (soft). The SWEI was performed with 0% to 30% compression of the breast tissue model. The shear modulus of the tumor exhibited noticeably high nonlinearity compared to soft background tissue above 10% overall applied compression. As a result, the elastic modulus contrast of the tumor to the surrounding tissue was increased from 0.46 at 0% compression to 1.45 at 30% compression.
Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.
Energy Technology Data Exchange (ETDEWEB)
Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-08-01
Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.
Extreme non-linear elasticity and transformation optics
DEFF Research Database (Denmark)
Gersborg, Allan Roulund; Sigmund, Ole
2010-01-01
realizations correspond to minimizers of elastic energy potentials for extreme values of the mechanical Poisson's ratio ν . For TE (Hz) polarized light an incompressible transformation ν = 1/2 is ideal and for TM (E z) polarized light one should use a compressible transformation with negative Poissons's ratio......Transformation optics is a powerful concept for designing novel optical components such as high transmission waveguides and cloaking devices. The selection of specific transformations is a non-unique problem. Here we reveal that transformations which allow for all dielectric and broadband optical...... ν = -1. For the TM polarization the mechanical analogy corresponds to a modified Liao functional known from the transformation optics literature. Finally, the analogy between ideal transformations and solid mechanical material models automates and broadens the concept of transformation optics...
Nitzan, Sarah H; Zega, Valentina; Li, Mo; Ahn, Chae H; Corigliano, Alberto; Kenny, Thomas W; Horsley, David A
2015-03-12
Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.
Lefèvre, Victor; Lopez-Pamies, Oscar
2017-02-01
This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response - under finite deformations and finite electric fields - of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method - this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics - to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi
Equivalent Representation Form of Oscillators with Elastic and Damping Nonlinear Terms
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others.
Adaptive, Small-Rotation-Based, Corotational Technique for Analysis of 2D Nonlinear Elastic Frames
Directory of Open Access Journals (Sweden)
Jaroon Rungamornrat
2014-01-01
Full Text Available This paper presents an efficient and accurate numerical technique for analysis of two-dimensional frames accounted for both geometric nonlinearity and nonlinear elastic material behavior. An adaptive remeshing scheme is utilized to optimally discretize a structure into a set of elements where the total displacement can be decomposed into the rigid body movement and one possessing small rotations. This, therefore, allows the force-deformation relationship for the latter part to be established based on small-rotation-based kinematics. Nonlinear elastic material model is integrated into such relation via the prescribed nonlinear moment-curvature relationship. The global force-displacement relation for each element can be derived subsequently using corotational formulations. A final system of nonlinear algebraic equations along with its associated gradient matrix for the whole structure is obtained by a standard assembly procedure and then solved numerically by Newton-Raphson algorithm. A selected set of results is then reported to demonstrate and discuss the computational performance including the accuracy and convergence of the proposed technique.
Whiteley, J. P.
2017-10-01
Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.
International Nuclear Information System (INIS)
Baltacioglu, A.K.; Civalek, O.; Akgoez, B.; Demir, F.
2011-01-01
This paper presents nonlinear static analysis of a rectangular laminated composite thick plate resting on nonlinear two-parameter elastic foundation with cubic nonlinearity. The plate formulation is based on first-order shear deformation theory (FSDT). The governing equation of motion for a rectangular laminated composite thick plate is derived by using the von Karman equation. The nonlinear static deflections of laminated plates on elastic foundation are investigated using the discrete singular convolution method. The effects of foundation and geometric parameters of plates on nonlinear deflections are investigated. The validity of the present method is demonstrated by comparing the present results with those available in the literature. - Highlights: → Large deflection analysis of laminated composite plates are investigated. → As foundation, nonlinear elastic models have been used firstly. → The effects of three-parameter foundation are investigated in detail.
International Nuclear Information System (INIS)
Ruas, V.
1982-09-01
A class of simplicial finite elements for solving incompressible elasticity problems in n-dimensional space, n=2 or 3, is presented. An asymmetric structure of the shape functions with respect to the centroid of the simplex, renders them particularly stable in the large strain case, in which the incompressibility condition is nonlinear. It is proved that under certain assembling conditions of the elements, there exists a solution to the corresponding discrete problems. Numerical examples illustrate the efficiency of the method. (Author) [pt
Czech Academy of Sciences Publication Activity Database
Dos Santos, S.; Vejvodová, Šárka; Převorovský, Zdeněk
2009-01-01
Roč. 19, č. 2 (2009), s. 14-14 ISSN 1213-3825. [NDT in PROGRESS. 12.11.2009-14.11.2009, Praha] R&D Projects: GA ČR GA106/07/1393; GA MPO(CZ) FR-TI1/274 Institutional research plan: CEZ:AV0Z20760514 Keywords : nonlinear elastic wave spectroscopy (NEWS) * ESAM * time reversal (TR) * TR-NEWS imaging * tomography * DORT Subject RIV: BI - Acoustics
A nonlinear magneto-thermo-elastic coupled hysteretic constitutive model for magnetostrictive alloys
International Nuclear Information System (INIS)
Jin Ke; Kou Yong; Zheng Xiaojing
2012-01-01
This paper presents a general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive alloys. The model considered here is thermodynamically motivated and based on the Gibbs free energy function. A nonlinear part of the elastic strain arising from magnetic domain rotation induced by the pre-stress is taken into account. Furthermore, the movement of the domain walls is incorporated to describe hysteresis based on Jiles–Atherton's model. Then a set of closed and analytical expressions of the constitutive law for the magnetostrictive rods and films are obtained, and the parameters appearing in the model can be determined by those measurable experiments in mechanics and physics. Comparing this model with other existing models in this field, the quantitative results show that the relationships obtained here are more effective to describe the effects of the pre-stress or in-plane residual stress and ambient temperature on the magnetization or the magnetostriction hysteresis loops. - Highlights: ► A general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive materials is proposed. ► Model is thermodynamically motivated and the reversible magnetic domain rotation and irreversible domain wall motion are taken. ► The predictions are in good accordance with the experimental data including both rods and films. ► Magnetostrictive alloys are sensitive to environment temperature and pre-stress or residual stress.
Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads
Directory of Open Access Journals (Sweden)
Donald Mark Santee
2006-01-01
Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.
Cox, B. S.; Groh, R. M. J.; Avitabile, D.; Pirrera, A.
2018-07-01
The buckling and post-buckling behaviour of slender structures is increasingly being harnessed for smart functionalities. Equally, the post-buckling regime of many traditional engineering structures is not being used for design and may therefore harbour latent load-bearing capacity for further structural efficiency. Both applications can benefit from a robust means of modifying and controlling the post-buckling behaviour for a specific purpose. To this end, we introduce a structural design paradigm termed modal nudging, which can be used to tailor the post-buckling response of slender engineering structures without any significant increase in mass. Modal nudging uses deformation modes of stable post-buckled equilibria to perturb the undeformed baseline geometry of the structure imperceptibly, thereby favouring the seeded post-buckling response over potential alternatives. The benefits of this technique are enhanced control over the post-buckling behaviour, such as modal differentiation for smart structures that use snap-buckling for shape adaptation, or alternatively, increased load-carrying capacity, increased compliance or a shift from imperfection sensitivity to imperfection insensitivity. Although these concepts are, in theory, of general applicability, we concentrate here on planar frame structures analysed using the nonlinear finite element method and numerical continuation procedures. Using these computational techniques, we show that planar frame structures may exhibit isolated regions of stable equilibria in otherwise unstable post-buckling regimes, or indeed stable equilibria entirely disconnected from the natural structural response. In both cases, the load-carrying capacity of these isolated stable equilibria is greater than the natural structural response of the frames. Using the concept of modal nudging it is possible to "nudge" the frames onto these equilibrium paths of greater load-carrying capacity. Due to the scale invariance of modal nudging
On the Geometrically Nonlinear Elastic Response of Class θ = 1 Tensegrity Prisms
Directory of Open Access Journals (Sweden)
Ida Mascolo
2018-03-01
Full Text Available The present work studies the geometrically nonlinear response of class θ = 1 tensegrity prisms modeled as a collection of elastic springs reacting in tension (strings or cables or compression (bars, under uniform uniaxial loading. The incremental equilibrium equations of the structure are numerically solved through a path-following procedure, with the aim of modeling the mechanical behavior of the structure in the large displacement regime. Several numerical results are presented with reference to a variety of physical models, which use two different materials for the cables and the bars, and show different aspect ratios associated with either “standard” or “expanded” configurations. An experimental validation of the predicted constitutive response is conducted with reference to a “thick” and a “slender” model, observing rather good theory vs. experiment matching. The given numerical and experimental results highlight that the elastic response of the examined structures may switch from stiffening to softening, depending on the geometry of the system, the magnitude of the external load, and the applied prestress. The outcomes of the current study confirm previous literature results on the elastic response of minimal tensegrity prisms, and pave the way to the use of tensegrity systems as nonlinear spring units forming tunable mechanical metamaterials.
A 2D nonlinear multiring model for blood flow in large elastic arteries
Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves
2017-12-01
In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.
Directory of Open Access Journals (Sweden)
Jessamine P Winer
2009-07-01
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.
On the geometrically nonlinear elastic response of class θ = 1 tensegrity prisms
Mascolo, Ida; Amendola, Ada; Zuccaro, Giulio; Feo, Luciano; Fraternali, Fernando
2018-03-01
The present work studies the geometrically nonlinear response of class ϑ=1 tensegrity prisms modeled as a collection of elastic springs reacting in tension (strings or cables) or compression (bars), under uniform uniaxial loading. The incremental equilibrium equations of the structure are numerically solved through a path-following procedure, with the aim of modeling the mechanical behavior of the structure in the large displacement regime. Several numerical results are presented with reference to a variety of physical models, which use two different materials for the cables and the bars, and show different aspect ratios associated with either 'standard' or 'expanded' configurations. An experimental validation of the predicted constitutive response is conducted with reference to a 'thick' and a 'slender' model, observing rather good theory vs. experiment matching. The given numerical and experimental results highlight that the elastic response of the examined structures may switch from stiffening to softening, depending on the geometry of the system, the magnitude of the external load, and the applied prestress. The outcomes of the current study confirm previous literature results on the elastic response of minimal tensegrity prisms, and pave the way to the use of tensegrity systems as nonlinear spring units forming tunable mechanical metamaterials.
Régnier, Julie; Bonilla, Luis-Fabian; Bard, Pierre-Yves; Bertrand, Etienne; Hollender, Fabrice; Kawase, Hiroshi; Sicilia, Deborah; Arduino, Pedro; Amorosi, Angelo; Asimaki, Dominiki; Pisano, F.
2016-01-01
PREdiction of NOn‐LINear soil behavior (PRENOLIN) is an international benchmark aiming to test multiple numerical simulation codes that are capable of predicting nonlinear seismic site response with various constitutive models. One of the objectives of this project is the assessment of the
Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies
Sozio, Fabio; Yavari, Arash
2017-01-01
In this paper we formulate the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework. It is assumed that the body grows as a result of addition of new (stress-free or pre-stressed) material on part of its boundary. We construct Riemannian material manifolds for a growing body with metrics explicitly depending on the history of applied external loads and deformation during accretion and the growth velocity. We numerically solve the governing equilibrium equations in the case of neo-Hookean solids and compare the accretion and residual stresses with those calculated using the linear mechanics of surface growth.
Kamali, M.; Shamsi, M.; Saidi, A. R.
2018-03-01
As a first endeavor, the effect of nonlinear elastic foundation on the postbuckling behavior of smart magneto-electro-elastic (MEE) composite nanotubes is investigated. The composite nanotube is affected by a non-uniform thermal environment. A typical MEE composite nanotube consists of microtubules (MTs) and carbon nanotubes (CNTs) with a MEE cylindrical nanoshell for smart control. It is assumed that the nanoscale layers of the system are coupled by a polymer matrix or filament network depending on the application. In addition to thermal loads, magneto-electro-mechanical loads are applied to the composite nanostructure. Length scale effects are taken into account using the nonlocal elasticity theory. The principle of virtual work and von Karman's relations are used to derive the nonlinear governing differential equations of MEE CNT-MT nanotubes. Using Galerkin's method, nonlinear critical buckling loads are determined. Various types of non-uniform temperature distribution in the radial direction are considered. Finally, the effects of various parameters such as the nonlinear constant of elastic medium, thermal loading factor and small scale coefficient on the postbuckling of MEE CNT-MT nanotubes are studied.
Metamaterials-based sensor to detect and locate nonlinear elastic sources
Energy Technology Data Exchange (ETDEWEB)
Gliozzi, Antonio S.; Scalerandi, Marco [Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino (Italy); Miniaci, Marco; Bosia, Federico [Department of Physics, University of Torino, Via Pietro Giuria 1, 10125 Torino (Italy); Pugno, Nicola M. [Laboratory of Bio-Inspired and Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento (Italy); Center for Materials and Microsystems, Fondazione Bruno Kessler, Via Sommarive 18, 38123 Povo (Trento) (Italy); School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom)
2015-10-19
In recent years, acoustic metamaterials have attracted increasing scientific interest for very diverse technological applications ranging from sound abatement to ultrasonic imaging, mainly due to their ability to act as band-stop filters. At the same time, the concept of chaotic cavities has been recently proposed as an efficient tool to enhance the quality of nonlinear signal analysis, particularly in the ultrasonic/acoustic case. The goal of the present paper is to merge the two concepts in order to propose a metamaterial-based device that can be used as a natural and selective linear filter for the detection of signals resulting from the propagation of elastic waves in nonlinear materials, e.g., in the presence of damage, and as a detector for the damage itself in time reversal experiments. Numerical simulations demonstrate the feasibility of the approach and the potential of the device in providing improved signal-to-noise ratios and enhanced focusing on the defect locations.
Metamaterials-based sensor to detect and locate nonlinear elastic sources
International Nuclear Information System (INIS)
Gliozzi, Antonio S.; Scalerandi, Marco; Miniaci, Marco; Bosia, Federico; Pugno, Nicola M.
2015-01-01
In recent years, acoustic metamaterials have attracted increasing scientific interest for very diverse technological applications ranging from sound abatement to ultrasonic imaging, mainly due to their ability to act as band-stop filters. At the same time, the concept of chaotic cavities has been recently proposed as an efficient tool to enhance the quality of nonlinear signal analysis, particularly in the ultrasonic/acoustic case. The goal of the present paper is to merge the two concepts in order to propose a metamaterial-based device that can be used as a natural and selective linear filter for the detection of signals resulting from the propagation of elastic waves in nonlinear materials, e.g., in the presence of damage, and as a detector for the damage itself in time reversal experiments. Numerical simulations demonstrate the feasibility of the approach and the potential of the device in providing improved signal-to-noise ratios and enhanced focusing on the defect locations
A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials
Li, Chen; Liao, Yufei
2018-03-01
Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.
Navon, M. I.; Stefanescu, R.; Fuelberg, H. E.; Marchand, M.
2012-12-01
NASA's launch of the GOES-R Lightning Mapper (GLM) in 2015 will provide continuous, full disc, high resolution total lightning (IC + CG) data. The data will be available at a horizontal resolution of approximately 9 km. Compared to other types of data, the assimilation of lightning data into operational numerical models has received relatively little attention. Previous efforts of lightning assimilation mostly have employed nudging. This paper will describe the implementation of 1D+3D/4D Var assimilation schemes of existing ground-based WTLN (Worldwide Total Lightning Network) lightning observations using non-linear observation operators in the incremental WRFDA system. To mimic the expected output of GLM, the WTLN data were used to generate lightning super-observations characterized by flash rates/81 km2/20 min. A major difficulty associated with variational approaches is the complexity of the observation operator that defines the model equivalent of lightning. We use Convective Available Potential Energy (CAPE) as a proxy between lightning data and model variables. This operator is highly nonlinear. Marecal and Mahfouf (2003) have shown that nonlinearities can prevent direct assimilation of rainfall rates in the ECMWF 4D-VAR (using the incremental formulation proposed by Courtier et al. (1994)) from being successful. Using data from the 2011 Tuscaloosa, AL tornado outbreak, we have proved that the direct assimilation of lightning data into the WRF 3D/4D - Var systems is limited due to this incremental approach. Severe threshold limits must be imposed on the innovation vectors to obtain an improved analysis. We have implemented 1D+3D/4D Var schemes to assimilate lightning observations into the WRF model. Their use avoids innovation vector constrains from preventing the inclusion of a greater number of lightning observations Their use also minimizes the problem that nonlinearities in the moist convective scheme can introduce discontinuities in the cost function
Detecting Damage in Composite Material Using Nonlinear Elastic Wave Spectroscopy Methods
Meo, Michele; Polimeno, Umberto; Zumpano, Giuseppe
2008-05-01
Modern aerospace structures make increasing use of fibre reinforced plastic composites, due to their high specific mechanical properties. However, due to their brittleness, low velocity impact can cause delaminations beneath the surface, while the surface may appear to be undamaged upon visual inspection. Such damage is called barely visible impact damage (BVID). Such internal damages lead to significant reduction in local strengths and ultimately could lead to catastrophic failures. It is therefore important to detect and monitor damages in high loaded composite components to receive an early warning for a well timed maintenance of the aircraft. Non-linear ultrasonic spectroscopy methods are promising damage detection and material characterization tools. In this paper, two different non-linear elastic wave spectroscopy (NEWS) methods are presented: single mode nonlinear resonance ultrasound (NRUS) and nonlinear wave modulation technique (NWMS). The NEWS methods were applied to detect delamination damage due to low velocity impact (<12 J) on various composite plates. The results showed that the proposed methodology appear to be highly sensitive to the presence of damage with very promising future NDT and structural health monitoring applications.
Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study
Carvalho, Gabriel D.
2013-11-11
We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity. © 2013 American Physical Society.
Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study
Carvalho, Gabriel D.; Miranda, José A.; Gadê lha, Hermes
2013-01-01
We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity. © 2013 American Physical Society.
Directory of Open Access Journals (Sweden)
Spannenberg Jescica
2017-09-01
Full Text Available Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.
Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions
Khajehtourian, Romik
Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium. The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium. In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The
Response statistics of rotating shaft with non-linear elastic restoring forces by path integration
Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael
2017-07-01
Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.
Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee
In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.
Compatible-strain mixed finite element methods for incompressible nonlinear elasticity
Faghih Shojaei, Mostafa; Yavari, Arash
2018-05-01
We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.
Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping
2015-10-01
We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.
Hamilton-Ostrogradsky principle in the theory of nonlinear elasticity with the combined approach
International Nuclear Information System (INIS)
Sporykhin, A.N.
1995-01-01
The assignment of a portion of the edge conditions in the deformed state and a portion of them in the initial state so that the initial and deformed states of the body are unknowns is a characteristic feature of the statement of a number of technological problems. Haber and Haber and Abel have performed studies in this direction, where constitutive relationships have been constructed within the framework of a linearly elastic material. Use of the displacements of individual particles as variable parameters in these relationships has required additional conditions that do not follow from the formulated problem. Use of familiar variational principles described in Euler coordinates is rendered difficult by the complexity of edge-condition formulation in the special case when the initial state is unknown. The latter is governed by the fact that variational principles are derived from the initial formulations open-quotes in Lagrangian coordinates,close quotes by recalculating the operation functional. Using Lagrange's principle, Novikov and Sporykhin constructed constitutive equations in the general case of a nonlinearly elastic body with edge conditions assigned in different configurations. An analogous problem is solved in this paper using the Hamilton-Ostrogradsky principle
Geometric method for stability of non-linear elastic thin shells
Ivanova, Jordanka
2002-01-01
PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surfac...
Nonlinear Hydroelastic Waves Generated due to a Floating Elastic Plate in a Current
Directory of Open Access Journals (Sweden)
Ping Wang
2017-01-01
Full Text Available Effects of underlying uniform current on the nonlinear hydroelastic waves generated due to an infinite floating plate are studied analytically, under the hypotheses that the fluid is homogeneous, incompressible, and inviscid. For the case of irrotational motion, the Laplace equation is the governing equation, with the boundary conditions expressing a balance among the hydrodynamics, the uniform current, and elastic force. It is found that the convergent series solutions, obtained by the homotopy analysis method (HAM, consist of the nonlinear hydroelastic wave profile and the velocity potential. The impacts of important physical parameters are discussed in detail. With the increment of the following current intensity, we find that the amplitudes of the hydroelastic waves decrease very slightly, while the opposing current produces the opposite effect on the hydroelastic waves. Furthermore, the amplitudes of waves increase very obviously for higher opposing current speed but reduce very slightly for higher following current speed. A larger amplitude of the incident wave increases the hydroelastic wave deflections for both opposing and following current, while for Young’s modulus of the plate there is the opposite effect.
Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud
2016-09-01
The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.
Mixing of two co-directional Rayleigh surface waves in a nonlinear elastic material.
Morlock, Merlin B; Kim, Jin-Yeon; Jacobs, Laurence J; Qu, Jianmin
2015-01-01
The mixing of two co-directional, initially monochromatic Rayleigh surface waves in an isotropic, homogeneous, and nonlinear elastic solid is investigated using analytical, finite element method, and experimental approaches. The analytical investigations show that while the horizontal velocity component can form a shock wave, the vertical velocity component can form a pulse independent of the specific ratios of the fundamental frequencies and amplitudes that are mixed. This analytical model is then used to simulate the development of the fundamentals, second harmonics, and the sum and difference frequency components over the propagation distance. The analytical model is further extended to include diffraction effects in the parabolic approximation. Finally, the frequency and amplitude ratios of the fundamentals are identified which provide maximum amplitudes of the second harmonics as well as of the sum and difference frequency components, to help guide effective material characterization; this approach should make it possible to measure the acoustic nonlinearity of a solid not only with the second harmonics, but also with the sum and difference frequency components. Results of the analytical investigations are then confirmed using the finite element method and the experimental feasibility of the proposed technique is validated for an aluminum specimen.
On the hyperporous non-linear elasticity model for fusion-relevant pebble beds
International Nuclear Information System (INIS)
Di Maio, P.A.; Giammusso, R.; Vella, G.
2010-01-01
Packed pebble beds are particular granular systems composed of a large amount of small particles, arranged in irregular lattices and surrounded by a gas filling interstitial spaces. Due to their heterogeneous structure, pebble beds have non-linear and strongly coupled thermal and mechanical behaviours whose constitutive models seem limited, being not suitable for fusion-relevant design-oriented applications. Within the framework of the modelling activities promoted for the lithiated ceramics and beryllium pebble beds foreseen in the Helium-Cooled Pebble Bed breeding blanket concept of DEMO, at the Department of Nuclear Engineering of the University of Palermo (DIN) a thermo-mechanical constitutive model has been set-up assuming that pebble beds can be considered as continuous, homogeneous and isotropic media. The present paper deals with the DIN non-linear elasticity constitutive model, based on the assumption that during the reversible straining of a pebble bed its effective logarithmic bulk modulus depends on the equivalent pressure according to a modified power law and its effective Poisson modulus remains constant. In these hypotheses the functional dependence of the effective tangential and secant bed deformation moduli on either the equivalent pressure or the volumetric strain have been derived in a closed analytical form. A procedure has been, then, defined to assess the model parameters for a given pebble bed from its oedometric test results and it has been applied to both polydisperse lithium orthosilicate and single size beryllium pebble beds.
Liu, Lili
2014-05-22
We present theoretical studies for the third-order elastic constants (TOECs) of superconducting antiperovskites MNNi 3 (M = Zn, Cd, Mg, Al, Ga, and In) using the density functional theory (DFT) and homogeneous deformation method. From the nonlinear least-square fitting, the elastic constants are extracted from a polynomial fit to the calculated strain-energy data. Calculated second-order elastic constants (SOECs) are compared with the previous theoretical calculations, and a very good agreement was found. The nonlinear effects often play an important role when the finite strains are larger than approximately 2.5 %. Besides, we have computed the pressure derivatives of SOECs and provided rough estimations for the Grüneisen constants of long-wavelength acoustic modes by using the calculated TOECs. © 2014 Springer Science+Business Media New York.
Liu, Lili; Wu, Xiaozhi; Wang, Rui; Gan, Liyong; Wei, Qunyi
2014-01-01
We present theoretical studies for the third-order elastic constants (TOECs) of superconducting antiperovskites MNNi 3 (M = Zn, Cd, Mg, Al, Ga, and In) using the density functional theory (DFT) and homogeneous deformation method. From the nonlinear least-square fitting, the elastic constants are extracted from a polynomial fit to the calculated strain-energy data. Calculated second-order elastic constants (SOECs) are compared with the previous theoretical calculations, and a very good agreement was found. The nonlinear effects often play an important role when the finite strains are larger than approximately 2.5 %. Besides, we have computed the pressure derivatives of SOECs and provided rough estimations for the Grüneisen constants of long-wavelength acoustic modes by using the calculated TOECs. © 2014 Springer Science+Business Media New York.
Directory of Open Access Journals (Sweden)
Yurii M. Streliaiev
2016-06-01
Full Text Available Three-dimensional quasistatic contact problem of two linearly elastic bodies' interaction with Coulomb friction taken into account is considered. The boundary conditions of the problem have been simplified by the modification of the Coulomb's law of friction. This modification is based on the introducing of a delay in normal contact tractions that bound tangent contact tractions in the Coulomb's law of friction expressions. At this statement the problem is reduced to a sequence of similar systems of nonlinear integral equations describing bodies' interaction at each step of loading. A method for an approximate solution of the integral equations system corresponded to each step of loading is applied. This method consists of system regularization, discretization of regularized system and iterative process application for solving the discretized system. A numerical solution of a contact problem of an elastic sphere with an elastic half-space interaction under increasing and subsequently decreasing normal compressive force has been obtained.
International Nuclear Information System (INIS)
Mirzade, Fikret Kh.
2005-01-01
The propagation of longitudinal strain wave in a plate with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the nonequilibrium laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation and relaxation of lattice defects on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of shock fronts. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate to linear and nonlinear elastic modulus, and spatial dispersion are determined
Meerson, Baruch; Fouxon, Itzhak; Vilenkin, Arkady
2008-02-01
We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald
Gorb, Yuliya; Walton, Jay R.
2010-01-01
We model and analyze the response of nonlinear, residually stressed elastic bodies subjected to small amplitude vibrations superimposed upon large deformations. The problem derives from modeling the use of intravascular ultrasound (IVUS) imaging
Angela Mihai, L.; Goriely, Alain
2013-01-01
Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects
International Nuclear Information System (INIS)
Civalek, Ö.
2014-01-01
In the present study nonlinear static and dynamic responses of shallow spherical shells resting on Winkler–Pasternak elastic foundations are carried out. The formulation of the shells is based on the Donnell theory. The nonlinear governing equations of motion of shallow shells are discretized in space and time domains using the discrete singular convolution and the differential quadrature methods, respectively. The validity of the present method is demonstrated by comparing the present results with those available in the open literature. The effects of the Winkler and Pasternak foundation parameters on nonlinear static and dynamic response of shells are investigated. Some results are also presented for circular plate as special case. Damping effect on nonlinear dynamic response of shells is studied. It is important to state that the increase in damping parameter causes decrease in the dynamic response of the shells. It is shown that the shear parameter of the foundation has a significant influence on the dynamic and static response of the shells. Also, the response of the shell is decreased with the increasing value of the shear parameter of the foundation. Parametric studies considering different geometric variables have also been investigated. -- Highlights: • Nonlinear responses of shallow spherical shells are presented. • The effects of foundation parameters are investigated. • Damping effect on nonlinear dynamic response of shells is also studied
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. Copyright © 2012 Elsevier Ltd. All rights reserved.
Nonlinear Elasticity of Borocarbide Superconductor YNi2B2C: A First-Principles Study
Directory of Open Access Journals (Sweden)
Lili Liu
2017-01-01
Full Text Available First-principles calculations combined with homogeneous deformation methods are used to investigate the second- and third-order elastic constants of YNi2B2C with tetragonal structure. The predicted lattice constants and second-order elastic constants of YNi2B2C agree well with the available data. The effective second-order elastic constants are obtained from the second- and third-order elastic constants for YNi2B2C. Based on the effective second-order elastic constants, Pugh’s modulus ratio, Poisson’s ratio, and Vickers hardness of YNi2B2C under high pressure are further investigated. It is shown that the ductility of YNi2B2C increases with increasing pressure.
Knight, Norman F., Jr.; Warren, Jerry E.; Elliott, Kenny B.; Song, Kyongchan; Raju, Ivatury S.
2012-01-01
Elastic-plastic, large-deflection nonlinear thermo-mechanical stress analyses are performed for the Space Shuttle external tank s intertank stringers. Detailed threedimensional finite element models are developed and used to investigate the stringer s elastic-plastic response for different thermal and mechanical loading events from assembly through flight. Assembly strains caused by initial installation on an intertank panel are accounted for in the analyses. Thermal loading due to tanking was determined to be the bounding loading event. The cryogenic shrinkage caused by tanking resulted in a rotation of the intertank chord flange towards the center of the intertank, which in turn loaded the intertank stringer feet. The analyses suggest that the strain levels near the first three fasteners remain sufficiently high that a failure may occur. The analyses also confirmed that the installation of radius blocks on the stringer feet ends results in an increase in the stringer capability.
Energy Technology Data Exchange (ETDEWEB)
Tahara, Masaki [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Kim, Hee Young, E-mail: heeykim@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Inamura, Tomonari; Hosoda, Hideki [Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Miyazaki, Shuichi, E-mail: miyazaki@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Center of Excellence for Advanced Materials Research, King Abdulaziz University, P.O. Box 80203, Jeddah 21589 (Saudi Arabia); School of Materials Science and Engineering and ERI, Gyeongsang National University, 900 Gazwadong, Jinju, Gyeongnam 660-701 (Korea, Republic of)
2013-11-15
Highlights: ► {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉{sub β}* rel rods and {1 1 1}{sub β}* rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation.
International Nuclear Information System (INIS)
Tahara, Masaki; Kim, Hee Young; Inamura, Tomonari; Hosoda, Hideki; Miyazaki, Shuichi
2013-01-01
Highlights: ► {110} β 〈11 ¯ 0〉 β transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉 β * rel rods and {1 1 1} β * rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110} β 〈11 ¯ 0〉 β transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation
Energy Technology Data Exchange (ETDEWEB)
Byers, Loren W. [Los Alamos National Laboratory; Ten Cate, James A. [Los Alamos National Laboratory; Johnson, Paul A. [Los Alamos National Laboratory
2012-06-28
Nonlinear resonance ultrasound spectroscopy experiments conducted on concrete cores, one chemically and mechanically damaged by alkali-silica reactivity, and one undamaged, show that this material displays highly nonlinear wave behavior, similar to many other damaged materials. They find that the damaged sample responds more nonlinearly, manifested by a larger resonant peak and modulus shift as a function of strain amplitude. The nonlinear response indicates that there is a hysteretic influence in the stress-strain equation of state. Further, as in some other materials, slow dynamics are present. The nonlinear response they observe in concrete is an extremely sensitive indicator of damage. Ultimately, nonlinear wave methods applied to concrete may be used to guide mixing, curing, or other production techniques, in order to develop materials with particular desired qualities such as enhanced strength or chemical resistance, and to be used for damage inspection.
Czech Academy of Sciences Publication Activity Database
Kosík, Adam; Feistauer, M.; Hadrava, Martin; Horáček, Jaromír
2015-01-01
Roč. 267, September (2015), s. 382-396 ISSN 0096-3003 R&D Projects: GA ČR(CZ) GAP101/11/0207 Institutional support: RVO:61388998 Keywords : discontinuous Galerkin method * nonlinear elasticity * compressible viscous flow * fluid–structure interaction Subject RIV: BI - Acoustics Impact factor: 1.345, year: 2015 http://www.sciencedirect.com/science/article/pii/S0096300315002453/pdfft?md5=02d46bc730e3a7fb8a5008aaab1da786&pid=1-s2.0-S0096300315002453-main.pdf
Huang, Yonghui; Yang, Zhicheng; Liu, Airong; Fu, Jiyang
2018-05-28
The buckling behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) shallow arches with elastic rotational constraints under uniform radial load is investigated in this paper. The nonlinear equilibrium equation of the FG-GPLRC shallow arch with elastic rotational constraints under uniform radial load is established using the Halpin-Tsai micromechanics model and the principle of virtual work, from which the critical buckling load of FG-GPLRC shallow arches with elastic rotational constraints can be obtained. This paper gives special attention to the effect of the GPL distribution pattern, weight fraction, geometric parameters, and the constraint stiffness on the buckling load. The numerical results show that all of the FG-GPLRC shallow arches with elastic rotational constraints have a higher buckling load-carrying capacity compared to the pure epoxy arch, and arches of the distribution pattern X have the highest buckling load among four distribution patterns. When the GPL weight fraction is constant, the thinner and larger GPL can provide the better reinforcing effect to the FG-GPLRC shallow arch. However, when the value of the aspect ratio is greater than 4, the flakiness ratio is greater than 103, and the effect of GPL's dimensions on the buckling load of the FG-GPLRC shallow arch is less significant. In addition, the buckling model of FG-GPLRC shallow arch with elastic rotational constraints is changed as the GPL distribution patterns or the constraint stiffness changes. It is expected that the method and the results that are presented in this paper will be useful as a reference for the stability design of this type of arch in the future.
Lucchetti, Liana; Fraccia, Tommaso P; Ciciulla, Fabrizio; Bellini, Tommaso
2017-07-10
Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced birefringence, we can readily extract the twist elastic coefficient K 22 of thermotropic and lyotropic chiral nematics (N*). The value of K 22 we obtain for chiral doped 5CB thermotropic N* well matches those reported in the literature. With this same strategy, we could determine for the first time K 22 of the N* phase of concentrated aqueous solutions of DNA oligomers, bypassing the limitations that so far prevented measuring the elastic constants of this class of liquid crystalline materials. The present study also enlightens the significant nonlinear optical response of DNA liquid crystals.
Claessens, T E; Georgakopoulos, D; Afanasyeva, M; Vermeersch, S J; Millar, H D; Stergiopulos, N; Westerhof, N; Verdonck, P R; Segers, P
2006-04-01
The linear time-varying elastance theory is frequently used to describe the change in ventricular stiffness during the cardiac cycle. The concept assumes that all isochrones (i.e., curves that connect pressure-volume data occurring at the same time) are linear and have a common volume intercept. Of specific interest is the steepest isochrone, the end-systolic pressure-volume relationship (ESPVR), of which the slope serves as an index for cardiac contractile function. Pressure-volume measurements, achieved with a combined pressure-conductance catheter in the left ventricle of 13 open-chest anesthetized mice, showed a marked curvilinearity of the isochrones. We therefore analyzed the shape of the isochrones by using six regression algorithms (two linear, two quadratic, and two logarithmic, each with a fixed or time-varying intercept) and discussed the consequences for the elastance concept. Our main observations were 1) the volume intercept varies considerably with time; 2) isochrones are equally well described by using quadratic or logarithmic regression; 3) linear regression with a fixed intercept shows poor correlation (R(2) volume intercept of the ESPVR. In conclusion, the linear time-varying elastance fails to provide a sufficiently robust model to account for changes in pressure and volume during the cardiac cycle in the mouse ventricle. A new framework accounting for the nonlinear shape of the isochrones needs to be developed.
International Nuclear Information System (INIS)
Ruffino, E.; Scalerandi, M.
2000-01-01
As discovered by recent quasi-static and dynamic resonance experiments, the classical nonlinear theory fails in describing the hysteretic behaviour of nonlinear mesoscopic materials like rocks, concrete, etc. The paper applies the local interaction simulation approach (LISA) for studying such kind of nonclassical nonlinearity. To this purpose, in the LISA treatment of ultrasonic wave propagation has been included a phenomenological model, based on the PM space approach, of the local mesoscopic features of rocks and other materials with localized damages. A quantitative comparison of simulation and experimental results in quasi-static experiments is also presented
DEFF Research Database (Denmark)
Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari
2010-01-01
and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However......, as with other analytical techniques, certain limitations restrict the wide application of perturbation methods, most important of which is the dependence of these methods on the existence of a small parameter in the equation. Disappointingly, the majority of nonlinear problems have no small parameter at all......Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...
Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall
Garashchuk, Ivan R.; Sinelshchikov, Dmitry I.; Kudryashov, Nikolay A.
2018-05-01
Contrast agent microbubbles, which are encapsulated gas bubbles, are widely used to enhance ultrasound imaging. There are also several new promising applications of the contrast agents such as targeted drug delivery and noninvasive therapy. Here we study three models of the microbubble dynamics: a nonencapsulated bubble oscillating close to an elastic wall, a simple coated bubble and a coated bubble near an elastic wall.We demonstrate that complex dynamics can occur in these models. We are particularly interested in the multistability phenomenon of bubble dynamics. We show that coexisting attractors appear in all of these models, but for higher acoustic pressures for the models of an encapsulated bubble.We demonstrate how several tools can be used to localize the coexisting attractors. We provide some considerations why the multistability can be undesirable for applications.
Nonlinear shear wave in a non Newtonian visco-elastic medium
Energy Technology Data Exchange (ETDEWEB)
Banerjee, D.; Janaki, M. S.; Chakrabarti, N. [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700 064 (India); Chaudhuri, M. [Max-Planck-Institut fuer extraterrestrische Physik, 85741 Garching (Germany)
2012-06-15
An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau-Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries equation. This model has application from laboratory to astrophysical plasmas as well as in biological systems.
Analysis of elastic nonlinearity for impact damage detection in composite laminates
International Nuclear Information System (INIS)
Frau, A; Porcu, M C; Aymerich, F; Pieczonka, L; Staszewski, W J
2015-01-01
This paper concerns the experimental analysis of nonlinear response features of a composite laminate plate for impact damage detection. The measurement procedure is based on the Scaling Subtraction Method (SSM) and consists in exciting the damaged specimen with two sinusoidal signals at different amplitude. The linearly rescaled response signal at low amplitude excitation is subtracted from the response at large amplitude excitation to extract the nonlinear signatures. The latter are analysed in the time domain to infer the presence of damage. Results are compared with frequency domain analyses using the nonlinear vibro-acoustic modulation technique (NWMS). Changes in amplitude and phase as well as modulation effects of the acquired responses are also monitored. Surface-bonded, low profile piezoceramic transducers are used for excitation and sensing. Both measurements techniques are applied to detect barely visible impact damage in laminate composite plate. Non-destructive penetrant-enhanced X-ray inspections are carried out to characterize the extent of internal damage. The behavior of the nonlinear features and the sensitivity of each technique are also investigated in the paper. (paper)
Hu, Zhan; Zheng, Gangtie
2016-08-01
A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.
Knight, Norman F., Jr.; Song, Kyongchan; Elliott, Kenny B.; Raju, Ivatury S.; Warren, Jerry E.
2012-01-01
Elastic-plastic, large-deflection nonlinear stress analyses are performed for the external hat-shaped stringers (or stiffeners) on the intertank portion of the Space Shuttle s external tank. These stringers are subjected to assembly strains when the stringers are initially installed on an intertank panel. Four different stringer-feet configurations including the baseline flat-feet, the heels-up, the diving-board, and the toes-up configurations are considered. The assembly procedure is analytically simulated for each of these stringer configurations. The location, size, and amplitude of the strain field associated with the stringer assembly are sensitive to the assumed geometry and assembly procedure. The von Mises stress distributions from these simulations indicate that localized plasticity will develop around the first eight fasteners for each stringer-feet configuration examined. However, only the toes-up configuration resulted in high assembly hoop strains.
BOERTJENS, G. J.; VAN HORSSEN, W. T.
2000-08-01
In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.
Connolly, Joe; Carlson, Jan-Renee; Kopasakis, George; Woolwine, Kyle
2015-01-01
This paper covers the development of an integrated nonlinear dynamic model for a variable cycle turbofan engine, supersonic inlet, and convergent-divergent nozzle that can be integrated with an aeroelastic vehicle model to create an overall Aero-Propulso-Servo-Elastic (APSE) modeling tool. The primary focus of this study is to provide a means to capture relevant thrust dynamics of a full supersonic propulsion system by using relatively simple quasi-one dimensional computational fluid dynamics (CFD) methods that will allow for accurate control algorithm development and capture the key aspects of the thrust to feed into an APSE model. Previously, propulsion system component models have been developed and are used for this study of the fully integrated propulsion system. An overview of the methodology is presented for the modeling of each propulsion component, with a focus on its associated coupling for the overall model. To conduct APSE studies the described dynamic propulsion system model is integrated into a high fidelity CFD model of the full vehicle capable of conducting aero-elastic studies. Dynamic thrust analysis for the quasi-one dimensional dynamic propulsion system model is presented along with an initial three dimensional flow field model of the engine integrated into a supersonic commercial transport.
DESTRUCTION CRITERION IN MODEL OF NON-LINEAR ELASTIC PLASTIC MEDIUM
Directory of Open Access Journals (Sweden)
O. L. Shved
2014-01-01
Full Text Available The paper considers a destruction criterion in a specific phenomenological model of elastic plastic medium which significantly differs from the known criteria. In case of vector interpretation of rank-2 symmetric tensors yield surface in the Cauchy stress space is formed by closed piecewise concave surfaces of its deviator sections with due account of experimental data. Section surface is determined by normal vector which is selected from two private vectors of criterial “deviator” operator. Such selection is not always possible in the case of anisotropy growth. It is expected that destruction can only start when a process point in the stress space is located in the current deviator section of the yield surface. It occurs when a critical point appears in the section, and a private value of an operator becomes N-fold in the point that determines the private vector corresponding to the normal vector. Unique and reasonable selection of the normal vector becomes impossible in the critical point and an yield criteria loses its significance in the point.When the destruction initiation is determined there is a possibility of a special case due to the proposed conic form of the yield surface. The deviator section degenerates into the point at the yield surface peak. Criterion formulation at the surface peak lies in the fact that there is no physically correct solution while using a state equation in regard to elastic distortion measures with a fixed tensor of elastic turn. Such usage of the equation is always possible for the rest points of the yield surface and it is considered as an obligatory condition for determination of the deviator section. A critical point is generally absent at any deviator section of the yield surface for isotropic material. A limiting value of the mean stress has been calculated at uniform tension.
Erler, Norbert; Groß, Michael
2015-05-01
Since many years the relevance of fibre-reinforced polymers is steadily increasing in fields of engineering, especially in aircraft and automotive industry. Due to the high strength in fibre direction, but the possibility of lightweight construction, these composites replace more and more traditional materials as metals. Fibre-reinforced polymers are often manufactured from glass or carbon fibres as attachment parts or from steel or nylon cord as force transmission parts. Attachment parts are mostly subjected to small strains, but force transmission parts usually suffer large deformations in at least one direction. Here, a geometrically nonlinear formulation is necessary. Typical examples are helicopter rotor blades, where the fibres have the function to stabilize the structure in order to counteract large centrifugal forces. For long-run analyses of rotor blade deformations, we have to apply numerically stable time integrators for anisotropic materials. This paper presents higher-order accurate and numerically stable time stepping schemes for nonlinear elastic fibre-reinforced continua with anisotropic stress behaviour.
Nonlinear analysis of the inflation of an initially flat, circular, elastic disk
International Nuclear Information System (INIS)
Christensen, R.M.; Feng, W.W.
1986-01-01
An approximate analysis is given for the inflation of a thin, flat circular disk of elastomeric material. The analysis results in a closed-form analytical solution for the maximum displacement as a function of pressure. The method is illustrated through the use of a Mooney-Rivlin material model. The results are compared with the exact solution, obtained by numerical means, and they are satisfactory, up into the range of several hundred percent strain. The method greatly simplifies the procedure for reducing test data, from this type of test, to nonlinear range mechanical properties
Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J
2017-11-01
The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Civalek, Oemer
2005-01-01
The nonlinear dynamic response of doubly curved shallow shells resting on Winkler-Pasternak elastic foundation has been studied for step and sinusoidal loadings. Dynamic analogues of Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by numerical examples. The shear parameter G of the Pasternak foundation and the stiffness parameter K of the Winkler foundation have been found to have a significant influence on the dynamic response of the shell. It is concluded from the present study that the HDQ-FD methodolgy is a simple, efficient, and accurate method for the nonlinear analysis of doubly curved shallow shells resting on two-parameter elastic foundation
Real-time simulation of the nonlinear visco-elastic deformations of soft tissues.
Basafa, Ehsan; Farahmand, Farzam
2011-05-01
Mass-spring-damper (MSD) models are often used for real-time surgery simulation due to their fast response and fairly realistic deformation replication. An improved real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was developed and tested. The mechanical realization of conventional MSD models was improved using nonlinear springs and nodal dampers, while their high computational efficiency was maintained using an adapted implicit integration algorithm. New practical algorithms for model parameter tuning, collision detection, and simulation were incorporated. The model was able to replicate complex biological soft tissue mechanical properties under large deformations, i.e., the nonlinear and viscoelastic behaviors. The simulated response of the model after tuning of its parameters to the experimental data of a deer liver sample, closely tracked the reference data with high correlation and maximum relative differences of less than 5 and 10%, for the tuning and testing data sets respectively. Finally, implementation of the proposed model and algorithms in a graphical environment resulted in a real-time simulation with update rates of 150 Hz for interactive deformation and haptic manipulation, and 30 Hz for visual rendering. The proposed real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was efficient, realistic, and accurate in ex vivo testing. This model is a suitable candidate for testing in vivo during laparoscopic surgery.
Directory of Open Access Journals (Sweden)
Chenji Wei
2018-02-01
Full Text Available Gas transport in shale gas reservoirs is largely affected by rock properties such as permeability. These properties are often sensitive to the in-situ stress state changes. Accurate modeling of shale gas transport in shale reservoir rocks considering the stress sensitive effects on rock petrophysical properties is important for successful shale gas extraction. Nonlinear elasticity in stress sensitive reservoir rocks depicts the nonlinear stress-strain relationship, yet it is not thoroughly studied in previous reservoir modeling works. In this study, an improved coupled flow and geomechanics model that considers nonlinear elasticity is proposed. The model is based on finite element methods, and the nonlinear elasticity in the model is validated with experimental data on shale samples selected from the Longmaxi Formation in Sichuan Basin China. Numerical results indicate that, in stress sensitive shale rocks, nonlinear elasticity affects shale permeability, shale porosity, and distributions of effective stress and pore pressure. Elastic modulus change is dependent on not only in-situ stress state but also stress history path. Without considering nonlinear elasticity, the modeling of shale rock permeability in Longmaxi Formation can overestimate permeability values by 1.6 to 53 times.
Li, Qian; Matula, Thomas J; Tu, Juan; Guo, Xiasheng; Zhang, Dong
2013-02-21
It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear 'Cross law' to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius-time curves and the numerical simulations demonstrate that the 'compression-only' behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., 'shear-thinning' and 'strain-softening') in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity.
International Nuclear Information System (INIS)
Li Qian; Tu Juan; Guo Xiasheng; Zhang Dong; Matula, Thomas J
2013-01-01
It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear ‘Cross law’ to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius–time curves and the numerical simulations demonstrate that the ‘compression-only’ behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., ‘shear-thinning’ and ‘strain-softening’) in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity. (paper)
Contoyannis, Paul; Hurley, Jeremiah; Grootendorst, Paul; Jeon, Sung-Hee; Tamblyn, Robyn
2005-09-01
The price elasticity of demand for prescription drugs is a crucial parameter of interest in designing pharmaceutical benefit plans. Estimating the elasticity using micro-data, however, is challenging because insurance coverage that includes deductibles, co-insurance provisions and maximum expenditure limits create a non-linear price schedule, making price endogenous (a function of drug consumption). In this paper we exploit an exogenous change in cost-sharing within the Quebec (Canada) public Pharmacare program to estimate the price elasticity of expenditure for drugs using IV methods. This approach corrects for the endogeneity of price and incorporates the concept of a 'rational' consumer who factors into consumption decisions the price they expect to face at the margin given their expected needs. The IV method is adapted from an approach developed in the public finance literature used to estimate income responses to changes in tax schedules. The instrument is based on the price an individual would face under the new cost-sharing policy if their consumption remained at the pre-policy level. Our preferred specification leads to expenditure elasticities that are in the low range of previous estimates (between -0.12 and -0.16). Naïve OLS estimates are between 1 and 4 times these magnitudes. (c) 2005 John Wiley & Sons, Ltd.
Xu, Jingping; Tripathy, Sakya; Rubin, Jonathan M; Stidham, Ryan W; Johnson, Laura A; Higgins, Peter D R; Kim, Kang
2012-03-01
Strain developed under quasi-static deformation has been mostly used in ultrasound elasticity imaging (UEI) to determine the stiffness change of tissues. However, the strain measure in UEI is often less sensitive to a subtle change of stiffness. This is particularly true for Crohn's disease where we have applied strain imaging to the differentiation of acutely inflamed bowel from chronically fibrotic bowel. In this study, a new nonlinear elastic parameter of the soft tissues is proposed to overcome this limit. The purpose of this study is to evaluate the newly proposed method and demonstrate its feasibility in the UEI. A nonlinear characteristic of soft tissues over a relatively large dynamic range of strain was investigated. A simplified tissue model based on a finite element (FE) analysis was integrated with a laboratory developed ultrasound radio-frequency (RF) signal synthesis program. Two-dimensional speckle tracking was applied to this model to simulate the nonlinear behavior of the strain developed in a target inclusion over the applied average strain to the surrounding tissues. A nonlinear empirical equation was formulated and optimized to best match the developed strain-to-applied strain relation obtained from the FE simulation. The proposed nonlinear equation was applied to in vivo measurements and nonlinear parameters were further empirically optimized. For an animal model, acute and chronic inflammatory bowel disease was induced in Lewis rats with trinitrobenzene sulfonic acid (TNBS)-ethanol treatments. After UEI, histopathology and direct mechanical measurements were performed on the excised tissues. The extracted nonlinear parameter from the developed strain-to-applied strain relation differentiated the three different tissue types with 1.96 ± 0.12 for normal, 1.50 ± 0.09 for the acutely inflamed and 1.03 ± 0.08 for the chronically fibrotic tissue. T-tests determined that the nonlinear parameters between normal, acutely inflamed and fibrotic tissue
International Nuclear Information System (INIS)
Singh, B.N.; Lal, Achchhe
2010-01-01
This study deals with the stochastic post-buckling and nonlinear free vibration analysis of a laminated composite plate resting on a two parameters Pasternak foundation with Winkler cubic nonlinearity having uncertain system properties. The system properties are modeled as basic random variables. A C 0 nonlinear finite element formulation of the random problem based on higher-order shear deformation theory in the von Karman sense is presented. A direct iterative method in conjunction with a stochastic nonlinear finite element method proposed earlier by the authors is extended to analyze the effect of uncertainty in system properties on the post-buckling and nonlinear free vibration of the composite plates having Winler type of geometric nonlinearity. Mean as well as standard deviation of the responses have been obtained for various combinations of geometric parameters, foundation parameters, stacking sequences and boundary conditions and compared with those available in the literature and Monte Carlo simulation.
National Aeronautics and Space Administration — The overall goal of the project is to develop reliable reduced order modeling technologies to automatically generate nonlinear, parameter-varying (PV),...
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Shahriar Dastjerdi
2016-06-01
Full Text Available Nonlinear bending analysis of orthotropic annular/circular graphene sheets has been studied based on the non-local elasticity theory. The first order shear deformation theory (FSDT is applied in combination with the nonlinear Von-Karman strain field. The obtained differential equations are solved by using two methods, first the differential quadrature method (DQM and a new semi-analytical polynomial method (SAPM which is innovated by the authors. Applying the DQM or SAPM, the differential equations are transformed to nonlinear algebraic equations system. Then the Newton–Raphson iterative scheme is used. First, the obtained results from DQM and SAPM are compared and it is concluded that although the SAPM’s formulation is considerably simpler than DQM, however, the SAPM’s results are so close to DQM. The results are validated with available papers. Finally, the effects of small scale parameter on the results, the comparison between local and non-local theories, and linear to nonlinear analyses are investigated.
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Chaudhari Virendra Kumar
2017-01-01
Full Text Available This paper deals with the investigation of nonlinear free vibration behavior of elastically supported carbon nanotube reinforced composite (CNTRC beam subjected to thermal loading with random system properties. Material properties of each constituent’s material, volume fraction exponent and foundation parameters are considered as uncorrelated Gaussian random input variables. The beam is supported by a Pasternak foundation with Winkler cubic nonlinearity. The higher order shear deformation theory (HSDT with von-Karman non-linearity is used to formulate the governing equation using Hamilton principle. Convergence and validation study is carried out through the comparison with the available results in the literature for authenticity and accuracy of the present approach used in the analysis. First order perturbation technique (FOPT,Second order perturbation technique (SOPT and Monte Carlo simulation (MCS methods are employed to investigate the effect of geometric configuration, volume fraction exponent, foundation parameters, distribution of reinforcement and thermal loading on nonlinear vibration characteristics CNTRC beam.The present work signifies the accurate analysis of vibrational behaviour influences by different random variables. Results are presented in terms of mean, variance (COV and probability density function (PDF for various aforementioned parameters.
DEFF Research Database (Denmark)
Schløer, Signe; Bredmose, Henrik; Bingham, Harry B.
2016-01-01
The response of an offshore wind turbine tower and its monopile foundation has been investigated when exposed to linear and fully nonlinear irregular waves on four different water depths. The investigation focuses on the consequences of including full nonlinearity in the wave kinematics. The line...
Elastic metamaterial beam with remotely tunable stiffness
Energy Technology Data Exchange (ETDEWEB)
Qian, Wei [University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240 (China); Yu, Zhengyue [School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Wang, Xiaole [School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Lai, Yun [College of Physics, Optoelectronics and Energy & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006 (China); Yellen, Benjamin B., E-mail: yellen@duke.edu [University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240 (China); Department of Mechanical Engineering and Materials Science, Duke University, P.O. Box 90300, Hudson Hall, Durham, North Carolina 27708 (United States)
2016-02-07
We demonstrate a dynamically tunable elastic metamaterial, which employs remote magnetic force to adjust its vibration absorption properties. The 1D metamaterial is constructed from a flat aluminum beam milled with a linear array of cylindrical holes. The beam is backed by a thin elastic membrane, on which thin disk-shaped permanent magnets are mounted. When excited by a shaker, the beam motion is tracked by a Laser Doppler Vibrometer, which conducts point by point scanning of the vibrating element. Elastic waves are unable to propagate through the beam when the driving frequency excites the first elastic bending mode in the unit cell. At these frequencies, the effective mass density of the unit cell becomes negative, which induces an exponentially decaying evanescent wave. Due to the non-linear elastic properties of the membrane, the effective stiffness of the unit cell can be tuned with an external magnetic force from nearby solenoids. Measurements of the linear and cubic static stiffness terms of the membrane are in excellent agreement with experimental measurements of the bandgap shift as a function of the applied force. In this implementation, bandgap shifts by as much as 40% can be achieved with ∼30 mN of applied magnetic force. This structure has potential for extension in 2D and 3D, providing a general approach for building dynamically tunable elastic metamaterials for applications in lensing and guiding elastic waves.
Elastic metamaterial beam with remotely tunable stiffness
Qian, Wei; Yu, Zhengyue; Wang, Xiaole; Lai, Yun; Yellen, Benjamin B.
2016-02-01
We demonstrate a dynamically tunable elastic metamaterial, which employs remote magnetic force to adjust its vibration absorption properties. The 1D metamaterial is constructed from a flat aluminum beam milled with a linear array of cylindrical holes. The beam is backed by a thin elastic membrane, on which thin disk-shaped permanent magnets are mounted. When excited by a shaker, the beam motion is tracked by a Laser Doppler Vibrometer, which conducts point by point scanning of the vibrating element. Elastic waves are unable to propagate through the beam when the driving frequency excites the first elastic bending mode in the unit cell. At these frequencies, the effective mass density of the unit cell becomes negative, which induces an exponentially decaying evanescent wave. Due to the non-linear elastic properties of the membrane, the effective stiffness of the unit cell can be tuned with an external magnetic force from nearby solenoids. Measurements of the linear and cubic static stiffness terms of the membrane are in excellent agreement with experimental measurements of the bandgap shift as a function of the applied force. In this implementation, bandgap shifts by as much as 40% can be achieved with ˜30 mN of applied magnetic force. This structure has potential for extension in 2D and 3D, providing a general approach for building dynamically tunable elastic metamaterials for applications in lensing and guiding elastic waves.
International Nuclear Information System (INIS)
Batou, A.; Soize, C.; Brie, N.
2013-01-01
Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading
Energy Technology Data Exchange (ETDEWEB)
Batou, A., E-mail: anas.batou@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Brie, N., E-mail: nicolas.brie@edf.fr [EDF R and D, Département AMA, 1 avenue du général De Gaulle, 92140 Clamart (France)
2013-09-15
Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading.
Directory of Open Access Journals (Sweden)
Mustapha Lahmar
2015-04-01
Full Text Available On the basis of the V. K. Stokes micro-continuum theory, the effects of couple stresses on the nonlinear dynamic response of the unbalanced Jeffcott’s flexible rotor supported by layered hydrodynamic journal bearings is presented in this paper. A nonlinear transient modified Reynolds’ equation is derived and discretized by the finite element method to obtain the fluid-film pressure field as well as the film thickness by means of the implicit Euler method. The nonlinear orbits of the rotor center are determined by solving the nonlinear differential equations of motion with the explicit Euler’s scheme taking into account the flexibility of rotor. According to the obtained results, the combined effects of couple stresses due to the presence of polymer additives in lubricant and the pressure dependent viscosity on the nonlinear dynamic response of the rotor-bearing system are significant and cannot be ignored or overlooked. As expected, these effects are more noticeable for polymers characterized by higher length molecular chains.
Lucchetti, Liana; Fraccia, Tommaso P.; Ciciulla, Fabrizio; Bellini, Tommaso
2017-01-01
Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced bi...
Gorb, Yuliya
2010-11-01
We model and analyze the response of nonlinear, residually stressed elastic bodies subjected to small amplitude vibrations superimposed upon large deformations. The problem derives from modeling the use of intravascular ultrasound (IVUS) imaging to interrogate atherosclerotic plaques in vivo in large arteries. The goal of this investigation is twofold: (i) introduce a modeling framework for residual stress that unlike traditional Fung type classical opening angle models may be used for a diseased artery, and (ii) investigate the sensitivity of the spectra of small amplitude high frequency time harmonic vibrations superimposed on a large deformation to the details of the residual stress stored in arteries through a numerical simulation using physiologic parameter values under both low and high blood pressure loadings. The modeling framework also points the way towards an inverse problem using IVUS techniques to estimate residual stress in healthy and diseased arteries. © 2010 Elsevier Ltd. All rights reserved.
Angela Mihai, L.
2013-03-01
Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.
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Allam M. N. M.
2017-12-01
Full Text Available Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations.Variable material properties such as Young’s moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.
International Nuclear Information System (INIS)
Belendez, A.; Belendez, T.; Neipp, C.; Hernandez, A.; Alvarez, M.L.
2009-01-01
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a system typified as a mass attached to a stretched elastic wire. The restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system (0 ≤ λ ≤ 1). For λ = 1 and small values of x, the restoring force does not have a dominant term proportional to x. We find this perturbation method works very well for the whole range of parameters involved, and excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions and the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitude. This error corresponds to λ = 1, while for λ < 1 the relative error is much lower. For example, its value is as low as 0.062% for λ = 0.5.
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Jaroszewicz Jerzy
2018-01-01
Full Text Available The work is devoted to methods of analysis of vibrations and stability of discrete-continuous, multi-parameter models of beams, shafts, rotors, vanes, converting to homogeneous and one-dimensional. The properties of Cauchy's influence function and the characteristic series method were used to solve the boundary problem. It has been shown that the methods are an effective tool for solving boundary problems described by ordinary fourth-and second-order differential equations with variable parameters. Particular attention should be paid to the solution of the border problem of two-parameter elastic systems with variable distribution of parameters. Universal beam-specific equations with typical support conditions including vertical support, which do not depend on beam shape and axial load type, are recorded. The shape and type of load are considered in the form of an impact function that corresponds to any change in cross-section of the support and continuous axial load, so that the functions describing the stiffness, the mass and the continuous load are complete. As a result of the solution of the boundary vibration problem of freely bent support and any change in its cross-section, loaded with any longitudinal load, arranged on the resilient substrate, strict relations between the own frequency parameters and the load parameters were derived. Using the methods, simple calculations were made, easy to use in engineering practice and conditions of use were given. Experimental studies have confirmed the high accuracy of theoretical calculations using the proposed methods and formulas.
Bazan, Carlos; Hawkins, Trevor; Torres-Barba, David; Blomgren, Peter; Paolini, Paul
2011-08-22
We are exploring the viability of a novel approach to cardiocyte contractility assessment based on biomechanical properties of the cardiac cells, energy conservation principles, and information content measures. We define our measure of cell contraction as being the distance between the shapes of the contracting cell, assessed by the minimum total energy of the domain deformation (warping) of one cell shape into another. To guarantee a meaningful vis-à-vis correspondence between the two shapes, we employ both a data fidelity term and a regularization term. The data fidelity term is based on nonlinear features of the shapes while the regularization term enforces the compatibility between the shape deformations and that of a hyper-elastic material. We tested the proposed approach by assessing the contractile responses in isolated adult rat cardiocytes and contrasted these measurements against two different methods for contractility assessment in the literature. Our results show good qualitative and quantitative agreements with these methods as far as frequency, pacing, and overall behavior of the contractions are concerned. We hypothesize that the proposed methodology, once appropriately developed and customized, can provide a framework for computational cardiac cell biomechanics that can be used to integrate both theory and experiment. For example, besides giving a good assessment of contractile response of the cardiocyte, since the excitation process of the cell is a closed system, this methodology can be employed in an attempt to infer statistically significant model parameters for the constitutive equations of the cardiocytes.
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V. Y. Zaitsev
2017-09-01
Full Text Available Results of examination of experimental data on non-linear elasticity of rocks using experimentally determined pressure dependences of P- and S-wave velocities from various literature sources are presented. Overall, over 90 rock samples are considered. Interpretation of the data is performed using an effective-medium description in which cracks are considered as compliant defects with explicitly introduced shear and normal compliances without specifying a particular crack model with an a priori given ratio of the compliances. Comparison with the experimental data indicated abundance (∼ 80 % of cracks with the normal-to-shear compliance ratios that significantly exceed the values typical of conventionally used crack models (such as penny-shaped cuts or thin ellipsoidal cracks. Correspondingly, rocks with such cracks demonstrate a strongly decreased Poisson ratio including a significant (∼ 45 % portion of rocks exhibiting negative Poisson ratios at lower pressures, for which the concentration of not yet closed cracks is maximal. The obtained results indicate the necessity for further development of crack models to account for the revealed numerous examples of cracks with strong domination of normal compliance. Discovering such a significant number of naturally auxetic rocks is in contrast to the conventional viewpoint that occurrence of a negative Poisson ratio is an exotic fact that is mostly discussed for artificial structures.
Hsieh, Chih-Chen; Jain, Semant; Larson, Ronald G
2006-01-28
A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and FENE-Fraenkel (FF) springs yield a random-walk configuration at equilibrium. We compare the simulation results of the free-draining bead-FF-spring model with those for the bead-rod model in relaxation, start-up of uniaxial extensional, and simple shear flows, and find that both methods generate nearly identical results. The computational cost per time step for a free-draining BD simulation with the proposed bead-FF-spring model is about twice as high as the traditional bead-rod model with the midpoint algorithm of Liu [J. Chem. Phys. 90, 5826 (1989)]. Nevertheless, computations with the bead-FF-spring model are as efficient as those with the bead-rod model in extensional flow because the former allows larger time steps. Moreover, the Brownian contribution to the stress for the bead-FF-spring model is isotropic and therefore simplifies the calculation of the polymer stresses. In addition, hydrodynamic interaction can more easily be incorporated into the bead-FF-spring model than into the bead-rod model since the metric force arising from the non-Cartesian coordinates used in bead-rod simulations is absent from bead-spring simulations. Finally, with our newly developed bead-FF-spring model, existing computer codes for the bead-spring models can trivially be converted to ones for effective bead-rod simulations merely by replacing the usual FENE or Cohen spring law with a FENE-Fraenkel law, and this convertibility provides a very convenient way to perform multiscale BD simulations.
Kondo, Yuuki; Urayama, Kenji; Kidowaki, Masatoshi; Mayumi, Koichi; Takigawa, Toshikazu; Ito, Kohzo
2014-10-07
The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (σy/σx) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.
International Nuclear Information System (INIS)
Deb Nath, S.K.; Deb Nath, S.K.; Wong, C.H.; Deb Nath, S.K.
2014-01-01
Perfluoro polyethers (PFPEs) are widely used as hard disk lubricants for protecting carbon overcoat reducing friction between the hard disk interface and the head during the movement of head during reading and writing data in the hard disk. Due to temperature rise of PFPE Zdol lubricant molecules on a DLC surface, how polar end groups are detached from lubricant molecules during coating is described considering the effect of temperatures on the bond/break density of PFPE Zdol using the coarse-grained bead spring model based on finitely extensible nonlinear elastic potential. As PFPE Z contains no polar end groups, effects of temperature on the bond/break density (number of broken bonds/total number of bonds) are not so significant like PFPE Zdol. Effects of temperature on the bond/break density of PFPE Z on DLC surface are also discussed with the help of graphical results. How bond/break phenomenon affects the end bead density of PFPE Z and PFPE Zdol on DLC surface is discussed elaborately. How the overall bond length of PFPE Zdol increases with the increase of temperature which is responsible for its decomposition is discussed with the help of graphical results. At HAMR condition, as PFPE Z and PFPE Zdol are not suitable lubricant on a hard disk surface, it needs more investigations to obtain suitable lubricant. We study the effect of breaking of bonds of nonfunctional lubricant PFPE Z, functional lubricants such as PFPE Zdol and PFPE Ztetrao, and multi dented functional lubricants such as Ar-DS, ARJ-DD, and OHJ-DS on a DLC substrate with the increase of temperature when heating of all of the lubricants on a DLC substrate is carried out isothermally using the coarse-grained bead spring model by molecular dynamics simulations and suitable lubricant is selected which is suitable on a DLC substrate at high temperature.
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S. K. Deb Nath
2014-01-01
Full Text Available Perfluoropolyethers (PFPEs are widely used as hard disk lubricants for protecting carbon overcoat reducing friction between the hard disk interface and the head during the movement of head during reading and writing data in the hard disk. Due to temperature rise of PFPE Zdol lubricant molecules on a DLC surface, how polar end groups are detached from lubricant molecules during coating is described considering the effect of temperatures on the bond/break density of PFPE Zdol using the coarse-grained bead spring model based on finitely extensible nonlinear elastic potential. As PFPE Z contains no polar end groups, effects of temperature on the bond/break density (number of broken bonds/total number of bonds are not so significant like PFPE Zdol. Effects of temperature on the bond/break density of PFPE Z on DLC surface are also discussed with the help of graphical results. How bond/break phenomenonaffects the end bead density of PFPE Z and PFPE Zdol on DLC surface is discussed elaborately. How the overall bond length of PFPE Zdol increases with the increase of temperature which is responsible for its decomposition is discussed with the help of graphical results. At HAMR condition, as PFPE Z and PFPE Zdol are not suitable lubricant on a hard disk surface, it needs more investigations to obtain suitable lubricant. We study the effect of breaking of bonds of nonfunctional lubricant PFPE Z, functional lubricants such as PFPE Zdol and PFPE Ztetrao, and multidented functional lubricants such as ARJ-DS, ARJ-DD, and OHJ-DS on a DLC substrate with the increase of temperature when heating of all of the lubricants on a DLC substrate is carried out isothermally using the coarse-grained bead spring model by molecular dynamics simulations and suitable lubricant is selected which is suitable on a DLC substrate at high temperature.
Elastic properties of Gum Metal
International Nuclear Information System (INIS)
Kuramoto, Shigeru; Furuta, Tadahiko; Hwang, Junghwan; Nishino, Kazuaki; Saito, Takashi
2006-01-01
In situ X-ray diffraction measurements under tensile loading and dynamic mechanical analysis were performed to investigate the mechanisms of elastic deformation in Gum Metal. Tensile stress-strain curves for Gum Metal indicate that cold working substantially decreases the elastic modulus while increasing the yield strength, thereby confirming nonlinearity in the elastic range. The gradient of each curve decreased continuously to about one-third its original value near the elastic limit. As a result of this decrease in elastic modulus and nonlinearity, elastic deformability reaches 2.5% after cold working. Superelasticity is attributed to stress-induced martensitic transformations, although the large elastic deformation in Gum Metal is not accompanied by a phase transformation
International Nuclear Information System (INIS)
Yang, D.S.; Nguyen Minh, D.; Chanchole, S.; Gharbi, H.; Valli, P.; Bornert, M.
2010-01-01
Document available in extended abstract form only. The construction of underground nuclear waste repositories will strongly disturb the initial thermo-hydro-chemo-mechanical equilibrium of the site. In addition to direct mechanical perturbations during excavation, which induce redistribution of the stresses and possible damage of the surrounding rock mass, the ventilation of the galleries will also modify the moisture content of the rock, resulting in shrinking or swelling, and more generally modifying the physical-chemical properties of the material. Safety concerns about preservation of confining properties of rock mass at short and long time scales require a deep understanding of the hydro-mechanical behavior of the host rock. In particular the dependence of elastic, possibly anisotropic, moduli and nonlinear properties (plasticity, damage, creep...) as a function of the moisture level, need to be quantified. In addition, in order to construct physically based micromechanical models of these dependencies, the various micro-mechanisms at their origin and their characteristic scales need to be identified. Various independent studies agree on the decrease of overall rigidity and failure stress of argillite with increasing humidity. A recent study making use of optical full-field strain measurement techniques on centi-metric samples under uniaxial compression suggests that this apparent decrease of elastic properties on wet samples can be essentially explained by the presence of a millimetric network of 'meso-cracks', induced by the preliminary unconfined hydration process. Indeed, thanks to the full-field measurement technique, it was possible to show that the mechanical response of undamaged areas, in-between cracks, was very similar at all moisture contents, both in terms of average strains and strain fluctuations at the micrometric scale of the composite structure of the rock (matrix clay + other mineral inclusions). The preliminary hydro
International Nuclear Information System (INIS)
Yanqiu Zhu, Y.; Ma, R.; Whitby, R.; Acquah, S.
2013-01-01
We witnessed an initial hyped period and enthusiasm on carbon nano tubes in the 1990s later went through a significant expansion into nano tubes of other materials (metal di chalcogenides, boron nitride, etc.) as well as various nano wires and nano rods. While much of the hype might have gone, the research on one-dimensional (1D) nano materials has matured as one of the most active research areas within the nano science and nano technology community, flourishing with ample, exciting, and new research opportunities. Just like any other research frontier, researchers working in the 1D nano materials field are constantly striving to develop new fundamental science as well as potential applications. It remains a common belief that versatility and tunability of 1D nano materials would challenge many new rising tasks coming from our resource and energy demanding modern society. The traditional semiconductor industry has produced so many devices and systems from transistors, sensors, lasers, and LEDs to more sophisticated solar panels, which are now part of our daily lives. By down sizing the core components or parts to 1D form, one might wonder how fundamentally the dimensionality and morphology would impact the device performance, this is, as always, requiring us to fully understand the structure-property relationship in 1D nano materials. It may be equally crucial in connecting discovery-driven fundamental science to market-driven technology industry concerning potentially relevant findings derived from these novel materials. The importance of a platform that allows active researchers in this field to present their new development in a timely and efficient manner is therefore self-evident. Following the success of two early special issues devoted to 1D nano materials, this is the third one in a row organized by the same group of guest editors, attesting that such a platform has been well received by the readers
International Nuclear Information System (INIS)
Sasaki, Toshihiko; Kuramoto, Makoto; Yoshioka, Yasuo.
1990-01-01
This paper describes the method and the experiment for the determination of the x-ray elastic constants of Zn-Ni-alloy electroplate. For this material, the sin 2 ψ method is not adequate to use because this material shows severely curved sin 2 ψ diagrams. Therefore, a new method developed by the authors was explained first. This new method is effective for materials showing nonlinear sin 2 ψ diagrams. Secondly, the experiment was made on the application of this method to the Zn-Ni-alloy electroplate. And it was found out that the experimental data agreed well to the theory of this method. As a result, the following values were obtained as the x-ray elastic constants of the sample measured: (1+ν)/E=8.44 TPa -1 ν/E=2.02 TPa -1 (author)
International Nuclear Information System (INIS)
Baruah, D; Choudhury, S; Singh, K M; Ghatak, K P
2007-01-01
In this paper we study the carrier contribution to elastic constants in quantum confined heavily doped non-linear optical compounds on the basis of a newly formulated electron dispersion law taking into account the anisotropies of the effective electron masses and spin orbit splitting constants together with the proper inclusion of the crystal field splitting in the Hamiltonian within the framework of k.p formalism. All the results of heavily doped three, and two models of Kane for heavily doped III-V materials form special cases of our generalized analysis. It has been found, taking different heavily doped quantum confined materials that, the carrier contribution to the elastic constants increases with increase in electron statistics and decrease in film thickness in ladder like manners for all types of quantum confinements with different numerical values which are totally dependent on the energy band constants. The said contribution is greatest in quantum dots and least in quantum wells together with the fact the heavy doping enhances the said contributions for all types of quantum confined materials. We have suggested an experimental method of determining the carrier contribution to the elastic constants in nanostructured materials having arbitrary band structures
Non-reciprocity in nonlinear elastodynamics
Blanchard, Antoine; Sapsis, Themistoklis P.; Vakakis, Alexander F.
2018-01-01
Reciprocity is a fundamental property of linear time-invariant (LTI) acoustic waveguides governed by self-adjoint operators with symmetric Green's functions. The break of reciprocity in LTI elastodynamics is only possible through the break of time reversal symmetry on the micro-level, and this can be achieved by imposing external biases, adding nonlinearities or allowing for time-varying system properties. We present a Volterra-series based asymptotic analysis for studying spatial non-reciprocity in a class of one-dimensional (1D), time-invariant elastic systems with weak stiffness nonlinearities. We show that nonlinearity is neither necessary nor sufficient for breaking reciprocity in this class of systems; rather, it depends on the boundary conditions, the symmetries of the governing linear and nonlinear operators, and the choice of the spatial points where the non-reciprocity criterion is tested. Extension of the analysis to higher dimensions and time-varying systems is straightforward from a mathematical point of view (but not in terms of new non-reciprocal physical phenomena), whereas the connection of non-reciprocity and time irreversibility can be studied as well. Finally, we show that suitably defined non-reciprocity measures enable optimization, and can provide physical understanding of the nonlinear effects in the dynamics, enabling one to establish regimes of "maximum nonlinearity." We highlight the theoretical developments by means of a numerical example.
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
Yokoyama, Naoto; Takaoka, Masanori
2014-12-01
A single-wave-number representation of a nonlinear energy spectrum, i.e., a stretching-energy spectrum, is found in elastic-wave turbulence governed by the Föppl-von Kármán (FvK) equation. The representation enables energy decomposition analysis in the wave-number space and analytical expressions of detailed energy budgets in the nonlinear interactions. We numerically solved the FvK equation and observed the following facts. Kinetic energy and bending energy are comparable with each other at large wave numbers as the weak turbulence theory suggests. On the other hand, stretching energy is larger than the bending energy at small wave numbers, i.e., the nonlinearity is relatively strong. The strong correlation between a mode a(k) and its companion mode a(-k) is observed at the small wave numbers. The energy is input into the wave field through stretching-energy transfer at the small wave numbers, and dissipated through the quartic part of kinetic-energy transfer at the large wave numbers. Total-energy flux consistent with energy conservation is calculated directly by using the analytical expression of the total-energy transfer, and the forward energy cascade is observed clearly.
Quantum electrodynamics with 1D arti cial atoms
DEFF Research Database (Denmark)
Javadi, Alisa
A 1D atom, a single quantum emitter coupled to a single optical mode, exhibits rich quantum electrodynamic (QED) e_ects and is thought to be the key ingredient for many applications in quantuminformation processing. Single quantum dots (QD) in photonic-crystal waveguides (PCW) constitute a robust...... as expected from the theory. The value of g(2)(0) is around 1.08. The results con_rm the observation of an on-chip giant optical nonlinearity and the 1D atom behavior. Another direction in this thesis has been to investigate the e_ect of Anderson localization on the electrodynamics of QDs in PCWs. A large...
Partial breaking of N = 1, D = 10 supersymmetry
International Nuclear Information System (INIS)
Bellucci, S.
1999-01-01
In this paper is described the spontaneous partial breaking of N =1, D =10 supersymmetry to N = (1, 0), d = 6 and its dimensionally-reduced versions in the framework of nonlinear realizations. The basic Goldstone superfield is N = (1, 0), d = 6 hyper multiplet superfield satisfying a nonlinear generalization of the standard hyper multiplet constraint. It is here interpreted the generalized constraint as the manifestly world volume supersymmetric form of equations of motion of the type 1 super 5-brane in D 10. The related issues here addressed are a possible existence of brane extension of off-shell hyper multiplet actions, the possibility to utilize vector N = (1, 0), d =6 supermultiplet as the Goldstone one, and the description of 1/4 breaking of N =1, D = 11 supersymmetry
International Nuclear Information System (INIS)
Ledbetter, H.M.
1983-01-01
This chapter investigates the following five aspects of engineering-material solid-state elastic constants: general properties, interrelationships, relationships to other physical properties, changes during cooling from ambient to near-zero temperature, and near-zero-temperature behavior. Topics considered include compressibility, bulk modulus, Young's modulus, shear modulus, Poisson's ratio, Hooke's law, elastic-constant measuring methods, thermodynamic potentials, higher-order energy terms, specific heat, thermal expansivity, magnetic materials, structural phase transitions, polymers, composites, textured aggregates, and other-phenomena correlations. Some of the conclusions concerning polycrystalline elastic properties and their temperature dependence are: elastic constants are physical, not mechanical, properties which relate thermodynamically to other physical properties such as specific heat and thermal expansivity; elastic constants at low temperatures are nearly temperature independent, as required by the third law of thermodynamics; and elastic constants can be used to study directional properties of materials, such as textured aggregates and composites
Nonlinear dynamics between linear and impact limits
Pilipchuk, Valery N; Wriggers, Peter
2010-01-01
This book examines nonlinear dynamic analyses based on the existence of strongly nonlinear but simple counterparts to the linear models and tools. Discusses possible application to periodic elastic structures with non-smooth or discontinuous characteristics.
Experimental determination of third-order elastic constants of diamond.
Lang, J M; Gupta, Y M
2011-03-25
To determine the nonlinear elastic response of diamond, single crystals were shock compressed along the [100], [110], and [111] orientations to 120 GPa peak elastic stresses. Particle velocity histories and elastic wave velocities were measured by using laser interferometry. The measured elastic wave profiles were used, in combination with published acoustic measurements, to determine the complete set of third-order elastic constants. These constants represent the first experimental determination, and several differ significantly from those calculated by using theoretical models.
Support minimized inversion of acoustic and elastic wave scattering
International Nuclear Information System (INIS)
Safaeinili, A.
1994-01-01
This report discusses the following topics on support minimized inversion of acoustic and elastic wave scattering: Minimum support inversion; forward modelling of elastodynamic wave scattering; minimum support linearized acoustic inversion; support minimized nonlinear acoustic inversion without absolute phase; and support minimized nonlinear elastic inversion
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.
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
Constitutive modeling and control of 1D smart composite structures
Briggs, Jonathan P.; Ostrowski, James P.; Ponte-Castaneda, Pedro
1998-07-01
Homogenization techniques for determining effective properties of composite materials may provide advantages for control of stiffness and strain in systems using hysteretic smart actuators embedded in a soft matrix. In this paper, a homogenized model of a 1D composite structure comprised of shape memory alloys and a rubber-like matrix is presented. With proportional and proportional/integral feedback, using current as the input state and global strain as an error state, implementation scenarios include the use of tractions on the boundaries and a nonlinear constitutive law for the matrix. The result is a simple model which captures the nonlinear behavior of the smart composite material system and is amenable to experiments with various control paradigms. The success of this approach in the context of the 1D model suggests that the homogenization method may prove useful in investigating control of more general smart structures. Applications of such materials could include active rehabilitation aids, e.g. wrist braces, as well as swimming/undulating robots, or adaptive molds for manufacturing processes.
Social exploration of 1D games
DEFF Research Database (Denmark)
Valente, Andrea; Marchetti, Emanuela
2013-01-01
In this paper the apparently meaningless concept of a 1 dimensional computer game is explored, via netnography. A small number of games was designed and implemented, in close contact with online communities of players and developers, providing evidence that 1 dimension is enough to produce...... interesting gameplay, to allow for level design and even to leave room for artistic considerations on 1D rendering. General techniques to re-design classic 2D games into 1D are also emerging from this exploration....
Directory of Open Access Journals (Sweden)
Helbig K.
2006-12-01
Full Text Available The propagation of elastic waves is generally treated under four assumptions: - that the medium is isotropic,- that the medium is homogeneous, - that there is a one-to-one relationship between stress and strain, - that stresses are linearly related to strains (equivalently, that strains are linearly related to stresses. Real media generally violate at least some-and often all-of these assumptions. A valid theoretical description of wave propagation in real media thus depends on the qualitative and quantitative description of the relevant inhomogeneity, anisotropy, and non-linearity: one either has to assume (or show that the deviation from the assumption can - for the problem at hand - be neglected, or develop a theoretical description that is valid even under the deviation. While the effect of a single deviation from the ideal state is rather well understood, difficulties arise in the combination of several such deviations. Non-linear elasticity of anisotropic (triclinic rock samples has been reported, e. g. by P. Rasolofosaon and H. Yin at the 6th IWSA in Trondheim (Rasolofosaon and Yin, 1996. Non-linear anisotropic elasticity matters only for non-infinitesimalamplitudes, i. e. , at least in the vicinity of the source. How large this vicinity is depends on the accuracy of observation and interpretation one tries to maintain, on the source intensity, and on the level of non-linearity. This paper is concerned with the last aspect, i. e. , with the meaning of the numbers beyond the fact that they are the results of measurements. As a measure of the non-linearity of the material, one can use the strain level at which the effective stiffness tensor deviates significantly from the zero-strain stiffness tensor. Particularly useful for this evaluation is the eigensystem (six eigenstiffnesses and six eigenstrains of the stiffness tensor : the eigenstrains provide suitable strain typesfor the calculation of the effective stiffness tensor, and the
Fully digital 1-D, 2-D and 3-D multiscroll chaos as hardware pseudo random number generators
Mansingka, Abhinav S.; Radwan, Ahmed Gomaa; Salama, Khaled N.
2012-01-01
This paper introduces the first fully digital implementation of 1-D, 2-D and 3-D multiscroll chaos using the sawtooth nonlinearity in a 3rd order ODE with the Euler approximation. Systems indicate chaotic behaviour through phase space boundedness
A 2D nonlinear inversion of well-seismic data
International Nuclear Information System (INIS)
Métivier, Ludovic; Lailly, Patrick; Delprat-Jannaud, Florence; Halpern, Laurence
2011-01-01
Well-seismic data such as vertical seismic profiles are supposed to provide detailed information about the elastic properties of the subsurface at the vicinity of the well. Heterogeneity of sedimentary terrains can lead to far from negligible multiple scattering, one of the manifestations of the nonlinearity involved in the mapping between elastic parameters and seismic data. We present a 2D extension of an existing 1D nonlinear inversion technique in the context of acoustic wave propagation. In the case of a subsurface with gentle lateral variations, we propose a regularization technique which aims at ensuring the stability of the inversion in a context where the recorded seismic waves provide a very poor illumination of the subsurface. We deal with a huge size inverse problem. Special care has been taken for its numerical solution, regarding both the choice of the algorithms and the implementation on a cluster-based supercomputer. Our tests on synthetic data show the effectiveness of our regularization. They also show that our efforts in accounting for the nonlinearities are rewarded by an exceptional seismic resolution at distances of about 100 m from the well. They also show that the result is not very sensitive to errors in the estimation of the velocity distribution, as far as these errors remain realistic in the context of a medium with gentle lateral variations
International Nuclear Information System (INIS)
Leader, Elliot
1991-01-01
With very few unexplained results to challenge conventional ideas, physicists have to look hard to search for gaps in understanding. An area of physics which offers a lot more than meets the eye is elastic and diffractive scattering where particles either 'bounce' off each other, emerging unscathed, or just graze past, emerging relatively unscathed. The 'Blois' workshops provide a regular focus for this unspectacular, but compelling physics, attracting highly motivated devotees
Modeling an electric motor in 1-D
Butler, Thomas G.
1991-01-01
Quite often the dynamicist will be faced with having an electric drive motor as a link in the elastic path of a structure such that the motor's characteristics must be taken into account to properly represent the dynamics of the primary structure. He does not want to model it so accurately that he could get detailed stress and displacements in the motor proper, but just sufficiently to represent its inertia loading and elastic behavior from its mounting bolts to its drive coupling. Described here is how the rotor and stator of such a motor can be adequately modeled as a colinear pair of beams.
Rotation, inversion and perversion in anisotropic elastic cylindrical tubes and membranes
Goriely, A.; Tabor, M.
2013-01-01
Cylindrical tubes and membranes are universal structural elements found in biology and engineering over a wide range of scales.Working in the framework of nonlinear elasticity, we consider the possible deformations of elastic cylindrical shells
On nonlinear thermo-electro-elasticity.
Mehnert, Markus; Hossain, Mokarram; Steinmann, Paul
2016-06-01
Electro-active polymers (EAPs) for large actuations are nowadays well-known and promising candidates for producing sensors, actuators and generators. In general, polymeric materials are sensitive to differential temperature histories. During experimental characterizations of EAPs under electro-mechanically coupled loads, it is difficult to maintain constant temperature not only because of an external differential temperature history but also because of the changes in internal temperature caused by the application of high electric loads. In this contribution, a thermo-electro-mechanically coupled constitutive framework is proposed based on the total energy approach. Departing from relevant laws of thermodynamics, thermodynamically consistent constitutive equations are formulated. To demonstrate the performance of the proposed thermo-electro-mechanically coupled framework, a frequently used non-homogeneous boundary-value problem, i.e. the extension and inflation of a cylindrical tube, is solved analytically. The results illustrate the influence of various thermo-electro-mechanical couplings.
Nonlinearly coupled thermo-visco-elasticity
Czech Academy of Sciences Publication Activity Database
Roubíček, Tomáš
2013-01-01
Roč. 20, č. 3 (2013), s. 1243-1275 ISSN 1021-9722 R&D Projects: GA ČR GAP201/10/0357 Institutional support: RVO:61388998 Keywords : kelvin-voigt rheology * small strains * nonsimple materials Subject RIV: BA - General Mathematics Impact factor: 0.971, year: 2013 http://link.springer.com/article/10.1007%2Fs00030-012-0207-9
Synthesis of 1-D ZnO nanorods and polypyrrole/1-D ZnO ...
Indian Academy of Sciences (India)
1-D ZnO nanorods and PPy/1-D ZnO nanocomposites were prepared by the surfactant-assisted precipitation and in situ polymerization method, respectively. The synthesized nanorods and nanocomposites were characterized by UV–Vis spectrophotometer, Fourier transform-infrared spectroscopy (FTIR), X-ray diffraction ...
A nonlinear beam model to describe the postbuckling of wide neo-Hookean beams
Lubbers, Luuk A.; van Hecke, Martin; Coulais, Corentin
2017-09-01
Wide beams can exhibit subcritical buckling, i.e. the slope of the force-displacement curve can become negative in the postbuckling regime. In this paper, we capture this intriguing behaviour by constructing a 1D nonlinear beam model, where the central ingredient is the nonlinearity in the stress-strain relation of the beams constitutive material. First, we present experimental and numerical evidence of a transition to subcritical buckling for wide neo-Hookean hyperelastic beams, when their width-to-length ratio exceeds a critical value of 12%. Second, we construct an effective 1D energy density by combining the Mindlin-Reissner kinematics with a nonlinearity in the stress-strain relation. Finally, we establish and solve the governing beam equations to analytically determine the slope of the force-displacement curve in the postbuckling regime. We find, without any adjustable parameters, excellent agreement between the 1D theory, experiments and simulations. Our work extends the understanding of the postbuckling of structures made of wide elastic beams and opens up avenues for the reverse-engineering of instabilities in soft and metamaterials.
Development of a 3D consistent 1D neutronics model for reactor core simulation
International Nuclear Information System (INIS)
Lee, Ki Bog; Joo, Han Gyu; Cho, Byung Oh; Zee, Sung Quun
2001-02-01
In this report a 3D consistent 1D model based on nonlinear analytic nodal method is developed to reproduce the 3D results. During the derivation, the current conservation factor (CCF) is introduced which guarantees the same axial neutron currents obtained from the 1D equation as the 3D reference values. Furthermore in order to properly use 1D group constants, a new 1D group constants representation scheme employing tables for the fuel temperature, moderator density and boron concentration is developed and functionalized for the control rod tip position. To test the 1D kinetics model with CCF, several steady state and transient calculations were performed and compared with 3D reference values. The errors of K-eff values were reduced about one tenth when using CCF without significant computational overhead. And the errors of power distribution were decreased to the range of one fifth or tenth at steady state calculation. The 1D kinetics model with CCF and the 1D group constant functionalization employing tables as a function of control rod tip position can provide preciser results at the steady state and transient calculation. Thus it is expected that the 1D kinetics model derived in this report can be used in the safety analysis, reactor real time simulation coupled with system analysis code, operator support system etc.
Modeling of 1D motion of interstitial clusters in iron under HVEM irradiation
International Nuclear Information System (INIS)
Satoh, Y.; Hamaoka, T.; Matsui, H.
2007-01-01
Full text of publication follows: We examined 1D motion of interstitial clusters in Fe under electron irradiation at room temperature using high voltage electron microscopy (HVEM). We found that some impurities have essential effects on the experimental 1D motion behavior. The characteristics of experimental 1D motion were obtained as follows: 1) 1D motion appears as discrete jumps (namely, stepwise positional changes) at irregular intervals. 2) Sometimes a set of several successive jumps occurs between certain two points (back and forth motion). 3) The frequency of 1D jumps is almost proportional to the electron beam intensity, while the distribution of 1D jump distance does not change much with the intensity. Very few 1D jumps are observed with a 200 kV TEM at room temperature. 4) The distance and the frequency of 1D jumps are greatly reduced in a specimen of low purities. Taking account for effects of impurities, we propose a mechanism of the experimental 1D jumps, as follows. Small interstitial clusters are regarded to be essentially mobile as crowdion bundles. Then interstitial clusters in a stationary state are trapped by impurity atom(s), due to elastic interactions between impurities and crowdion bundle. The electron irradiation changes the cluster into a mobile state by a detrapping: for example, the impurity atom is displaced to apart from the crowdion bundle. Then the crowdion bundle makes a free 1D migration until it is trapped by another impurity atom. Because of small activation energy for 1D migration, we cannot observe the detailed 1D random walk process, but a stepwise positional change from an impurity to another impurity. The average size of interstitial clusters observed in the present experiments was around 5 nm, corresponding to a bundle of 300 crowdions. In a rough estimate assuming that an impurity atom on any crowdion in the crowdion bundle prevent the migration of the bundle, the mean free path is about 75 nm and 7.5 nm at the impurity
Extended-Range Ultrarefractive 1D Photonic Crystal Prisms
Ting, David Z.
2007-01-01
A proposal has been made to exploit the special wavelength-dispersive characteristics of devices of the type described in One-Dimensional Photonic Crystal Superprisms (NPO-30232) NASA Tech Briefs, Vol. 29, No. 4 (April 2005), page 10a. A photonic crystal is an optical component that has a periodic structure comprising two dielectric materials with high dielectric contrast (e.g., a semiconductor and air), with geometrical feature sizes comparable to or smaller than light wavelengths of interest. Experimental superprisms have been realized as photonic crystals having three-dimensional (3D) structures comprising regions of amorphous Si alternating with regions of SiO2, fabricated in a complex process that included sputtering. A photonic crystal of the type to be exploited according to the present proposal is said to be one-dimensional (1D) because its contrasting dielectric materials would be stacked in parallel planar layers; in other words, there would be spatial periodicity in one dimension only. The processes of designing and fabricating 1D photonic crystal superprisms would be simpler and, hence, would cost less than do those for 3D photonic crystal superprisms. As in 3D structures, 1D photonic crystals may be used in applications such as wavelength-division multiplexing. In the extended-range configuration, it is also suitable for spectrometry applications. As an engineered structure or artificially engineered material, a photonic crystal can exhibit optical properties not commonly found in natural substances. Prior research had revealed several classes of photonic crystal structures for which the propagation of electromagnetic radiation is forbidden in certain frequency ranges, denoted photonic bandgaps. It had also been found that in narrow frequency bands just outside the photonic bandgaps, the angular wavelength dispersion of electromagnetic waves propagating in photonic crystal superprisms is much stronger than is the angular wavelength dispersion obtained
1D Printing of Recyclable Robots
DEFF Research Database (Denmark)
Cellucci, Daniel; MacCurdy, Robert; Lipson, Hod
2017-01-01
Recent advances in 3D printing are revolutionizing manufacturing, enabling the fabrication of structures with unprecedented complexity and functionality. Yet biological systems are able to fabricate systems with far greater complexity using a process that involves assembling and folding a linear...... string. Here, we demonstrate a 1D printing system that uses an approach inspired by the ribosome to fabricate a variety of specialized robotic automata from a single string of source material. This proof-ofconcept system involves both a novel manufacturing platform that configures the source material...... using folding and a computational optimization tool that allows designs to be produced from the specification of high-level goals. We show that our 1D printing system is able to produce three distinct robots from the same source material, each of which is capable of accomplishing a specialized...
Zhao, Xin
2013-01-01
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
Composite Beam Theory with Material Nonlinearities and Progressive Damage
Jiang, Fang
Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping
Remarks on stability of magneto-elastic shocks
Directory of Open Access Journals (Sweden)
Włodzimierz Domański
2015-12-01
Full Text Available The problem of stability of plane shock waves for a model of perfect magnetoelasticityis investigated. Important mathematical properties, like loss of strict hyperbolicityand loss of genuine nonlinearity, and their consequences for the stability ofmagneto-elastic shocks are discussed. It is shown that some of these shocks do not satisfyclassical Lax stability conditions. Both compressible and incompressible models ofmagneto-elasticity are discussed.[b]Keywords[/b]: perfect magneto-elasticity, shock waves, stability conditions
Electron–soliton dynamics in chains with cubic nonlinearity
International Nuclear Information System (INIS)
Sales, M O; Moura, F A B F de
2014-01-01
In our work, we consider the problem of electronic transport mediated by coupling with solitonic elastic waves. We study the electronic transport in a 1D unharmonic lattice with a cubic interaction between nearest neighboring sites. The electron-lattice interaction was considered as a linear function of the distance between neighboring atoms in our study. We numerically solve the dynamics equations for the electron and lattice and compute the dynamics of an initially localized electronic wave-packet. Our results suggest that the solitonic waves that exist within this nonlinear lattice can control the electron dynamics along the chain. Moreover, we demonstrate that the existence of a mobile electron–soliton pair exhibits a counter-intuitive dependence with the value of the electron-lattice coupling. (paper)
A New Application of the Channel Packet Method for Low Energy 1-D Elastic Scattering
2006-09-01
matter. On a cosmic scale, we wonder if a collision between an asteroid and Earth led to the extinction of the dinosaurs . Collisions are important...in Figure 12. In an effort to have the computation time reasonable was chosen to be for this simulation. In order to represent the intermediate...linear regions joined by the two labeled points. However, based on Figure 13 the two potential functions are reasonably close and so one would not
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.
1D-VAR Retrieval Using Superchannels
Liu, Xu; Zhou, Daniel; Larar, Allen; Smith, William L.; Schluessel, Peter; Mango, Stephen; SaintGermain, Karen
2008-01-01
Since modern ultra-spectral remote sensors have thousands of channels, it is difficult to include all of them in a 1D-var retrieval system. We will describe a physical inversion algorithm, which includes all available channels for the atmospheric temperature, moisture, cloud, and surface parameter retrievals. Both the forward model and the inversion algorithm compress the channel radiances into super channels. These super channels are obtained by projecting the radiance spectra onto a set of pre-calculated eigenvectors. The forward model provides both super channel properties and jacobian in EOF space directly. For ultra-spectral sensors such as Infrared Atmospheric Sounding Interferometer (IASI) and the NPOESS Airborne Sounder Testbed Interferometer (NAST), a compression ratio of more than 80 can be achieved, leading to a significant reduction in computations involved in an inversion process. Results will be shown applying the algorithm to real IASI and NAST data.
International Nuclear Information System (INIS)
Topchyan, I.I.; Dokhner, R.D.
1977-01-01
The effect of reorientation of anisotropic point defects in uniform fields of elastic stresses on the relaxation of the elastic coefficients of a crystal was investigated in the nonlinear elasticity theory approximation. In calculating the interaction of point defects with elastic-stress fields was taken into consideration. The expression for the relaxations of the elasticity coefficients are obtained in an analytical form. The relaxation of the second-order elasticity coefficients is due to the dimentional interaction of a point defect with an applied-stress field, whereas the relaxation of the higher-order elasticity coefficients is determined both by dimentional and module effects
1-D hybrid code for FRM dynamics
International Nuclear Information System (INIS)
Stark, R.A.; Miley, G.H.
1985-01-01
A 1-D radial hybrid code has been written to study the start-up of the FRM via neutral-beam injection. This code, named FROST (Field Reversed One-dimensional STart-up), models the plasma as azimuthal symmetric with no axial dependence. A multi-group method in energy and canonical angular momentum describes the large-orbit ions from the beam. This method is designed to be more efficient than those employing particle tracking, since the characteristic timescale of the simulation is the ion slowing down time, rather than the much shorter cyclotron period. A time-differentiated Grad-Shafranov equation couples the ion current to massless fluid equations describing electrons and low energy ions. Flux coordinates are used in this fluid model, in preference to an Eulerian framework, so that coupling of plasma at the two different radii of a closed flux surface may be treated with ease. Since a fluid treatment for electrons is invalid near a field null, a separate model for the electron current has been included for this region, a unique feature. Results of simulation of injection into a 2XIIB-like plasma are discussed. Electron currents are found to retard, but not prevent reversal of the magnetic field at the plasma center
Quantum entanglement in inhomogeneous 1D systems
Ramírez, Giovanni
2018-04-01
The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our inhomogeneous system, the inhomogeneity parameter, h, allows us to tune different regimes where a volumetric violation of the area law appears. We apply the strong disorder renormalization group to describe the maximally entangled state of the system in a strong inhomogeneity regime. Moreover, in a weak inhomogeneity regime, we use a continuum approximation to describe the state as a thermo-field double in a conformal field theory with an effective temperature which is proportional to the inhomogeneity parameter of the system. The latter description also shows that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature R = h2, providing another example of the relation between quantum entanglement and space-time geometry. The results we discuss here were already published before, but here we present a more didactic exposure of basic concepts of the rainbow system for the students attending the Latin American School of Physics "Marcos Moshinsky" 2017.
Three-field modeling for MARS 1-D code
International Nuclear Information System (INIS)
Hwang, Moonkyu; Lim, Ho-Gon; Jeong, Jae-Jun; Chung, Bub-Dong
2006-01-01
In this study, the three-field modeling of the two-phase mixture is developed. The finite difference equations for the three-field equations thereafter are devised. The solution scheme has been implemented into the MARS 1-D code. The three-field formulations adopted are similar to those for MARS 3-D module, in a sense that the mass and momentum are treated separately for the entrained liquid and continuous liquid. As in the MARS-3D module, the entrained liquid and continuous liquid are combined into one for the energy equation, assuming thermal equilibrium between the two. All the non-linear terms are linearized to arrange the finite difference equation set into a linear matrix form with respect to the unknown arguments. The problems chosen for the assessment of the newly added entrained field consist of basic conceptual tests. Among the tests are gas-only test, liquid-only test, gas-only with supplied entrained liquid test, Edwards pipe problem, and GE level swell problem. The conceptual tests performed confirm the sound integrity of the three-field solver
Nonlinear Dynamic Phenomena in Mechanics
Warminski, Jerzy; Cartmell, Matthew P
2012-01-01
Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear
Introduction to nonlinear finite element analysis
Kim, Nam-Ho
2015-01-01
This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: · Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems · Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory · ...
Low band gap frequencies and multiplexing properties in 1D and 2D mass spring structures
International Nuclear Information System (INIS)
Aly, Arafa H; Mehaney, Ahmed
2016-01-01
This study reports on the propagation of elastic waves in 1D and 2D mass spring structures. An analytical and computation model is presented for the 1D and 2D mass spring systems with different examples. An enhancement in the band gap values was obtained by modeling the structures to obtain low frequency band gaps at small dimensions. Additionally, the evolution of the band gap as a function of mass value is discussed. Special attention is devoted to the local resonance property in frequency ranges within the gaps in the band structure for the corresponding infinite periodic lattice in the 1D and 2D mass spring system. A linear defect formed of a row of specific masses produces an elastic waveguide that transmits at the narrow pass band frequency. The frequency of the waveguides can be selected by adjusting the mass and stiffness coefficients of the materials constituting the waveguide. Moreover, we pay more attention to analyze the wave multiplexer and DE-multiplexer in the 2D mass spring system. We show that two of these tunable waveguides with alternating materials can be employed to filter and separate specific frequencies from a broad band input signal. The presented simulation data is validated through comparison with the published research, and can be extended in the development of resonators and MEMS verification. (paper)
Nonlinear elastic properties of bulk metallic glasses Zr52.5Ti5Cu17.9Ni14.6Al10 and Pd40Cu30Ni10P20
International Nuclear Information System (INIS)
Kobelev, N.P.; Kolyvanov, E.L.; Khonik, V.A.
2005-01-01
The influence of uniaxial compression on the propagation of ultrasonic vibrations in Zr 52.5 Ti 5 Cu 17.9 Ni 14.6 Al 10 and Pd 40 Cu 30 Ni 10 P 20 bulk metallic glasses produced by melt quenching at a rate of 100 K/s is investigated. Elastic deformation was realized by compression of the samples along their long axis up to strains of about 1 GPa. Deriving of major ratios used during the calculation of the third-order elastic moduli of the glasses is described in brief, the results of the calculations being provided. A qualitative agreement between the calculated results and available data on the influence of the uniform pressure on the sound wave propagation rate was obtained [ru
Escape of O(3P), O(1D), and O(1S) from the Martian atmosphere
Fox, Jane L.; Hać, Aleksander B.
2018-01-01
We have computed here the escape probabilities, fluxes and rates for hot O atoms that are initially produced in the ground state and the first two excited metastable states, O(1D)and O(1S), in the Martian thermosphere by dissociative recombination of O2+. In order to compare our results with those of our previous calculations and with those of others, we have employed here the pre-MAVEN models that we have used previously. To compute the escape probabilities, we have employed the Monte Carlo escape code that has been described previously, but we here use for the first time energy-dependent elastic cross sections for collisions of the energetic O atoms with each of the twelve background species in our model. We also incorporate three mechanisms that interchange identities of the O(3P) and O(1D) atoms, including collisional excitation of O(3P) to O(1D), quenching of O(1D) to O(3P), and excitation exchange of O(1D) with O(3P). We find that the escape probabilities of O atoms that are produced initially as O(1D) are reduced compared to those in which these processes are not included, but the escape probabilities of O atoms that are initially produced as O(3P) are not significantly reduced. As a guide for our future research and those of other investigators, we review here what is known about the interactions of O atoms with other species in which the energies of the O atoms are altered, and several other sources of hot and escaping O, many of which have been suggested by other investigators. We will incorporate these data in a future MAVEN-like model.
Elastic scattering and quasi-elastic transfers
International Nuclear Information System (INIS)
Mermaz, M.C.
1978-01-01
Experiments are presented which it will be possible to carry out at GANIL on the elastic scattering of heavy ions: diffraction phenomena if the absorption is great, refraction phenomena if absorption is low. The determination of the optical parameters can be performed. The study of the quasi-elastic transfer reactions will make it possible to know the dynamics of the nuclear reactions, form exotic nuclei and study their energy excitation spectrum, and analyse the scattering and reaction cross sections [fr
International Nuclear Information System (INIS)
Boyd, R.W.
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics
Nonlinear rock behavior and its implications on deeper-level platinum mining
CSIR Research Space (South Africa)
Watson, BP
2008-10-01
Full Text Available Uniaxial tests performed on core from instrumented sites at Amandelbult 1 shaft, Impala 10 shaft and Union Section Spud-shaft showed a nonlinear elastic relationship between applied load and induced deformation. This nonlinear behaviour does...
Branicio, Paulo S.; Vastola, Guglielmo; Jhon, Mark H.; Sullivan, Michael B.; Shenoy, Vivek B.; Srolovitz, David J.
2016-10-01
The deformation of graphene due to the chemisorption of hydrogen atoms on its surface and the long-range elastic interaction between hydrogen atoms induced by these deformations are investigated using a multiscale approach based on first principles, empirical interactions, and continuum modeling. Focus is given to the intrinsic low-temperature structure and interactions. Therefore, all calculations are performed at T =0 , neglecting possible temperature or thermal fluctuation effects. Results from different methods agree well and consistently describe the local deformation of graphene on multiple length scales reaching 500 Å . The results indicate that the elastic interaction mediated by this deformation is significant and depends on the deformation of the graphene sheet both in and out of plane. Surprisingly, despite the isotropic elasticity of graphene, within the linear elastic regime, atoms elastically attract or repel each other depending on (i) the specific site they are chemisorbed; (ii) the relative position of the sites; (iii) and if they are on the same or on opposite surface sides. The interaction energy sign and power-law decay calculated from molecular statics agree well with theoretical predictions from linear elasticity theory, considering in-plane or out-of-plane deformations as a superposition or in a coupled nonlinear approach. Deviations on the exact power law between molecular statics and the linear elastic analysis are evidence of the importance of nonlinear effects on the elasticity of monolayer graphene. These results have implications for the understanding of the generation of clusters and regular formations of hydrogen and other chemisorbed atoms on graphene.
Shoepe, Todd C; Ramirez, David A; Almstedt, Hawley C
2010-01-01
Elastic bands added to traditional free-weight techniques have become a part of suggested training routines in recent years. Because of the variable loading patterns of elastic bands (i.e., greater stretch produces greater resistance), it is necessary to quantify the exact loading patterns of bands to identify the volume and intensity of training. The purpose of this study was to determine the length vs. tension properties of multiple sizes of a set of commonly used elastic bands to quantify the resistance that would be applied to free-weight plus elastic bench presses (BP) and squats (SQ). Five elastic bands of varying thickness were affixed to an overhead support beam. Dumbbells of varying weights were progressively added to the free end while the linear deformation was recorded with each subsequent weight increment. The resistance was plotted as a factor of linear deformation, and best-fit nonlinear logarithmic regression equations were then matched to the data. For both the BP and SQ loading conditions and all band thicknesses tested, R values were greater than 0.9623. These data suggest that differences in load exist as a result of the thickness of the elastic band, attachment technique, and type of exercise being performed. Facilities should adopt their own form of loading quantification to match their unique set of circumstances when acquiring, researching, and implementing elastic band and free-weight exercises into the training programs.
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.
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.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
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
Boundary value problems of holomorphic vector functions in 1D QCs
International Nuclear Information System (INIS)
Gao Yang; Zhao Yingtao; Zhao Baosheng
2007-01-01
By means of the generalized Stroh formalism, two-dimensional (2D) problems of one-dimensional (1D) quasicrystals (QCs) elasticity are turned into the boundary value problems of holomorphic vector functions in a given region. If the conformal mapping from an ellipse to a circle is known, a general method for solving the boundary value problems of holomorphic vector functions can be presented. To illustrate its utility, by using the necessary and sufficient condition of boundary value problems of holomorphic vector functions, we consider two basic 2D problems in 1D QCs, that is, an elliptic hole and a rigid line inclusion subjected to uniform loading at infinity. For the crack problem, the intensity factors of phonon and phason fields are determined, and the physical sense of the results relative to phason and the difference between mechanical behaviors of the crack problem in crystals and QCs are figured out. Moreover, the same procedure can be used to deal with the elastic problems for 2D and three-dimensional (3D) QCs
Hyperbolicity of the Nonlinear Models of Maxwell's Equations
Serre, Denis
. We consider the class of nonlinear models of electromagnetism that has been described by Coleman & Dill [7]. A model is completely determined by its energy density W(B,D). Viewing the electromagnetic field (B,D) as a 3×2 matrix, we show that polyconvexity of W implies the local well-posedness of the Cauchy problem within smooth functions of class Hs with s>1+d/2. The method follows that designed by Dafermos in his book [9] in the context of nonlinear elasticity. We use the fact that B×D is a (vectorial, non-convex) entropy, and we enlarge the system from 6 to 9 equations. The resulting system admits an entropy (actually the energy) that is convex. Since the energy conservation law does not derive from the system of conservation laws itself (Faraday's and Ampère's laws), but also needs the compatibility relations divB=divD=0 (the latter may be relaxed in order to take into account electric charges), the energy density is not an entropy in the classical sense. Thus the system cannot be symmetrized, strictly speaking. However, we show that the structure is close enough to symmetrizability, so that the standard estimates still hold true.
DEFF Research Database (Denmark)
van der Laan, Paul; Sørensen, Niels N.
2017-01-01
A one-dimensional version of EllipSys, labeled as EllipSys1D is presented. Three atmospheric boundary layer test cases are used to show that results of EllipSys1D are exactly the same or very similar as results of EllipSys3D, while EllipSys1D uses 3 to 4 orders of magnitude less CPU hours compared...
Modeling dynamic acousto-elastic testing experiments: validation and perspectives.
Gliozzi, A S; Scalerandi, M
2014-10-01
Materials possessing micro-inhomogeneities often display a nonlinear response to mechanical solicitations, which is sensitive to the confining pressure acting on the sample. Dynamic acoustoelastic testing allows measurement of the instantaneous variations in the elastic modulus due to the change of the dynamic pressure induced by a low-frequency wave. This paper shows that a Preisach-Mayergoyz space based hysteretic multi-state elastic model provides an explanation for experimental observations in consolidated granular media and predicts memory and nonlinear effects comparable to those measured in rocks.
Design, implementation and analysis of fully digital 1-D controllable multiscroll chaos
Mansingka, Abhinav S.; Radwan, Ahmed G.; Salama, Khaled N.
2011-01-01
This paper introduces the fully digital implementation of a 1-D multiscroll chaos generator based on a staircase nonlinearity in the 3rd-order jerk system using the Euler approximation. For the first time, digital design is exploited to provide real-time controllability of (i) number of scrolls, (ii) position in 1-D space, (iii) Euler step size and (iv) system parameter. The effect of variations in these fields on the maximum Lyapunov exponent (MLE) is analyzed. The system is implemented using Verilog HDL and synthesized on an Xilinx Virtex 4 FPGA, exhibiting area utilization less than 3.5% and high performance with experimentally verified throughput up to 3.33 Gbits/s. This fully digital system enables applications in modulation schemes and chaos-based cryptosystems without analog to digital conversion. © 2011 IEEE.
Design, implementation and analysis of fully digital 1-D controllable multiscroll chaos
Mansingka, Abhinav S.
2011-12-01
This paper introduces the fully digital implementation of a 1-D multiscroll chaos generator based on a staircase nonlinearity in the 3rd-order jerk system using the Euler approximation. For the first time, digital design is exploited to provide real-time controllability of (i) number of scrolls, (ii) position in 1-D space, (iii) Euler step size and (iv) system parameter. The effect of variations in these fields on the maximum Lyapunov exponent (MLE) is analyzed. The system is implemented using Verilog HDL and synthesized on an Xilinx Virtex 4 FPGA, exhibiting area utilization less than 3.5% and high performance with experimentally verified throughput up to 3.33 Gbits/s. This fully digital system enables applications in modulation schemes and chaos-based cryptosystems without analog to digital conversion. © 2011 IEEE.
Continuum mechanics elasticity, plasticity, viscoelasticity
Dill, Ellis H
2006-01-01
FUNDAMENTALS OF CONTINUUM MECHANICSMaterial ModelsClassical Space-TimeMaterial BodiesStrainRate of StrainCurvilinear Coordinate SystemsConservation of MassBalance of MomentumBalance of EnergyConstitutive EquationsThermodynamic DissipationObjectivity: Invariance for Rigid MotionsColeman-Mizel ModelFluid MechanicsProblems for Chapter 1BibliographyNONLINEAR ELASTICITYThermoelasticityMaterial SymmetriesIsotropic MaterialsIncompressible MaterialsConjugate Measures of Stress and StrainSome Symmetry GroupsRate Formulations for Elastic MaterialsEnergy PrinciplesGeometry of Small DeformationsLinear ElasticitySpecial Constitutive Models for Isotropic MaterialsMechanical Restrictions on the Constitutive RelationsProblems for Chapter 2BibliographyLINEAR ELASTICITYBasic EquationsPlane StrainPlane StressProperties of SolutionsPotential EnergySpecial Matrix NotationThe Finite Element Method of SolutionGeneral Equations for an Assembly of ElementsFinite Element Analysis for Large DeformationsProblems for Chapter 3Bibliograph...
Finite elements of nonlinear continua
Oden, John Tinsley
1972-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
Modeling for control of an inflatable space reflector, the nonlinear 1-D case
Voß, T.; Scherpen, J.M.A.; Onck, P.R.
2008-01-01
In this paper we develop a mathematical model of the dynamics for an inflatable space reflector, which can be used to design a controller for the shape of the inflatable structure. Inflatable structures have very nice properties, suitable for aerospace applications. We can construct e.g. a huge
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.
Weyl geometry and the nonlinear mechanics of distributed point defects
Yavari, A.; Goriely, A.
2012-01-01
The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects
Riemann-Cartan geometry of nonlinear disclination mechanics
Yavari, A.; Goriely, A.
2012-01-01
In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining
Multi-level methods for solving multigroup transport eigenvalue problems in 1D slab geometry
International Nuclear Information System (INIS)
Anistratov, D. Y.; Gol'din, V. Y.
2009-01-01
A methodology for solving eigenvalue problems for the multigroup neutron transport equation in 1D slab geometry is presented. In this paper we formulate and compare different variants of nonlinear multi-level iteration methods. They are defined by means of multigroup and effective one-group low-order quasi diffusion (LOQD) equations. We analyze the effects of utilization of the effective one-group LOQD problem for estimating the eigenvalue. We present numerical results to demonstrate the performance of the iteration algorithms in different types of reactor-physics problems. (authors)
Robust 1D inversion and analysis of helicopter electromagnetic (HEM) data
DEFF Research Database (Denmark)
Tølbøll, R.J.; Christensen, N.B.
2006-01-01
but can resolve layer boundary to a depth of more than 100 m. Modeling experiments also show that the effect of altimeter errors on the inversion results is serious. We suggest a new interpretation scheme for HEM data founded solely on full nonlinear 1D inversion and providing layered-earth models...... supported by datamisfit parameters and a quantitative model-parameter analysis. The backbone of the scheme is the removal of cultural coupling effects followed by a multilayer inversion that in turn provides reliable starting models for a subsequent few-layer inversion. A new procedure for correlation...
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Elasticity theory and applications
Saada, Adel S; Hartnett, James P; Hughes, William F
2013-01-01
Elasticity: Theory and Applications reviews the theory and applications of elasticity. The book is divided into three parts. The first part is concerned with the kinematics of continuous media; the second part focuses on the analysis of stress; and the third part considers the theory of elasticity and its applications to engineering problems. This book consists of 18 chapters; the first of which deals with the kinematics of continuous media. The basic definitions and the operations of matrix algebra are presented in the next chapter, followed by a discussion on the linear transformation of points. The study of finite and linear strains gradually introduces the reader to the tensor concept. Orthogonal curvilinear coordinates are examined in detail, along with the similarities between stress and strain. The chapters that follow cover torsion; the three-dimensional theory of linear elasticity and the requirements for the solution of elasticity problems; the method of potentials; and topics related to cylinders, ...
Modeling Pseudo-elastic Behavior of Springback
International Nuclear Information System (INIS)
Xia, Z. Cedric
2005-01-01
constant. In the context of this investigation we refer psuedoelastic behavior in the most general sense as any deviation from linearity in the unloading curve. The non-linearity leads to a hysteresis loop upon reloading. The approach is based on the non-conventional theory with a vanishing elastic region as advanced by Dafalias and Popov. The treatment is purely phenomenological where we don't distinguish between macroscopic plasticity and micro-plasticity. The macroscopic uniaxial stress-strain curve is used to define effective plastic response in the same manner as classical plasticity theory except that the nonlinearity during unloading and reloading are incorporated into plasticity. It is shown that such models can be easily formulated within the context of elastoplasticity without violating any physical mechanisms of deformation. Springback for a plane strain bending model is used to demonstrate the potential effect if such a model is applied
Energy Device Applications of Synthesized 1D Polymer Nanomaterials.
Huang, Long-Biao; Xu, Wei; Hao, Jianhua
2017-11-01
1D polymer nanomaterials as emerging materials, such as nanowires, nanotubes, and nanopillars, have attracted extensive attention in academia and industry. The distinctive, various, and tunable structures in the nanoscale of 1D polymer nanomaterials present nanointerfaces, high surface-to-volume ratio, and large surface area, which can improve the performance of energy devices. In this review, representative fabrication techniques of 1D polymer nanomaterials are summarized, including electrospinning, template-assisted, template-free, and inductively coupled plasma methods. The recent advancements of 1D polymer nanomaterials in energy device applications are demonstrated. Lastly, existing challenges and prospects of 1D polymer nanomaterials for energy device applications are presented. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Energy Technology Data Exchange (ETDEWEB)
Popovic, Marta; Zaja, Roko [Laboratory for Molecular Ecotoxicology, Division for Marine and Environmental Research, Rudjer Boskovic Institute, Bijenicka 54, 10 000 Zagreb (Croatia); Fent, Karl [University of Applied Sciences Northwestern Switzerland, School of Life Sciences, Gründenstrasse 40, CH-4132 Muttenz (Switzerland); Swiss Federal Institute of Technology (ETH Zürich), Department of Environmental System Sciences, Institute of Biogeochemistry and Pollution Dynamics, CH-8092 Zürich (Switzerland); Smital, Tvrtko, E-mail: smital@irb.hr [Laboratory for Molecular Ecotoxicology, Division for Marine and Environmental Research, Rudjer Boskovic Institute, Bijenicka 54, 10 000 Zagreb (Croatia)
2014-10-01
Polyspecific transporters from the organic anion transporting polypeptide (OATP/Oatp) superfamily mediate the uptake of a wide range of compounds. In zebrafish, Oatp1d1 transports conjugated steroid hormones and cortisol. It is predominantly expressed in the liver, brain and testes. In this study we have characterized the transport of xenobiotics by the zebrafish Oatp1d1 transporter. We developed a novel assay for assessing Oatp1d1 interactors using the fluorescent probe Lucifer yellow and transient transfection in HEK293 cells. Our data showed that numerous environmental contaminants interact with zebrafish Oatp1d1. Oatp1d1 mediated the transport of diclofenac with very high affinity, followed by high affinity towards perfluorooctanesulfonic acid (PFOS), nonylphenol, gemfibrozil and 17α-ethinylestradiol; moderate affinity towards carbaryl, diazinon and caffeine; and low affinity towards metolachlor. Importantly, many environmental chemicals acted as strong inhibitors of Oatp1d1. A strong inhibition of Oatp1d1 transport activity was found by perfluorooctanoic acid (PFOA), chlorpyrifos-methyl, estrone (E1) and 17β-estradiol (E2), followed by moderate to low inhibition by diethyl phthalate, bisphenol A, 7-acetyl-1,1,3,4,4,6-hexamethyl-1,2,3,4 tetrahydronapthalene and clofibrate. In this study we identified Oatp1d1 as a first Solute Carrier (SLC) transporter involved in the transport of a wide range of xenobiotics in fish. Considering that Oatps in zebrafish have not been characterized before, our work on zebrafish Oatp1d1 offers important new insights on the understanding of uptake processes of environmental contaminants, and contributes to the better characterization of zebrafish as a model species. - Highlights: • We optimized a novel assay for determination of Oatp1d1 interactors • Oatp1d1 is the first SLC characterized fish xenobiotic transporter • PFOS, nonylphenol, diclofenac, EE2, caffeine are high affinity Oatp1d1substrates • PFOA, chlorpyrifos
International Nuclear Information System (INIS)
Popovic, Marta; Zaja, Roko; Fent, Karl; Smital, Tvrtko
2014-01-01
Polyspecific transporters from the organic anion transporting polypeptide (OATP/Oatp) superfamily mediate the uptake of a wide range of compounds. In zebrafish, Oatp1d1 transports conjugated steroid hormones and cortisol. It is predominantly expressed in the liver, brain and testes. In this study we have characterized the transport of xenobiotics by the zebrafish Oatp1d1 transporter. We developed a novel assay for assessing Oatp1d1 interactors using the fluorescent probe Lucifer yellow and transient transfection in HEK293 cells. Our data showed that numerous environmental contaminants interact with zebrafish Oatp1d1. Oatp1d1 mediated the transport of diclofenac with very high affinity, followed by high affinity towards perfluorooctanesulfonic acid (PFOS), nonylphenol, gemfibrozil and 17α-ethinylestradiol; moderate affinity towards carbaryl, diazinon and caffeine; and low affinity towards metolachlor. Importantly, many environmental chemicals acted as strong inhibitors of Oatp1d1. A strong inhibition of Oatp1d1 transport activity was found by perfluorooctanoic acid (PFOA), chlorpyrifos-methyl, estrone (E1) and 17β-estradiol (E2), followed by moderate to low inhibition by diethyl phthalate, bisphenol A, 7-acetyl-1,1,3,4,4,6-hexamethyl-1,2,3,4 tetrahydronapthalene and clofibrate. In this study we identified Oatp1d1 as a first Solute Carrier (SLC) transporter involved in the transport of a wide range of xenobiotics in fish. Considering that Oatps in zebrafish have not been characterized before, our work on zebrafish Oatp1d1 offers important new insights on the understanding of uptake processes of environmental contaminants, and contributes to the better characterization of zebrafish as a model species. - Highlights: • We optimized a novel assay for determination of Oatp1d1 interactors • Oatp1d1 is the first SLC characterized fish xenobiotic transporter • PFOS, nonylphenol, diclofenac, EE2, caffeine are high affinity Oatp1d1substrates • PFOA, chlorpyrifos
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
Nonlinear and Nonequilibrium Dynamics in Geomaterials
TenCate, James A.; Pasqualini, Donatella; Habib, Salman; Heitmann, Katrin; Higdon, David; Johnson, Paul A.
2004-01-01
The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a s...
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.
Elasticity of energy consumption
International Nuclear Information System (INIS)
Stam, M.
2004-01-01
Insight is given into the price elasticities of several energy carriers. Next, attention is paid to the impact of the discussion on changes of the Regulating Energy Levy (REB, abbreviated in Dutch) in the Netherlands [nl
ATR kinase regulates its attenuation via PPM1D phosphatase ...
Indian Academy of Sciences (India)
Debadrita Bhattacharya
2018-02-07
Feb 7, 2018 ... generated in response to ultraviolet and ionizing radiation (Lu et al. 2005a, b; Cha ... nocopy' each other's effects by uncovering persistent ATR signalling that in ...... been shown to indirectly stabilize PPM1D by mediating the.
Severe Hypertriglyceridemia in Glut1D on Ketogenic Diet.
Klepper, Joerg; Leiendecker, Baerbel; Heussinger, Nicole; Lausch, Ekkehart; Bosch, Friedrich
2016-04-01
High-fat ketogenic diets are the only treatment available for Glut1 deficiency (Glut1D). Here, we describe an 8-year-old girl with classical Glut1D responsive to a 3:1 ketogenic diet and ethosuximide. After 3 years on the diet a gradual increase of blood lipids was followed by rapid, severe asymptomatic hypertriglyceridemia (1,910 mg/dL). Serum lipid apheresis was required to determine liver, renal, and pancreatic function. A combination of medium chain triglyceride-oil and a reduction of the ketogenic diet to 1:1 ratio normalized triglyceride levels within days but triggered severe myoclonic seizures requiring comedication with sultiam. Severe hypertriglyceridemia in children with Glut1D on ketogenic diets may be underdiagnosed and harmful. In contrast to congenital hypertriglyceridemias, children with Glut1D may be treated effectively by dietary adjustments alone. Georg Thieme Verlag KG Stuttgart · New York.
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.
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.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
TBC1D24 genotype–phenotype correlation
Balestrini, Simona; Milh, Mathieu; Castiglioni, Claudia; Lüthy, Kevin; Finelli, Mattea J.; Verstreken, Patrik; Cardon, Aaron; Stražišar, Barbara Gnidovec; Holder, J. Lloyd; Lesca, Gaetan; Mancardi, Maria M.; Poulat, Anne L.; Repetto, Gabriela M.; Banka, Siddharth; Bilo, Leonilda; Birkeland, Laura E.; Bosch, Friedrich; Brockmann, Knut; Cross, J. Helen; Doummar, Diane; Félix, Temis M.; Giuliano, Fabienne; Hori, Mutsuki; Hüning, Irina; Kayserili, Hulia; Kini, Usha; Lees, Melissa M.; Meenakshi, Girish; Mewasingh, Leena; Pagnamenta, Alistair T.; Peluso, Silvio; Mey, Antje; Rice, Gregory M.; Rosenfeld, Jill A.; Taylor, Jenny C.; Troester, Matthew M.; Stanley, Christine M.; Ville, Dorothee; Walkiewicz, Magdalena; Falace, Antonio; Fassio, Anna; Lemke, Johannes R.; Biskup, Saskia; Tardif, Jessica; Ajeawung, Norbert F.; Tolun, Aslihan; Corbett, Mark; Gecz, Jozef; Afawi, Zaid; Howell, Katherine B.; Oliver, Karen L.; Berkovic, Samuel F.; Scheffer, Ingrid E.; de Falco, Fabrizio A.; Oliver, Peter L.; Striano, Pasquale; Zara, Federico
2016-01-01
Objective: To evaluate the phenotypic spectrum associated with mutations in TBC1D24. Methods: We acquired new clinical, EEG, and neuroimaging data of 11 previously unreported and 37 published patients. TBC1D24 mutations, identified through various sequencing methods, can be found online (http://lovd.nl/TBC1D24). Results: Forty-eight patients were included (28 men, 20 women, average age 21 years) from 30 independent families. Eighteen patients (38%) had myoclonic epilepsies. The other patients carried diagnoses of focal (25%), multifocal (2%), generalized (4%), and unclassified epilepsy (6%), and early-onset epileptic encephalopathy (25%). Most patients had drug-resistant epilepsy. We detail EEG, neuroimaging, developmental, and cognitive features, treatment responsiveness, and physical examination. In silico evaluation revealed 7 different highly conserved motifs, with the most common pathogenic mutation located in the first. Neuronal outgrowth assays showed that some TBC1D24 mutations, associated with the most severe TBC1D24-associated disorders, are not necessarily the most disruptive to this gene function. Conclusions: TBC1D24-related epilepsy syndromes show marked phenotypic pleiotropy, with multisystem involvement and severity spectrum ranging from isolated deafness (not studied here), benign myoclonic epilepsy restricted to childhood with complete seizure control and normal intellect, to early-onset epileptic encephalopathy with severe developmental delay and early death. There is no distinct correlation with mutation type or location yet, but patterns are emerging. Given the phenotypic breadth observed, TBC1D24 mutation screening is indicated in a wide variety of epilepsies. A TBC1D24 consortium was formed to develop further research on this gene and its associated phenotypes. PMID:27281533
Impact of CD1d deficiency on metabolism.
Directory of Open Access Journals (Sweden)
Maya E Kotas
Full Text Available Invariant natural killer T cells (iNKTs are innate-like T cells that are highly concentrated in the liver and recognize lipids presented on the MHC-like molecule CD1d. Although capable of a myriad of responses, few essential functions have been described for iNKTs. Among the many cell types of the immune system implicated in metabolic control and disease, iNKTs seem ideally poised for such a role, yet little has been done to elucidate such a possible function. We hypothesized that lipid presentation by CD1d could report on metabolic status and engage iNKTs to regulate cellular lipid content through their various effector mechanisms. To test this hypothesis, we examined CD1d deficient mice in a variety of metabolically stressed paradigms including high fat feeding, choline-deficient feeding, fasting, and acute inflammation. CD1d deficiency led to a mild exacerbation of steatosis during high fat or choline-deficient feeding, accompanied by impaired hepatic glucose tolerance. Surprisingly, however, this phenotype was not observed in Jα18⁻/⁻ mice, which are deficient in iNKTs but express CD1d. Thus, CD1d appears to modulate some metabolic functions through an iNKT-independent mechanism.
Holographic memory system based on projection recording of computer-generated 1D Fourier holograms.
Betin, A Yu; Bobrinev, V I; Donchenko, S S; Odinokov, S B; Evtikhiev, N N; Starikov, R S; Starikov, S N; Zlokazov, E Yu
2014-10-01
Utilization of computer generation of holographic structures significantly simplifies the optical scheme that is used to record the microholograms in a holographic memory record system. Also digital holographic synthesis allows to account the nonlinear errors of the record system to improve the microholograms quality. The multiplexed record of holograms is a widespread technique to increase the data record density. In this article we represent the holographic memory system based on digital synthesis of amplitude one-dimensional (1D) Fourier transform holograms and the multiplexed record of these holograms onto the holographic carrier using optical projection scheme. 1D Fourier transform holograms are very sensitive to orientation of the anamorphic optical element (cylindrical lens) that is required for encoded data object reconstruction. The multiplex record of several holograms with different orientation in an optical projection scheme allowed reconstruction of the data object from each hologram by rotating the cylindrical lens on the corresponding angle. Also, we discuss two optical schemes for the recorded holograms readout: a full-page readout system and line-by-line readout system. We consider the benefits of both systems and present the results of experimental modeling of 1D Fourier holograms nonmultiplex and multiplex record and reconstruction.
WE-E-9A-01: Ultrasound Elasticity
Energy Technology Data Exchange (ETDEWEB)
Emelianov, S [University of Texas at Austin, Austin, TX (United States); Hall, T [University of WI-Madison, Madison, WI (United States); Bouchard, R [UT MD Anderson Cancer Center and UTHSC at Houston Graduate School of Biomed, Houston, TX (United States)
2014-06-15
Principles and techniques of ultrasound-based elasticity imaging will be presented, including quasistatic strain imaging, shear wave elasticity imaging, and their implementations in available systems. Deeper exploration of quasistatic methods, including elastic relaxation, and their applications, advantages, artifacts and limitations will be discussed. Transient elastography based on progressive and standing shear waves will be explained in more depth, along with applications, advantages, artifacts and limitations, as will measurement of complex elastic moduli. Comparisons will be made between ultrasound radiation force techniques, MR elastography, and the simple A mode plus mechanical plunger technique. Progress in efforts, such as that by the Quantitative Imaging Biomarkers Alliance, to reduce the differences in the elastic modulus reported by different commercial systems will be explained. Dr. Hall is on an Advisory Board for Siemens Ultrasound and has a research collaboration with them, including joint funding by R01CA140271 for nonlinear elasticity imaging. Learning Objectives: Be reminded of the long history of palpation of tissue elasticity for critical medical diagnosis and the relatively recent advances to be able to image tissue strain in response to an applied force. Understand the differences between shear wave speed elasticity measurement and imaging and understand the factors affecting measurement and image frame repletion rates. Understand shear wave propagation effects that can affect measurements, such as essentially lack of propagation in fluids and boundary effects, so important in thin layers. Know characteristics of available elasticity imaging phantoms, their uses and limitations. Understand thermal and cavitational limitations affecting radiation force-based shear wave imaging. Have learning and references adequate to for you to use in teaching elasticity imaging to residents and technologists. Be able to explain how elasticity measurement
WE-E-9A-01: Ultrasound Elasticity
International Nuclear Information System (INIS)
Emelianov, S; Hall, T; Bouchard, R
2014-01-01
Principles and techniques of ultrasound-based elasticity imaging will be presented, including quasistatic strain imaging, shear wave elasticity imaging, and their implementations in available systems. Deeper exploration of quasistatic methods, including elastic relaxation, and their applications, advantages, artifacts and limitations will be discussed. Transient elastography based on progressive and standing shear waves will be explained in more depth, along with applications, advantages, artifacts and limitations, as will measurement of complex elastic moduli. Comparisons will be made between ultrasound radiation force techniques, MR elastography, and the simple A mode plus mechanical plunger technique. Progress in efforts, such as that by the Quantitative Imaging Biomarkers Alliance, to reduce the differences in the elastic modulus reported by different commercial systems will be explained. Dr. Hall is on an Advisory Board for Siemens Ultrasound and has a research collaboration with them, including joint funding by R01CA140271 for nonlinear elasticity imaging. Learning Objectives: Be reminded of the long history of palpation of tissue elasticity for critical medical diagnosis and the relatively recent advances to be able to image tissue strain in response to an applied force. Understand the differences between shear wave speed elasticity measurement and imaging and understand the factors affecting measurement and image frame repletion rates. Understand shear wave propagation effects that can affect measurements, such as essentially lack of propagation in fluids and boundary effects, so important in thin layers. Know characteristics of available elasticity imaging phantoms, their uses and limitations. Understand thermal and cavitational limitations affecting radiation force-based shear wave imaging. Have learning and references adequate to for you to use in teaching elasticity imaging to residents and technologists. Be able to explain how elasticity measurement
National Research Council Canada - National Science Library
Drazin, P. G
1992-01-01
This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...
Gasinski, Leszek
2005-01-01
Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.
Morphoelasticity: A theory of elastic growth
Goriely, Alain; Moulton, Derek
2011-01-01
This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional setting, illustrating the key relationship between growth, the elastic response of the material, and the generation of residual stresses. The general three-dimensional theory of morphoelasticity is then developed from conservation of mass and momentum balance equations. In the formulation, the multiplicative decomposition of the deformation tensor, the standard approach in morphoelasticity, is derived in a new way. A discussion of continuous growth is also included. The chapter concludes by working through a sample problem of a growing cylindrical tube. A stability analysis is formulated, and the effect of growth on mucosal folding, a commonly seen instability in biological tubes, is demonstrated.
Morphoelasticity: A theory of elastic growth
Goriely, Alain
2011-10-11
This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional setting, illustrating the key relationship between growth, the elastic response of the material, and the generation of residual stresses. The general three-dimensional theory of morphoelasticity is then developed from conservation of mass and momentum balance equations. In the formulation, the multiplicative decomposition of the deformation tensor, the standard approach in morphoelasticity, is derived in a new way. A discussion of continuous growth is also included. The chapter concludes by working through a sample problem of a growing cylindrical tube. A stability analysis is formulated, and the effect of growth on mucosal folding, a commonly seen instability in biological tubes, is demonstrated.
Asymptotic behaviour of a rescattering series for nonlinear reggeons
International Nuclear Information System (INIS)
Akkelin, S.V.; Martynov, E.S.
1990-01-01
A series of elastic re-scattering (both quasi-eikonal and U-matrix ones) for reggeons with nonlinear trajectories are estimated asymptotically. The calculations are performed for models of supercritical and dipole pomerons. A weak dependence of the series of re-scattering on reggeon trajectory nonlinearity is revealed. 13 refs.; 3 figs
Structural transformation in monolayer materials: a 2D to 1D transformation.
Momeni, Kasra; Attariani, Hamed; LeSar, Richard A
2016-07-20
Reducing the dimensions of materials to atomic scales results in a large portion of atoms being at or near the surface, with lower bond order and thus higher energy. At such scales, reduction of the surface energy and surface stresses can be the driving force for the formation of new low-dimensional nanostructures, and may be exhibited through surface relaxation and/or surface reconstruction, which can be utilized for tailoring the properties and phase transformation of nanomaterials without applying any external load. Here we used atomistic simulations and revealed an intrinsic structural transformation in monolayer materials that lowers their dimension from 2D nanosheets to 1D nanostructures to reduce their surface and elastic energies. Experimental evidence of such transformation has also been revealed for one of the predicted nanostructures. Such transformation plays an important role in bi-/multi-layer 2D materials.
Flutter analysis of an airfoil with multiple nonlinearities and uncertainties
Directory of Open Access Journals (Sweden)
Haitao Liao
2013-09-01
Full Text Available An original method for calculating the limit cycle oscillations of nonlinear aero-elastic system is presented. The problem of determining the maximum vibration amplitude of limit cycle is transformed into a nonlinear optimization problem. The harmonic balance method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated and used to analyse the limit cycle oscillations of an airfoil with multiple nonlinearities and uncertainties. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.
Thermoelectric Power Factor Limit of a 1D Nanowire
Chen, I.-Ju; Burke, Adam; Svilans, Artis; Linke, Heiner; Thelander, Claes
2018-04-01
In the past decade, there has been significant interest in the potentially advantageous thermoelectric properties of one-dimensional (1D) nanowires, but it has been challenging to find high thermoelectric power factors based on 1D effects in practice. Here we point out that there is an upper limit to the thermoelectric power factor of nonballistic 1D nanowires, as a consequence of the recently established quantum bound of thermoelectric power output. We experimentally test this limit in quasiballistic InAs nanowires by extracting the maximum power factor of the first 1D subband through I -V characterization, finding that the measured maximum power factors conform to the theoretical limit. The established limit allows the prediction of the achievable power factor of a specific nanowire material system with 1D electronic transport based on the nanowire dimension and mean free path. The power factor of state-of-the-art semiconductor nanowires with small cross section and high crystal quality can be expected to be highly competitive (on the order of mW /m K2 ) at low temperatures. However, they have no clear advantage over bulk materials at, or above, room temperature.
Valley-symmetric quasi-1D transport in ballistic graphene
Lee, Hu-Jong
We present our recent studies on gate-defined valley-symmetric one-dimensional (1D) carrier guiding in ballistic monolayer graphene and valley-symmetry-protected topological 1D transport in ballistic bilayer graphene. Successful carrier guiding was realized in ballistic monolayer graphene even in the absence of a band gap by inducing a high distinction ( more than two orders of magnitude) in the carrier density between the region of a quasi-1D channel and the rest of the top-gated regions. Conductance of a channel shows quantized values in units of 4e2/ h, suggesting that the valley symmetry is preserved. For the latter, the topological 1D conduction was realized between two closely arranged insulating regions with inverted band gaps, induced under a pair of split dual gating with polarities opposite to each other. The maximum conductance along the boundary channel showed 4e2/ h, again with the preserved valley symmetry. The 1D topological carrier guiding demonstrated in this study affords a promising route to robust valleytronic applications and sophisticated valley-associated functionalities based on 2D materials. This work was funded by the National Research Foundation of Korea.
Nonlinear dynamics and control of a vibrating rectangular plate
Shebalin, J. V.
1983-01-01
The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.
A model with isospin doublet U(1)D gauge symmetry
Nomura, Takaaki; Okada, Hiroshi
2018-05-01
We propose a model with an extra isospin doublet U(1)D gauge symmetry, in which we introduce several extra fermions with odd parity under a discrete Z2 symmetry in order to cancel the gauge anomalies out. A remarkable issue is that we impose nonzero U(1)D charge to the Standard Model Higgs, and it gives the most stringent constraint to the vacuum expectation value of a scalar field breaking the U(1)D symmetry that is severer than the LEP bound. We then explore relic density of a Majorana dark matter candidate without conflict of constraints from lepton flavor violating processes. A global analysis is carried out to search for parameters which can accommodate with the observed data.
Elastic anisotropy of crystals
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Das, Y.C.; Kedia, K.K.
1977-01-01
No realistic analytical work in the area of Shells on Elastic Foundations has been reported in the literature. Various foundation models have been proposed by several authors. These models involve one or more than one parameters to characterise the foundation medium. Some of these models cannot be used to derive the basic equations governing the behaviour of shells on elastic foundations. In the present work, starting from an elastic continuum hypothesis, a mathematical model for foundation has been derived in curvilinear orthogonal coordinates by the help of principle of virtual displacements, treating one of the virtual displacements as known to satisfy certain given conditions at its edge surfaces. In this model, several foundation parameters can be considered and it can also be used for layered medium of both finite and infinite thickness. (Auth.)
Diffusion and particle mobility in 1D system
International Nuclear Information System (INIS)
Borman, V.D.; Johansson, B.; Skorodumova, N.V.; Tronin, I.V.; Tronin, V.N.; Troyan, V.I.
2006-01-01
The transport properties of one-dimensional (1D) systems have been studied theoretically. Contradictory experimental results on molecular transport in quasi-1D systems, such as zeolite structures, when both diffusion transport acceleration and the existence of the diffusion mode with lower particle mobility (single-file diffusion ( 2 >∼t 1/2 )) have been reported, are consolidated in a consistent model. Transition from the single-file diffusion mode to an Einstein-like diffusion 2 >∼t with diffusion coefficient increasing with the density has been predicted to occur at large observation times
Nonreciprocity of edge modes in 1D magnonic crystal
International Nuclear Information System (INIS)
Lisenkov, I.; Kalyabin, D.; Osokin, S.; Klos, J.W.; Krawczyk, M.; Nikitov, S.
2015-01-01
Spin waves propagation in 1D magnonic crystals is investigated theoretically. Mathematical model based on plane wave expansion method is applied to different types of magnonic crystals, namely bi-component magnonic crystal with symmetric/asymmetric boundaries and ferromagnetic film with periodically corrugated top surface. It is shown that edge modes in magnonic crystals may exhibit nonreciprocal behaviour at much lower frequencies than in homogeneous films. - Highlights: • Magnetostatic surface spin waves in 1D magnonic crystals were studied theoretically. • Mathematical model is based on plane wave method. • Mathematical model was applied to different types of magnonic crystals. • Stop band formation and nonreciprocity were obtained
Flood hazard assessment using 1D and 2D approaches
Petaccia, Gabriella; Costabile, Pierfranco; Macchione, Francesco; Natale, Luigi
2013-04-01
The EU flood risk Directive (Directive 2007/60/EC) prescribes risk assessment and mapping to develop flood risk management plans. Flood hazard mapping may be carried out with mathematical models able to determine flood-prone areas once realistic conditions (in terms of discharge or water levels) are imposed at the boundaries of the case study. The deterministic models are mainly based on shallow water equations expressed in their 1D or 2D formulation. The 1D approach is widely used, especially in technical studies, due to its relative simplicity, its computational efficiency and also because it requires topographical data not as expensive as the ones needed by 2D models. Even if in a great number of practical situations, such as modeling in-channel flows and not too wide floodplains, the 1D approach may provide results close to the prediction of a more sophisticated 2D model, it must be pointed out that the correct use of a 1D model in practical situations is more complex than it may seem. The main issues to be correctly modeled in a 1D approach are the definition of hydraulic structures such as bridges and buildings interacting with the flow and the treatment of the tributaries. Clearly all these aspects have to be taken into account also in the 2D modeling, but with fewer difficulties. The purpose of this paper is to show how the above cited issues can be described using a 1D or 2D unsteady flow modeling. In particular the Authors will show the devices that have to be implemented in 1D modeling to get reliable predictions of water levels and discharges comparable to the ones obtained using a 2D model. Attention will be focused on an actual river (Crati river) located in the South of Italy. This case study is quite complicated since it deals with the simulation of channeled flows, overbank flows, interactions with buildings, bridges and tributaries. Accurate techniques, intentionally developed by the Authors to take into account all these peculiarities in 1D and 2
Negative stiffness honeycombs as tunable elastic metamaterials
Goldsberry, Benjamin M.; Haberman, Michael R.
2018-03-01
Acoustic and elastic metamaterials are media with a subwavelength structure that behave as effective materials displaying atypical effective dynamic properties. These material systems are of interest because the design of their sub-wavelength structure allows for direct control of macroscopic wave dispersion. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify wave propagation in the metamaterial with an external stimulus is highly desirable for numerous applications and therefore remains a significant challenge in elastic metamaterials research. In this work, a honeycomb structure composed of a doubly periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable elastic metamaterial. The nonlinear static elastic response that results from large deformations of the NSH unit cell leads to a large variation in linear elastic wave dispersion associated with infinitesimal motion superposed on the externally imposed pre-strain. A finite element model is utilized to model the static deformation and subsequent linear wave motion at the pre-strained state. Analysis of the slowness surface and group velocity demonstrates that the NSH exhibits significant tunability and a high degree of anisotropy which can be used to guide wave energy depending on static pre-strain levels. In addition, it is shown that partial band gaps exist where only longitudinal waves propagate. The NSH therefore behaves as a meta-fluid, or pentamode metamaterial, which may be of use for applications of transformation elastodynamics such as cloaking and gradient index lens devices.
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.
Lai, Yun; Wu, Ying; Sheng, Ping; Zhang, Zhaoqing
2011-01-01
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.
Directory of Open Access Journals (Sweden)
Sergio Cesare Masin
2010-01-01
Full Text Available Participants estimated the imagined elongation of a spring while they were imagining that a load was stretching the spring. This elongation turned out to be a multiplicative function of spring length and load weight-a cognitive law analogous to Hooke¿s law of elasticity. Participants also estimated the total imagined elongation of springs joined either in series or in parallel. This total elongation was longer for serial than for parallel springs, and increased proportionally to the number of serial springs and inversely proportionally to the number of parallel springs. The results suggest that participants integrated load weight with imagined elasticity rather than with spring length.
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.
Elastic plastic fracture mechanics
International Nuclear Information System (INIS)
Simpson, L.A.
1978-07-01
The application of linear elastic fracture mechanics (LEFM) to crack stability in brittle structures is now well understood and widely applied. However, in many structural materials, crack propagation is accompanied by considerable crack-tip plasticity which invalidates the use of LEFM. Thus, present day research in fracture mechanics is aimed at developing parameters for predicting crack propagation under elastic-plastic conditions. These include critical crack-opening-displacement methods, the J integral and R-curve techniques. This report provides an introduction to these concepts and gives some examples of their applications. (author)
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...
A novel nonlinear damage resonance intermodulation effect for structural health monitoring
Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele
2017-04-01
This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.
Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.
2014-01-01
Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.
FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS
Directory of Open Access Journals (Sweden)
Bazhenov V.A.
2014-06-01
Full Text Available Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.
1985-03-20
performed a perturbation calculation suggested by Heitler [15] using a canonical transfo lition. The N + 2 level structure of fig. la) is assumed...fluctuating hyperfine fields, or rates r, and F can often be simply related to the re- ion-ion interactions. At low temperatures. phonon taxation time T, as we...competition of other possible elastic collision mechanisms will be ,.. discussed later. 2.3 Two Pulse Delayed Nutation Consider that two brief laser
Internal resonance of an elastic body levitated above high-Tc superconducting bulks
International Nuclear Information System (INIS)
Kokuzawa, T; Toshihiko, S; Yoshizawa, M
2010-01-01
In high-Tc superconducting magnetic levitation systems, levitated bodies can keep stable levitation with no contact and no control and thus their damping is very small. Thanks to these features, their applications to various apparatus are expected. However, on account of their small damping, the nonlinearity of electromagnetic levitation force can give notable effects upon motion of the levitated bodies. Therefore this nonlinearity must be taken into account to accurately analyze the dynamical behavior of the levitated bodies. Structures of such a levitated body can show elastic deformation if the large electromagnetic force acts on it. Therefore, we need to deal with the model as an elastic body. As mentioned above, nonlinear characteristics easily appear in this elastic vibration on account of the small damping. Especially when the ratio of the natural frequencies of the eigenmodes is integer, internal resonance can occur. This nonlinear resonance is derived from nonlinear interactions among the eigenmodes of the elastic levitated body. This kind of internal resonance of an elastic body appearing in high-Tc superconducting levitation systems has not been studied so far. This research especially deals with internal resonance of a beam supported at both its ends by electromagnetic forces acting on permanent magnets. The governing equation with the nonlinear boundary conditions for the dynamics of a levitated beam has been derived. Numerical results show internal resonance of the 1st mode and the 3rd mode. Experimental results are qualitatively in good agreement with numerical ones.
Crystal structure, characterization and magnetic properties of a 1D ...
Indian Academy of Sciences (India)
Crystal structure, characterization and magnetic properties of a 1D copper(II) polymer incorporating a Schiff base with carboxylate side arm. SHYAMAPADA SHIT MADHUSUDAN NANDY CORRADO RIZZOLI CÉDRIC DESPLANCHES SAMIRAN MITRA. Regular Article Volume 128 Issue 6 June 2016 pp 913-920 ...
Quantitative 1D saturation profiles on chalk by NMR
DEFF Research Database (Denmark)
Olsen, Dan; Topp, Simon; Stensgaard, Anders
1996-01-01
Quantitative one-dimensional saturation profiles showing the distribution of water and oil in chalk core samples are calculated from NMR measurements utilizing a 1D CSI spectroscopy pulse sequence. Saturation profiles may be acquired under conditions of fluid flow through the sample. Results reveal...
Anti-cytokine therapies in T1D
DEFF Research Database (Denmark)
Nepom, Gerald T; Ehlers, Mario; Mandrup-Poulsen, Thomas
2013-01-01
Therapeutic targeting of proinflammatory cytokines is clinically beneficial in several autoimmune disorders. Several of these cytokines are directly implicated in the pathogenesis of type 1 diabetes, suggesting opportunities for design of clinical trials in type 1 diabetes that incorporate select...... suitable for modulating the immune response in T1D....
Non-cooperative Brownian donkeys: A solvable 1D model
Jiménez de Cisneros, B.; Reimann, P.; Parrondo, J. M. R.
2003-12-01
A paradigmatic 1D model for Brownian motion in a spatially symmetric, periodic system is tackled analytically. Upon application of an external static force F the system's response is an average current which is positive for F 0 (absolute negative mobility). Under suitable conditions, the system approaches 100% efficiency when working against the external force F.
Inverse parameter identification for a branching 1 D arterial network
CSIR Research Space (South Africa)
Bogaers, Alfred EJ
2012-07-01
Full Text Available In this paper we investigate the invertability of a branching 1 D arterial blood flow network. We limit our investigation to a single bifurcating vessel, where the material properties, unloaded areas and variables characterizing the input and output...
Pretko, Michael; Radzihovsky, Leo
2018-05-01
Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models. As a further consequence, the duality implies that fracton phases are relevant to the study of interacting topological crystalline insulators.
Cocco, Alberto; Masin, Sergio Cesare
2010-01-01
Participants estimated the imagined elongation of a spring while they were imagining that a load was stretching the spring. This elongation turned out to be a multiplicative function of spring length and load weight--a cognitive law analogous to Hooke's law of elasticity. Participants also estimated the total imagined elongation of springs joined…
Two-phase 1D+1D model of a DMFC: development and validation on extensive operating conditions range
Energy Technology Data Exchange (ETDEWEB)
Casalegno, A.; Marchesi, R.; Parenti, D. [Dipartimento di Energetica, Politecnico di Milano (Italy)
2008-02-15
A two-phase 1D+1D model of a direct methanol fuel cell (DMFC) is developed, considering overall mass balance, methanol transport in gas phase through anode diffusion layer, methanol and water crossover. The model is quantitatively validated on an extensive range of operating conditions, 24 polarisation curves. The model accurately reproduces DMFC performance in the validation range and, outside this, it is able to predict values under feasible operating conditions. Finally, the estimations of methanol crossover flux are qualitatively and quantitatively similar to experimental measures and the main local quantities' trends are coherent with results obtained with more complex models. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
Corrugated Membrane Nonlinear Deformation Process Calculation
Directory of Open Access Journals (Sweden)
A. S. Nikolaeva
2015-01-01
Full Text Available Elastic elements are widely used in instrumentation. They are used to create a particular interference between the parts, for accumulating mechanical energy, as the motion transmission elements, elastic supports, and sensing elements of measuring devices. Device reliability and quality depend on the calculation accuracy of the elastic elements. A corrugated membrane is rather common embodiment of the elastic element.The corrugated membrane properties depend largely on its profile i.e. a generatrix of the meridian surface.Unlike other types of pressure elastic members (bellows, tube spring, the elastic characteristics of which are close to linear, an elastic characteristic of the corrugated membrane (typical movement versus external load is nonlinear. Therefore, the corrugated membranes can be used to measure quantities, nonlinearly related to the pressure (e.g., aircraft air speed, its altitude, pipeline fluid or gas flow rate. Another feature of the corrugated membrane is that significant movements are possible within the elastic material state. However, a significant non-linearity of membrane characteristics leads to severe complicated calculation.This article is aimed at calculating the corrugated membrane to obtain the elastic characteristics and the deformed shape of the membrane meridian, as well as at investigating the processes of buckling. As the calculation model, a thin-walled axisymmetric shell rotation is assumed. The material properties are linearly elastic. We consider a corrugated membrane of sinusoidal profile. The membrane load is a uniform pressure.The algorithm for calculating the mathematical model of an axisymmetric corrugated membrane of constant thickness, based on the Reissner’s theory of elastic thin shells, was realized as the author's program in C language. To solve the nonlinear problem were used a method of changing the subspace of control parameters, developed by S.S., Gavriushin, and a parameter marching method
Autonomic Vertical Elasticity of Docker Containers with ElasticDocker
Al-Dhuraibi , Yahya; Paraiso , Fawaz; Djarallah , Nabil; Merle , Philippe
2017-01-01
International audience; Elasticity is the key feature of cloud computing to scale computing resources according to application workloads timely. In the literature as well as in industrial products, much attention was given to the elasticity of virtual machines, but much less to the elasticity of containers. However, containers are the new trend for packaging and deploying microservices-based applications. Moreover, most of approaches focus on horizontal elasticity, fewer works address vertica...
Stability and boundary stabilization of 1-D hyperbolic systems
Bastin, Georges
2016-01-01
This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary...
Nonlinear viscoelastic properties of tissue assessed by ultrasound.
Sinkus, Ralph; Bercoff, Jeremy; Tanter, Mickaël; Gennisson, Jean-Luc; El-Khoury, Carl; Servois, Vincent; Tardivon, Anne; Fink, Mathias
2006-11-01
A technique to assess qualitatively the presence of higher-order viscoelastic parameters is presented. Low-frequency, monochromatic elastic waves are emitted into the material via an external vibrator. The resulting steady-state motion is detected in real time via an ultra fast ultrasound system using classical, one-dimensional (1-D) ultrasound speckle correlation for motion estimation. Total data acquisition lasts only for about 250 ms. The spectrum of the temporal displacement data at each image point is used for analysis. The presence of nonlinear effects is detected by inspection of the ratio of the second harmonics amplitude with respect to the total amplitude summed up to the second harmonic. Results from a polyacrylamide-based phantom indicate a linear response (i.e., the absence of higher harmonics) for this type of material at 65 Hz mechanical vibration frequency and about 100 microm amplitude. A lesion, artificially created by injection of glutaraldehyde into a beef specimen, shows the development of higher harmonics at the location of injection as a function of time. The presence of upper harmonics is clearly evident at the location of a malignant lesion within a mastectomy.
Fluid friction and wall viscosity of the 1D blood flow model.
Wang, Xiao-Fei; Nishi, Shohei; Matsukawa, Mami; Ghigo, Arthur; Lagrée, Pierre-Yves; Fullana, Jose-Maria
2016-02-29
We study the behavior of the pulse waves of water into a flexible tube for application to blood flow simulations. In pulse waves both fluid friction and wall viscosity are damping factors, and difficult to evaluate separately. In this paper, the coefficients of fluid friction and wall viscosity are estimated by fitting a nonlinear 1D flow model to experimental data. In the experimental setup, a distensible tube is connected to a piston pump at one end and closed at another end. The pressure and wall displacements are measured simultaneously. A good agreement between model predictions and experiments was achieved. For amplitude decrease, the effect of wall viscosity on the pulse wave has been shown as important as that of fluid viscosity. Copyright © 2016 Elsevier Ltd. All rights reserved.
Robust 1D inversion and analysis of helicopter electromagnetic (HEM) data
DEFF Research Database (Denmark)
Tølbøll, R.J.; Christensen, N.B.
2006-01-01
but can resolve layer boundary to a depth of more than 100 m. Modeling experiments also show that the effect of altimeter errors on the inversion results is serious. We suggest a new interpretation scheme for HEM data founded solely on full nonlinear 1D inversion and providing layered-earth models...... of test flights were performed using a frequency-domain, helicopter-borne electromagnetic (HEM) system. We perform a theoretical examination of the resolution capabilities of the applied system. Quantitative model parameter analyses show that the system only weakly resolves conductive, near-surface layers...... supported by datamisfit parameters and a quantitative model-parameter analysis. The backbone of the scheme is the removal of cultural coupling effects followed by a multilayer inversion that in turn provides reliable starting models for a subsequent few-layer inversion. A new procedure for correlation...
Identification of elastic properties of composite plate
International Nuclear Information System (INIS)
Kovalovs, A; Rucevskis, S
2011-01-01
Composite laminates are used extensively in the aerospace industry, especially for the fabrication of high-performance structures. The determination of stiffness parameters for complex materials, such as fibre-reinforced composites, is much more complicated than for isotropic materials. A conventional way is testing the coupon specimens, which are manufactured by technology similar to that used for the real, large structures. When such a method is used, the question arises of whether the material properties obtained from the coupon tests are the same as those in the large structure. Therefore, the determination of actual material properties for composite laminates using non-destructive evaluation techniques has been widely investigated. A number of various non-destructive evaluation techniques have been proposed for determining the material properties of composite laminates. In the present study, attention is focused on the identification of the elastic properties of laminated plate using vibration test data. The problem associated with vibration testing is converting the measured modal frequencies to elastic constants. A standard method for solving this problem is the use of a numerical-experimental model and optimization techniques. The identification functional represents the gap between the numerical model response and the experimental one. This gap should be minimized, taking into account the side constraints on the design variables (elastic constants). The minimization problem is solved by using non-linear mathematical programming techniques and sensitivity analysis. The results obtained were verified by comparing the experimentally measured eigenfrequencies with the numerical ones obtained by FEM at the point of optima
Designing interactively with elastic splines
DEFF Research Database (Denmark)
Brander, David; Bærentzen, Jakob Andreas; Fisker, Ann-Sofie
2018-01-01
We present an algorithm for designing interactively with C1 elastic splines. The idea is to design the elastic spline using a C1 cubic polynomial spline where each polynomial segment is so close to satisfying the Euler-Lagrange equation for elastic curves that the visual difference becomes neglig...... negligible. Using a database of cubic Bézier curves we are able to interactively modify the cubic spline such that it remains visually close to an elastic spline....
Elastic properties of Ti-24Nb-4Zr-8Sn single crystals with bcc crystal structure
International Nuclear Information System (INIS)
Zhang, Y.W.; Li, S.J.; Obbard, E.G.; Wang, H.; Wang, S.C.; Hao, Y.L.; Yang, R.
2011-01-01
Research highlights: → The single crystals of Ti2448 alloy with the bcc crystal structure were prepared. → The elastic moduli and constants were measured by several resonant methods. → The crystal shows significant elastic asymmetry in tension and compression. → The crystal exhibits weak nonlinear elasticity with large elastic strain ∼2.5%. → The crystal has weak atomic interactions against crystal distortion to low symmetry. - Abstract: Single crystals of Ti2448 alloy (Ti-24Nb-4Zr-8Sn in wt.%) were grown successfully using an optical floating-zone furnace. Several kinds of resonant methods gave consistent Young's moduli of 27.1, 56.3 and 88.1 GPa and shear moduli of 34.8, 11.0 and 14.6 GPa for the , and oriented single crystals, and C 11 , C 12 and C 44 of 57.2, 36.1 and 35.9 GPa respectively. Uniaxial testing revealed asymmetrical elastic behaviors of the crystals: tension caused elastic softening with a large reversible strain of ∼4% and a stress plateau of ∼250 MPa, whereas compression resulted in gradual elastic stiffening with much smaller reversible strain. The crystals exhibited weak nonlinear elasticity with a large elastic strain of ∼2.5% and a high strength, approaching ∼20% and ∼30% of its ideal shear and ideal tensile strength respectively. The crystals showed linear elasticity with a small elastic strain of ∼1%. These elastic deformation characteristics have been interpreted in terms of weakened atomic interactions against crystal distortion to low crystal symmetry under external applied stresses. These results are consistent with the properties of polycrystalline Ti2448, including high strength, low elastic modulus, large recoverable strain and weak strengthening effect due to grain refinement.
Heterogenous Intertemporal Elasticity of Substitution and Relative Risk Aversion
DEFF Research Database (Denmark)
Khorunzhina, Natalia; Gayle, Wayne-Roy
This paper investigates the existence and degree of variation across house holds and over time in the intertemporal elasticity of substitution (IES) and the coefficient of relative risk aversion (RRA) that is generated by habit forming preferences. To do so, we develop a new nonlinear GMM estimator...... in food consumption. Using these estimates, we develop bounds for the expectation of the implied heterogenous intertemporal elasticity of substitution and relative risk aversion that account for measurement errors and compute asymptotically valid confidence intervals on these bounds. We find...
Homogenized Elastic Properties of Graphene for Small Deformations
Directory of Open Access Journals (Sweden)
Jurica Sorić
2013-09-01
Full Text Available In this paper, we provide the quantification of the linear and non-linear elastic mechanical properties of graphene based upon the judicious combination of molecular mechanics simulation results and homogenization methods. We clarify the influence on computed results by the main model features, such as specimen size, chirality of microstructure, the effect of chosen boundary conditions (imposed displacement versus force and the corresponding plane stress transformation. The proposed approach is capable of explaining the scatter of the results for computed stresses, energy and stiffness and provides the bounds on graphene elastic properties, which are quite important in modeling and simulation of the virtual experiments on graphene-based devices.
Analytical Solutions to Nonlinear Conservative Oscillator with Fifth-Order Nonlinearity
DEFF Research Database (Denmark)
Sfahania, M. G.; Ganji, S. S.; Barari, Amin
2010-01-01
This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presen...
Approximation by planar elastic curves
DEFF Research Database (Denmark)
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....
Ident 1D - a novel software tool for an easy identification of material constitutive parameters
International Nuclear Information System (INIS)
Le Ber, L.; Cotoni, V.; Nicola, L.; Sainte Catherine, C.
1998-01-01
Non-linear finite element computations make use of very sophisticated constitutive equations for description of materials behaviour. The first difficulty encountered by potential users is the gap existing between raw material characterisation on uniaxial specimens and the knowledge of the required equation's parameters. There are very few software for this particular task. IDENT 1D is a special software developed under Matlab language in our laboratory, which is able to provide a complete optimised parameters set for implemented models. The originality of IDENT 1D is that no initial estimation of the material parameters is requested of the user. Two main examples are described in this article: the Lemaitre and Chaboche creep law coupled with damage and a non unified cyclic law proposed by Contesti and Cailletaud with a separation of plastic and viscous strain terms which is called DDI model. For both laws, the identification method is completely described. Each method is then applied to a set of experimental data. In both cases, the results of the parameters identification show a very good agreement with experimental data. (authors)
Test of 1D carbon-carbon composite prototype tiles for the SPIDER diagnostic calorimeter
Serianni, G.; Pimazzoni, A.; Canton, A.; Palma, M. Dalla; Delogu, R.; Fasolo, D.; Franchin, L.; Pasqualotto, R.; Tollin, M.
2017-08-01
Additional heating will be provided to the thermonuclear fusion experiment ITER by injection of neutral beams from accelerated negative ions. In the SPIDER test facility, under construction at Consorzio RFX in Padova (Italy), the production of negative ions will be studied and optimised. To this purpose the STRIKE (Short-Time Retractable Instrumented Kalorimeter Experiment) diagnostic will be used to characterise the SPIDER beam during short operation (several seconds) and to verify if the beam meets the ITER requirement regarding the maximum allowed beam non-uniformity (below ±10%). The most important measurements performed by STRIKE are beam uniformity, beamlet divergence and stripping losses. The major components of STRIKE are 16 1D-CFC (Carbon matrix-Carbon Fibre reinforced Composite) tiles, observed at the rear side by a thermal camera. The requirements of the 1D CFC material include a large thermal conductivity along the tile thickness (at least 10 times larger than in the other directions); low specific heat and density; uniform parameters over the tile surface; capability to withstand localised heat loads resulting in steep temperature gradients. So 1D CFC is a very anisotropic and delicate material, not commercially available, and prototypes are being specifically realised. This contribution gives an overview of the tests performed on the CFC prototype tiles, aimed at verifying their thermal behaviour. The spatial uniformity of the parameters and the ratio between the thermal conductivities are assessed by means of a power laser at Consorzio RFX. Dedicated linear and non-linear simulations are carried out to interpret the experiments and to estimate the thermal conductivities; these simulations are described and a comparison of the experimental data with the simulation results is presented.
Sandia reactor kinetics codes: SAK and PK1D
International Nuclear Information System (INIS)
Pickard, P.S.; Odom, J.P.
1978-01-01
The Sandia Kinetics code (SAK) is a one-dimensional coupled thermal-neutronics transient analysis code for use in simulation of reactor transients. The time-dependent cross section routines allow arbitrary time-dependent changes in material properties. The one-dimensional heat transfer routines are for cylindrical geometry and allow arbitrary mesh structure, temperature-dependent thermal properties, radiation treatment, and coolant flow and heat-transfer properties at the surface of a fuel element. The Point Kinetics 1 Dimensional Heat Transfer Code (PK1D) solves the point kinetics equations and has essentially the same heat-transfer treatment as SAK. PK1D can address extended reactor transients with minimal computer execution time
Developing 1D nanostructure arrays for future nanophotonics
Directory of Open Access Journals (Sweden)
Cooke DG
2006-01-01
Full Text Available AbstractThere is intense and growing interest in one-dimensional (1-D nanostructures from the perspective of their synthesis and unique properties, especially with respect to their excellent optical response and an ability to form heterostructures. This review discusses alternative approaches to preparation and organization of such structures, and their potential properties. In particular, molecular-scale printing is highlighted as a method for creating organized pre-cursor structure for locating nanowires, as well as vapor–liquid–solid (VLS templated growth using nano-channel alumina (NCA, and deposition of 1-D structures with glancing angle deposition (GLAD. As regards novel optical properties, we discuss as an example, finite size photonic crystal cavity structures formed from such nanostructure arrays possessing highQand small mode volume, and being ideal for developing future nanolasers.
Elasticity in Elastics-An in-vitro study.
Kamisetty, Supradeep Kumar; Nimagadda, Chakrapani; Begam, Madhoom Ponnachi; Nalamotu, Raghuveer; Srivastav, Trilok; Gs, Shwetha
2014-04-01
Orthodontic tooth movement results from application of forces to teeth. Elastics in orthodontics have been used both intra-orally and extra- orally to a great effect. Their use, combined with good patient co-operation provides the clinician with the ability to correct both anteroposterior and vertical discrepancies. Force decay over a period of time is a major problem in the clinical usage of latex elastics and synthetic elastomers. This loss of force makes it difficult for the clinician to determine the actual force transmitted to the dentition. It's the intent of the clinician to maintain optimal force values over desired period of time. The majority of the orthodontic elastics on the market are latex elastics. Since the early 1990s, synthetic products have been offered in the market for latex-sensitive patients and are sold as nonlatex elastics. There is limited information on the risk that latex elastics may pose to patients. Some have estimated that 0.12-6% of the general population and 6.2% of dental professionals have hypersensitivity to latex protein. There are some reported cases of adverse reactions to latex in the orthodontic population but these are very limited to date. Although the risk is not yet clear, it would still be inadvisable to prescribe latex elastics to a patient with a known latex allergy. To compare the in-vitro performance of latex and non latex elastics. Samples of 0.25 inch, latex and non latex elastics (light, medium, heavy elastics) were obtained from three manufacturers (Forestadent, GAC, Glenroe) and a sample size of ten elastics per group was tested. The properties tested included cross sectional area, internal diameter, initial force generated by the elastics, breaking force and the force relaxation for the different types of elastics. Force relaxation testing involved stretching the elastics to three times marketed internal diameter (19.05 mm) and measuring force level at intervals over a period of 48 hours. The data were
Enhancing Thermoelectric Performance Using Nonlinear Transport Effects
Jiang, Jian-Hua; Imry, Yoseph
2017-06-01
We study nonlinear transport effects on the maximum efficiency and power for both inelastic and elastic thermoelectric generators. The former device refers to phonon-assisted hopping in double quantum dots, while the latter device is represented by elastic tunneling through a single quantum dot. We find that nonlinear thermoelectric transport can lead to enhanced efficiency and power for both types of devices. A comprehensive survey of various quantum-dot energy, temperature, and parasitic heat conduction reveals that the nonlinear transport-induced improvements of the maximum efficiency and power are overall much more significant for inelastic devices than for elastic devices, even for temperature biases as small as Th=1.2 Tc (Th and Tc are the temperatures of the hot and cold reservoirs, respectively). The underlying mechanism is revealed as due to the fact that, unlike the Fermi distribution, the Bose distribution is not bounded when the temperature bias increases. A large flux density of absorbed phonons leads to a great enhancement of the electrical current, output power, and energy efficiency, dominating over the concurrent increase of the parasitic heat current. Our study reveals that nonlinear transport effects can be a useful tool for improving thermoelectric performance.
Finsler Geometry of Nonlinear Elastic Solids with Internal Structure
2017-01-01
the locally relaxed intermediate state of the crystal, following earlier classical differential–geometric treatments by the Japanese school [24]. Kondo...Remark 8. Components of F and f are defined in an identical fashion by Bejancu [12]. Tensor definitions (2.39) and (2.40) potentially differ in two ways...transformations (i.e., push-forwards and pull-backs) of vectors and tensors to be calculated in a completely analogous fashion to transformations between
Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
2016-08-03
called a nanopteron, is not only motivated theoretically and numerically, but are also visualized experimentally by means of a laser Doppler vibrometer...velocity, which clearly follow the prin- cipal solitary wave (highlighted in red color ). It should be noted that the velocities involved in the
Development of 1D Liner Compression Code for IDL
Shimazu, Akihisa; Slough, John; Pancotti, Anthony
2015-11-01
A 1D liner compression code is developed to model liner implosion dynamics in the Inductively Driven Liner Experiment (IDL) where FRC plasmoid is compressed via inductively-driven metal liners. The driver circuit, magnetic field, joule heating, and liner dynamics calculations are performed at each time step in sequence to couple these effects in the code. To obtain more realistic magnetic field results for a given drive coil geometry, 2D and 3D effects are incorporated into the 1D field calculation through use of correction factor table lookup approach. Commercial low-frequency electromagnetic fields solver, ANSYS Maxwell 3D, is used to solve the magnetic field profile for static liner condition at various liner radius in order to derive correction factors for the 1D field calculation in the code. The liner dynamics results from the code is verified to be in good agreement with the results from commercial explicit dynamics solver, ANSYS Explicit Dynamics, and previous liner experiment. The developed code is used to optimize the capacitor bank and driver coil design for better energy transfer and coupling. FRC gain calculations are also performed using the liner compression data from the code for the conceptual design of the reactor sized system for fusion energy gains.
Applications of AMPS-1D for solar cell simulation
Zhu, Hong; Kalkan, Ali Kaan; Hou, Jingya; Fonash, Stephen J.
1999-03-01
The AMPS-1D PC computer program is now used by over 70 groups world-wide for detector and solar cell analysis. It has proved to be a very powerful tool in understanding device operation and physics for single crystal, poly-crystalline and amorphous structures. For example, AMPS-1D has been successful in explaining the "red kink" [1] and the "transient effect" in CdS/CIGS poly-crystalline solar cells. It has been used to show that thin film poly-Si structures, with reasonable light trapping, are capable of competitive solar cell conversion efficiencies. In the case of a-Si:H structures, it has been used, for example, to settle the discrepancies in bandgap measurement, to predict the effective QE>1 phenomenon later seen in these materials [2], to determine the relative roles of interface and bulk properties, and to point the direction toward 16% triple junction structures. In general AMPS-1D is used for cell and detector design, material parameter sensitivity studies, and parameter extraction. Recently we have shown that it can be used to determine optimum structure and light and voltage biasing conditions in the material parameter extraction function. Information on AMPS can be found at www.psu.edu/dept/AMPS/amps_web/AMPS.html and at other web sites set up by user groups.
Coupling of Nod1D and HOTCHANNEL: static case
International Nuclear Information System (INIS)
Gomez T, A.M.; Ovando C, R.
2003-01-01
In this work the joining of the programs Nod1D and HOTCHANNEL, developed in the National Polytechnic Institute (IPN) and in the Electrical Research Institute (IIE) respectively is described. The first one allows to study the neutronic of a nuclear reactor and the second one allows to carry out the analysis of hot channel of a Boiling Water Reactor (BWR). Nod1 D is a program that it solves by nodal methods type finite element those diffusion equations in multigroup, and it is the static part of Nod Kin that it solves the diffusion equation in their time dependent part. For another side HOTCHANNEL is based on a mathematical model constituted by four conservation equations (two of mass conservation, one of motion quantity and one of energy), which are solved applying one discretization in implicit finite differences. Both programs have been verified in independent form using diverse test problems. In this work the modifications that were necessary to carry out to both for obtaining a coupled program that it provides the axial distribution of the neutron flux, the power, the burnup and the void fraction, among others parameters as much as neutronic as thermal hydraulics are described. Those are also mentioned limitations, advantages and disadvantages of the final product to which has been designated Nod1 D-HotChn. Diverse results for the Cycle 1 of the Laguna Verde Unit 1 reactor of the Nucleo electric central comparing them with those obtained directly with the CoreMasterPresto code are provided. (Author)
MARG1D: One dimensional outer region matching data code
International Nuclear Information System (INIS)
Tokuda, Shinji; Watanabe, Tomoko.
1995-08-01
A code MARG1D has been developed which computes outer region matching data of the one dimensional Newcomb equation. Matching data play an important role in the resistive (and non ideal) Magneto-hydrodynamic (MHD) stability analysis in a tokamak plasma. The MARG1D code computes matching data by using the boundary value method or by the eigenvalue method. Variational principles are derived for the problems to be solved and a finite element method is applied. Except for the case of marginal stability, the eigenvalue method is equivalent to the boundary value method. However, the eigenvalue method has the several advantages: it is a new method of ideal MHD stability analysis for which the marginally stable state can be identified, and it guarantees numerical stability in computing matching data close to marginal stability. We perform detailed numerical experiments for a model equation with analytical solutions and for the Newcomb equation in the m=1 mode theory. Numerical experiments show that MARG1D code gives the matching data with numerical stability and high accuracy. (author)
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...
A programmable nonlinear acoustic metamaterial
Directory of Open Access Journals (Sweden)
Tianzhi Yang
2017-09-01
Full Text Available Acoustic metamaterials with specifically designed lattices can manipulate acoustic/elastic waves in unprecedented ways. Whereas there are many studies that focus on passive linear lattice, with non-reconfigurable structures. In this letter, we present the design, theory and experimental demonstration of an active nonlinear acoustic metamaterial, the dynamic properties of which can be modified instantaneously with reversibility. By incorporating active and nonlinear elements in a single unit cell, a real-time tunability and switchability of the band gap is achieved. In addition, we demonstrate a dynamic “editing” capability for shaping transmission spectra, which can be used to create the desired band gap and resonance. This feature is impossible to achieve in passive metamaterials. These advantages demonstrate the versatility of the proposed device, paving the way toward smart acoustic devices, such as logic elements, diode and transistor.
International Nuclear Information System (INIS)
Vavra, G.
1978-01-01
Considered are the limit and the intermediate values of the Young modulus E, modulus of shear G and of linear modulus of compression K obtainable at various temperatures (4.2 to 1133 K) for single crystals of α-zirconium. Determined and presented are the corrected isotropic elasticity characteristics of E, G, K over the above range of temperatures of textured and non-textured α-Zr
Energy Technology Data Exchange (ETDEWEB)
Aprile, E; Cantale, G; Degli-Agosti, S; Hausammann, R; Heer, E; Hess, R; Lechanoine-LeLuc, C; Leo, W; Morenzoni, S; Onel, Y [Geneva Univ. (Switzerland). Dept. de Physique Nucleaire et Corpusculaire
1983-01-01
The aim of the elastic pp experimental program at SIN was to measure enough spin dependent parameters in order to do a direct experimental reconstruction of the elastic scattering amplitudes at a few energies between 400 and 600 MeV and at several angles between 38/sup 0/ cm and 90/sup 0/ cm. This reconstruction was not possible until recently due to lack of experimental data. Information instead has come mainly from phase shift analysis (PSA). The only way to extract the elastic scattering amplitudes without any hypotheses except those of basic symmetries, is to measure a sufficient set of spin dependent parameters at a given angle and energy. With this in view, the authors have measured at 448, 494, 515, 536 and 579 MeV, the polarization, the spin correlation parameters Asub(00nn), Asub(00ss), Asub(00kk), Asub(00ks), the 2-spin parameters Dsub(n0n0), Ksub(n00n), Dsub(s'0s0), Dsub(s'0k0) and the 3-spin parameters Msub(s'0sn), Msub(s'0kn) between 34/sup 0/ cm and 118/sup 0/ cm. A few of these parameters have also been measured at 560 and 470 MeV and at a few energies below 448 MeV. The indices refer to the polarization orientation of the scattered, recoil, beam and target particle respectively.
Some Differential Geometric Relations in the Elastic Shell
Directory of Open Access Journals (Sweden)
Xiaoqin Shen
2016-01-01
Full Text Available The theory of the elastic shells is one of the most important parts of the theory of solid mechanics. The elastic shell can be described with its middle surface; that is, the three-dimensional elastic shell with equal thickness comprises a series of overlying surfaces like middle surface. In this paper, the differential geometric relations between elastic shell and its middle surface are provided under the curvilinear coordinate systems, which are very important for forming two-dimensional linear and nonlinear elastic shell models. Concretely, the metric tensors, the determinant of metric matrix field, the Christoffel symbols, and Riemann tensors on the three-dimensional elasticity are expressed by those on the two-dimensional middle surface, which are featured by the asymptotic expressions with respect to the variable in the direction of thickness of the shell. Thus, the novelty of this work is that we can further split three-dimensional mechanics equations into two-dimensional variation problems. Finally, two kinds of special shells, hemispherical shell and semicylindrical shell, are provided as the examples.
Coupling of Nod1D and HOTCHANNEL: static case; Acoplamiento de Nod1D y HOTCHANNEL: caso estatico
Energy Technology Data Exchange (ETDEWEB)
Gomez T, A.M. [IPN-ESFM, 07738 Mexico D.F. (Mexico); Ovando C, R. [IIE-Gcia. de Energia Nuclear, Cuernavaca, Morelos (Mexico)]. e-mail: rovando@iie.org.mx
2003-07-01
In this work the joining of the programs Nod1D and HOTCHANNEL, developed in the National Polytechnic Institute (IPN) and in the Electrical Research Institute (IIE) respectively is described. The first one allows to study the neutronic of a nuclear reactor and the second one allows to carry out the analysis of hot channel of a Boiling Water Reactor (BWR). Nod1 D is a program that it solves by nodal methods type finite element those diffusion equations in multigroup, and it is the static part of Nod Kin that it solves the diffusion equation in their time dependent part. For another side HOTCHANNEL is based on a mathematical model constituted by four conservation equations (two of mass conservation, one of motion quantity and one of energy), which are solved applying one discretization in implicit finite differences. Both programs have been verified in independent form using diverse test problems. In this work the modifications that were necessary to carry out to both for obtaining a coupled program that it provides the axial distribution of the neutron flux, the power, the burnup and the void fraction, among others parameters as much as neutronic as thermal hydraulics are described. Those are also mentioned limitations, advantages and disadvantages of the final product to which has been designated Nod1 D-HotChn. Diverse results for the Cycle 1 of the Laguna Verde Unit 1 reactor of the Nucleo electric central comparing them with those obtained directly with the CoreMasterPresto code are provided. (Author)
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...
Cell Migration in 1D and 2D Nanofiber Microenvironments.
Estabridis, Horacio M; Jana, Aniket; Nain, Amrinder; Odde, David J
2018-03-01
Understanding how cells migrate in fibrous environments is important in wound healing, immune function, and cancer progression. A key question is how fiber orientation and network geometry influence cell movement. Here we describe a quantitative, modeling-based approach toward identifying the mechanisms by which cells migrate in fibrous geometries having well controlled orientation. Specifically, U251 glioblastoma cells were seeded onto non-electrospinning Spinneret based tunable engineering parameters fiber substrates that consist of networks of suspended 400 nm diameter nanofibers. Cells were classified based on the local fiber geometry and cell migration dynamics observed by light microscopy. Cells were found in three distinct geometries: adhering two a single fiber, adhering to two parallel fibers, and adhering to a network of orthogonal fibers. Cells adhering to a single fiber or two parallel fibers can only move in one dimension along the fiber axis, whereas cells on a network of orthogonal fibers can move in two dimensions. We found that cells move faster and more persistently in 1D geometries than in 2D, with cell migration being faster on parallel fibers than on single fibers. To explain these behaviors mechanistically, we simulated cell migration in the three different geometries using a motor-clutch based model for cell traction forces. Using nearly identical parameter sets for each of the three cases, we found that the simulated cells naturally replicated the reduced migration in 2D relative to 1D geometries. In addition, the modestly faster 1D migration on parallel fibers relative to single fibers was captured using a correspondingly modest increase in the number of clutches to reflect increased surface area of adhesion on parallel fibers. Overall, the integrated modeling and experimental analysis shows that cell migration in response to varying fibrous geometries can be explained by a simple mechanical readout of geometry via a motor-clutch mechanism.
D1/D5 systems in N=4 string theories
International Nuclear Information System (INIS)
Gava, Edi; Hammou, Amine B.; Morales, Jose F.; Narain, Kumar S.
2001-01-01
We propose CFT descriptions of the D1/D5 system in a class of freely acting Z 2 orbifolds/orientifolds of type IIB theory, with sixteen unbroken supercharges. The CFTs describing D1/D5 systems involve N=(4,4) or N=(4,0) sigma models on (R 3 xS 1 xT 4 x(T 4 ) N /S N )/Z 2 , where the action of Z 2 is diagonal and its precise nature depends on the model. We also discuss D1(D5)-brane states carrying non-trivial Kaluza-Klein charges, which correspond to excitations of two-dimensional CFTs of the type (R 3 xS 1 xT 4 ) N /S N xZ 2 N . The resulting multiplicities for two-charge bound states are shown to agree with the predictions of U-duality. We raise a puzzle concerning the multiplicities of three-charge systems, which is generically present in all vacuum configurations with sixteen unbroken supercharges studied so far, including the more familiar type IIB on K3 case: the constraints put on BPS counting formulae by U-duality are apparently in contradiction with any CFT interpretation. We argue that the presence of RR backgrounds appearing in the symmetric product CFT may provide a resolution of this puzzle. Finally, we show that the whole tower of D-instanton corrections to certain 'BPS saturated couplings' in the low energy effective actions match with the corresponding one-loop threshold corrections on the dual fundamental string side
1D energy transport in a strongly scattering laboratory model
International Nuclear Information System (INIS)
Wijk, Kasper van; Scales, John A.; Haney, Matthew
2004-01-01
Radiative transfer (RT) theory is often invoked to describe energy propagation in strongly scattering media. Fitting RT to measured wave field intensities is rather different at late times, when the transport is diffusive, than at intermediate times (around one extinction mean free time), when ballistic and diffusive behavior coexist. While there are many examples of late-time RT fits, we describe ultrasonic multiple scattering measurements with RT over the entire range of times--from ballistic to diffusive. In addition to allowing us to retrieve the scattering and absorption mean free paths independently, our results also support theoretical predictions in 1D that suggest an intermediate regime of diffusive (nonlocalized) behavior
ESO science data product standard for 1D spectral products
Micol, Alberto; Arnaboldi, Magda; Delmotte, Nausicaa A. R.; Mascetti, Laura; Retzlaff, Joerg
2016-07-01
The ESO Phase 3 process allows the upload, validation, storage, and publication of reduced data through the ESO Science Archive Facility. Since its introduction, 2 million data products have been archived and published; 80% of them are one-dimensional extracted and calibrated spectra. Central to Phase3 is the ESO science data product standard that defines metadata and data format of any product. This contribution describes the ESO data standard for 1d-spectra, its adoption by the reduction pipelines of selected instrument modes for in-house generation of reduced spectra, the enhanced archive legacy value. Archive usage statistics are provided.
1D-transport properties of single superconducting lead nanowires
DEFF Research Database (Denmark)
Michotte, S.; Mátéfi-Tempfli, Stefan; Piraux, L.
2003-01-01
of the nanowire is small enough to ensure a 1D superconducting regime in a wide temperature range below T. The non-zero resistance in the superconducting state and its variation caused by fluctuations of the superconducting order parameter were measured versus temperature, magnetic field, and applied DC current......We report on the transport properties of single superconducting lead nanowires grown by an electrodeposition technique, embedded in a nanoporous track-etched polymer membrane. The nanowires are granular, have uniform diameter of ̃40 nm and a very large aspect ratio (̃500). The diameter...
1-D blood flow modelling in a running human body.
Szabó, Viktor; Halász, Gábor
2017-07-01
In this paper an attempt was made to simulate blood flow in a mobile human arterial network, specifically, in a running human subject. In order to simulate the effect of motion, a previously published immobile 1-D model was modified by including an inertial force term into the momentum equation. To calculate inertial force, gait analysis was performed at different levels of speed. Our results show that motion has a significant effect on the amplitudes of the blood pressure and flow rate but the average values are not effected significantly.
1D equation for toroidal momentum transport in a tokamak
International Nuclear Information System (INIS)
Rozhansky, V A; Senichenkov, I Yu
2010-01-01
A 1D equation for toroidal momentum transport is derived for a given set of turbulent transport coefficients. The averaging is performed taking account of the poloidal variation of the toroidal fluxes and is based on the ambipolar condition of the zero net radial current through the flux surface. It is demonstrated that taking account of the Pfirsch-Schlueter fluxes leads to a torque in the toroidal direction which is proportional to the gradient of the ion temperature. This effect is new and has not been discussed before. The boundary condition at the separatrix, which is based on the results of the 2D simulations of the edge plasma, is formulated.
1D models for condensation induced water hammer in pipelines
International Nuclear Information System (INIS)
Bloemeling, Frank; Neuhas, Thorsten; Schaffrath, Andreas
2013-01-01
Condensation induced water hammer (CIWH) are caused by contact of steam and subcooled water. Thus, modeling the direct contact condensation is a crucial step towards the simulation of condensation induced water hammer with 1D pressure surge codes. Therefore, also the TUeV NORD SysTec GmbH and Co. KG inhouse pressure surge code DYVRO has been equipped with a new contact condensation model. The validation of DYVRO against an experiment dealing with CIWH is presented in this contribution. (orig.)
1D models for condensation induced water hammer in pipelines
Energy Technology Data Exchange (ETDEWEB)
Bloemeling, Frank; Neuhas, Thorsten; Schaffrath, Andreas [TUEV NORD SysTec GmbH und Co. KG, Hamburg (Germany)
2013-03-15
Condensation induced water hammer (CIWH) are caused by contact of steam and subcooled water. Thus, modeling the direct contact condensation is a crucial step towards the simulation of condensation induced water hammer with 1D pressure surge codes. Therefore, also the TUeV NORD SysTec GmbH and Co. KG inhouse pressure surge code DYVRO has been equipped with a new contact condensation model. The validation of DYVRO against an experiment dealing with CIWH is presented in this contribution. (orig.)
Form finding in elastic gridshells
Baek, Changyeob; Sageman-Furnas, Andrew O.; Jawed, Mohammad K.; Reis, Pedro M.
2018-01-01
Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.
Nonlinear morphoelastic plates II: Exodus to buckled states
McMahon, J.
2011-05-11
Morphoelasticity is the theory of growing elastic materials. The theory is based on the multiplicative decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing non-linear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed. © SAGE Publications 2011.
Nonlinear morphoelastic plates II: Exodus to buckled states
McMahon, J.; Goriely, A.; Tabor, M.
2011-01-01
Morphoelasticity is the theory of growing elastic materials. The theory is based on the multiplicative decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing non-linear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed. © SAGE Publications 2011.
Nonlinear buckling of woven fabrics, part I: elastic and non-elastic cases
CSIR Research Space (South Africa)
Anandjiwala, RD
2005-01-01
Full Text Available stream_source_info Anandjiwala_2006_d.pdf.txt stream_content_type text/plain stream_size 10 Content-Encoding ISO-8859-1 stream_name Anandjiwala_2006_d.pdf.txt Content-Type text/plain; charset=ISO-8859-1 ...
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
Elastic and viscoplastic properties
International Nuclear Information System (INIS)
Lebensohn, R.A.
2015-01-01
In this chapter, we review crystal elasticity and plasticity-based self-consistent theories and apply them to the determination of the effective response of polycrystalline aggregates. These mean-field formulations, which enable the prediction of the mechanical behaviour of polycrystalline aggregates based on the heterogeneous and/or directional properties of their constituent single crystal grains and phases, are ideal tools to establish relationships between microstructure and properties of these materials, ubiquitous among fuels and structural materials for nuclear systems. (author)
Natural Frequencies and Mode Shapes of a Nonlinear, Uniform Cantilevered Beam
National Research Council Canada - National Science Library
Marquez-Chisolm, Daniel J
2006-01-01
A series of experiments in 1975, referred to as the Princeton Beam Experiments, were performed to measure natural frequencies and create a nonlinear elastic deformation model to improve helicopter main beam designs...
Nonlinear analysis and enhancement of wing-based piezoaeroelastic energy harvesters
Abdelkefi, Abdessattar; Ghommem, Mehdi; Nuhait, Abdullah O.; Hajj, M. R.
2014-01-01
We investigate the level of harvested power from aeroelastic vibrations for an elastically mounted wing supported by nonlinear springs. The energy is harvested by attaching a piezoelectric transducer to the plunge degree of freedom. The considered
Czech Academy of Sciences Publication Activity Database
Dos Santos, S.; Dvořáková, Zuzana; Caliez, M.; Převorovský, Zdeněk
2015-01-01
Roč. 138, č. 3 (2015) ISSN 0001-4966 Institutional support: RVO:61388998 Keywords : acousto-mechanical characterization of skin aging * nonlinear elastic wave spectroscopy (NEWS) * PM-space statistical approach Subject RIV: BI - Acoustics
Fundamental topics for thermo-elastic stress analyses
International Nuclear Information System (INIS)
Biermann, M.
1989-01-01
This paper delivers a consistent collection of theoretical fundamentals needed to perform rather sound experimental stress analyses on thermo-elastic materials. An exposition of important concepts of symmetry and so-called peer groups, yielding the very base for a rational description of materials, goes ahead and is followed by an introduction to the constitutive theory of simple materials. Neat distinction is made between stress contributions determined by deformational and thermal impressions, on the one part, and stress constraints not accessible to strain gauging, on the other part. The mathematical formalism required for establishing constitutive equations is coherently developed from scratch and aided, albeit not subrogated, by intuition. The main intention goes to turning some of the recent advances in the nonlinear field theories of thermomechanics to practical account. A full success therein, obviously, results under the restriction to thermo-elasticity. In adverting to more particular subjects, the elementary static effects of nonlinear isotropic elasticity are pointed out. Due allowance is made for thermal effects likely to occur in heat conducting materials also beyond the isothermal or isentropic limit cases. Linearization of the constitutive equations for anisotropic thermo-elastic materials is then shown to entail the formulas of the classical theory. (orig./MM) [de
Design of a nonlinear torsional vibration absorber
Tahir, Ammaar Bin
larger than that in the latter. A nonlinear absorber design has been proposed comprising of thin beams as elastic elements. The geometric configuration of the proposed design has been shown to provide cubic stiffness nonlinearity in torsion. The values of design variables, namely the strength of nonlinearity alpha and torsional stiffness kalpha, were obtained by optimizing dimensions and material properties of the beams for a maximum vibration energy dissipation in the nonlinear absorber. A parametric study has also been conducted to analyze the effect of the magnitude of excitation provided to the system on the performance of a nonlinear absorber. It has been shown that the nonlinear absorber turns out to be more effective in terms of energy dissipation as compared to a linear absorber with an increase in the excitation level applied to the system.
Elastic-plastic dynamic analysis of a reactor building
International Nuclear Information System (INIS)
Umemura, Hajime; Tanaka, Hiroshi.
1976-01-01
The basic characteristics of the dynamic response of a reactor building to severe earthquake ground motion are very important for the evaluation of the safety of nuclear plant systems. A computer program for elastic-plastic dynamic analysis of reactor buildings using lumped mass models is developed. The box and cylindrical walls of boiling water reactor buildings are treated as vertical beams. The nonlinear moment-rotation and shear force-shear deformation relationships of walls are based in part upon the experiments of prototype structures. The geometrical non-linearity of the soil rocking spring due to foundation separation is also considered. The nonlinear equation of motion is expressed in incremental form using tangent stiffness matrices, following the algorithm developed by E.L. Wilson et al. The damping matrix in the equation is formulated as the combination of the energy evaluation method and Penzien-Wilson's approach to accomodate the different characteristics of soil and building damping. The analysis examples and the comparison of elastic and elastic-plastic analysis results are presented. (auth.)
Blood flow quantification using 1D CFD parameter identification
Brosig, Richard; Kowarschik, Markus; Maday, Peter; Katouzian, Amin; Demirci, Stefanie; Navab, Nassir
2014-03-01
Patient-specific measurements of cerebral blood flow provide valuable diagnostic information concerning cerebrovascular diseases rather than visually driven qualitative evaluation. In this paper, we present a quantitative method to estimate blood flow parameters with high temporal resolution from digital subtraction angiography (DSA) image sequences. Using a 3D DSA dataset and a 2D+t DSA sequence, the proposed algorithm employs a 1D Computational Fluid Dynamics (CFD) model for estimation of time-dependent flow values along a cerebral vessel, combined with an additional Advection Diffusion Equation (ADE) for contrast agent propagation. The CFD system, followed by the ADE, is solved with a finite volume approximation, which ensures the conservation of mass. Instead of defining a new imaging protocol to obtain relevant data, our cost function optimizes the bolus arrival time (BAT) of the contrast agent in 2D+t DSA sequences. The visual determination of BAT is common clinical practice and can be easily derived from and be compared to values, generated by a 1D-CFD simulation. Using this strategy, we ensure that our proposed method fits best to clinical practice and does not require any changes to the medical work flow. Synthetic experiments show that the recovered flow estimates match the ground truth values with less than 12% error in the mean flow rates.
Modeling atrazine transport in soil columns with HYDRUS-1D
Directory of Open Access Journals (Sweden)
John Leju Celestino Ladu
2011-09-01
Full Text Available Both physical and chemical processes affect the fate and transport of herbicides. It is useful to simulate these processes with computer programs to predict solute movement. Simulations were run with HYDRUS-1D to identify the sorption and degradation parameters of atrazine through calibration from the breakthrough curves (BTCs. Data from undisturbed and disturbed soil column experiments were compared and analyzed using the dual-porosity model. The study results show that the values of dispersivity are slightly lower in disturbed columns, suggesting that the more heterogeneous the structure is, the higher the dispersivity. Sorption parameters also show slight variability, which is attributed to the differences in soil properties, experimental conditions and methods, or other ecological factors. For both of the columns, the degradation rates were similar. Potassium bromide was used as a conservative non-reactive tracer to characterize the water movement in columns. Atrazine BTCs exhibited significant tailing and asymmetry, indicating non-equilibrium sorption during solute transport. The dual-porosity model was verified to best fit the BTCs of the column experiments. Greater or lesser concentration of atrazine spreading to the bottom of the columns indicated risk of groundwater contamination. Overall, HYDRUS-1D successfully simulated the atrazine transport in soil columns.
Analytic study of 1D diffusive relativistic shock acceleration
Energy Technology Data Exchange (ETDEWEB)
Keshet, Uri, E-mail: ukeshet@bgu.ac.il [Physics Department, Ben-Gurion University of the Negev, POB 653, Be' er-Sheva 84105 (Israel)
2017-10-01
Diffusive shock acceleration (DSA) by relativistic shocks is thought to generate the dN / dE ∝ E{sup −p} spectra of charged particles in various astronomical relativistic flows. We show that for test particles in one dimension (1D), p {sup −1}=1−ln[γ{sub d}(1+β{sub d})]/ln[γ{sub u}(1+β{sub u})], where β{sub u}(β{sub d}) is the upstream (downstream) normalized velocity, and γ is the respective Lorentz factor. This analytically captures the main properties of relativistic DSA in higher dimensions, with no assumptions on the diffusion mechanism. Unlike 2D and 3D, here the spectrum is sensitive to the equation of state even in the ultra-relativistic limit, and (for a J(üttner-Synge equation of state) noticeably hardens with increasing 1<γ{sub u}<57, before logarithmically converging back to p (γ{sub u→∞})=2. The 1D spectrum is sensitive to drifts, but only in the downstream, and not in the ultra-relativistic limit.
A Framework for Low-Communication 1-D FFT
Directory of Open Access Journals (Sweden)
Ping Tak Peter Tang
2013-01-01
Full Text Available In high-performance computing on distributed-memory systems, communication often represents a significant part of the overall execution time. The relative cost of communication will certainly continue to rise as compute-density growth follows the current technology and industry trends. Design of lower-communication alternatives to fundamental computational algorithms has become an important field of research. For distributed 1-D FFT, communication cost has hitherto remained high as all industry-standard implementations perform three all-to-all internode data exchanges (also called global transposes. These communication steps indeed dominate execution time. In this paper, we present a mathematical framework from which many single-all-to-all and easy-to-implement 1-D FFT algorithms can be derived. For large-scale problems, our implementation can be twice as fast as leading FFT libraries on state-of-the-art computer clusters. Moreover, our framework allows tradeoff between accuracy and performance, further boosting performance if reduced accuracy is acceptable.
Nonlinear continuum mechanics and large inelastic deformations
Dimitrienko, Yuriy I
2010-01-01
This book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics - kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead t...
Mathematical methods in elasticity imaging
Ammari, Habib; Garnier, Josselin; Kang, Hyeonbae; Lee, Hyundae; 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 uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic...
Energy Technology Data Exchange (ETDEWEB)
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.
International Nuclear Information System (INIS)
Mermaz, M.C.
1984-01-01
Diffraction and refraction play an important role in particle elastic scattering. The optical model treats correctly and simultaneously both phenomena but without disentangling them. Semi-classical discussions in terms of trajectories emphasize the refractive aspect due to the real part of the optical potential. The separation due to to R.C. Fuller of the quantal cross section into two components coming from opposite side of the target nucleus allows to understand better the refractive phenomenon and the origin of the observed oscillations in the elastic scattering angular distributions. We shall see that the real part of the potential is responsible of a Coulomb and a nuclear rainbow which allows to determine better the nuclear potential in the interior region near the nuclear surface since the volume absorption eliminates any effect of the real part of the potential for the internal partial scattering waves. Resonance phenomena seen in heavy ion scattering will be discussed in terms of optical model potential and Regge pole analysis. Compound nucleus resonances or quasi-molecular states can be indeed the more correct and fundamental alternative
Design guidance for elastic followup
International Nuclear Information System (INIS)
Naugle, F.V.
1983-01-01
The basic mechanism of elastic followup is discussed in relation to piping design. It is shown how mechanistic insight gained from solutions for a two-bar problem can be used to identify dominant design parameters and to determine appropriate modifications where elastic followup is a potential problem. It is generally recognized that quantitative criteria are needed for elastic followup in the creep range where badly unbalanced lines can pose potential problems. Approaches for criteria development are discussed
Income Elasticity of Environmental Amenities
Daniel Miles; Andrés Pereyra; Máximo Rossi
2000-01-01
In this paper we are concerned with the estimation of income elasticities of environmental amenities. The novelty is the application of econometric methods that take into account the problem of measurement errors when estimating these elasticities, which are common in microeconomic data and are not usually considered in the applied literature related with this issue. Our aim is to discuss whether the measurement error has signi…cant e¤ects on the elasticities. Data from the Expenditure Budget...
International Nuclear Information System (INIS)
Magomedov, A.M.
1986-01-01
Rates of propagation of longitudinal and transverse acoustic waves in samples as well as density of Tl, Pb, Sn, Bi, Cd, Zn and their binary alloys with indium are determined. The results obtained are used for calculation of elasticity constants of these materials. It is stated that concentration dependences of elasticity constants for indium alloys have non-linear character; negative deflection from the additive line is observed
International Nuclear Information System (INIS)
Khidirov, I.; Khajdarov, T.
1995-01-01
Elasticity characteristics of cubic and tetragonal phases of titanium nitride in the homogeneity range were studied for the first time by ultrasonic resonance method. It is established that the Young modulus, the shift and volume module of cubic titanium nitride elasticity in the homogeneity range change nonlinearly with decrease in nitrogen concentration and correlate with concentration dependences of other physical properties.15 refs., 2 figs
System Reduction in Nonlinear Multibody Dynamics of Wind Turbines
DEFF Research Database (Denmark)
Holm-Jørgensen, Kristian; Nielsen, Søren R.K.; Rubak, Rune
2007-01-01
In this paper the system reduction in nonlinear multibody dynamics of wind turbines is investigated for various updating schemes of the moving frame of reference. In one case, the moving frame of reference is updated to a stiff body, relative to which the elastic deformations are fixed at one end....... In the other case, the stiff body motion is defined as the chord line connecting the end points of the beam, and the elastic deformations are simply supported at the end points. The system reduction is performed by discretizing the spatial motion into a set of rigid body modes and linear elastic eigenmodes...
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
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
Control oriented 1D electrochemical model of lithium ion battery
International Nuclear Information System (INIS)
Smith, Kandler A.; Rahn, Christopher D.; Wang, Chao-Yang
2007-01-01
Lithium ion (Li-ion) batteries provide high energy and power density energy storage for diverse applications ranging from cell phones to hybrid electric vehicles (HEVs). For efficient and reliable systems integration, low order dynamic battery models are needed. This paper introduces a general method to generate numerically a fully observable/controllable state variable model from electrochemical kinetic, species and charge partial differential equations that govern the discharge/charge behavior of a Li-ion battery. Validated against a 313th order nonlinear CFD model of a 6 Ah HEV cell, a 12th order state variable model predicts terminal voltage to within 1% for pulse and constant current profiles at rates up to 50 C. The state equation is constructed in modal form with constant negative real eigenvalues distributed in frequency space from 0 to 10 Hz. Open circuit potential, electrode surface concentration/reaction distribution coupling and electrolyte concentration/ionic conductivity nonlinearities are explicitly approximated in the model output equation on a local, electrode-averaged and distributed basis, respectively. The balanced realization controllability/observability gramian indicates that the fast electrode surface concentration dynamics are more observable/controllable than the electrode bulk concentration dynamics (i.e. state of charge)
Traveling waves in a continuum model of 1D schools
Oza, Anand; Kanso, Eva; Shelley, Michael
2017-11-01
We construct and analyze a continuum model of a 1D school of flapping swimmers. Our starting point is a delay differential equation that models the interaction between a swimmer and its upstream neighbors' wakes, which is motivated by recent experiments in the Applied Math Lab at NYU. We coarse-grain the evolution equations and derive PDEs for the swimmer density and variables describing the upstream wake. We study the equations both analytically and numerically, and find that a uniform density of swimmers destabilizes into a traveling wave. Our model makes a number of predictions about the properties of such traveling waves, and sheds light on the role of hydrodynamics in mediating the structure of swimming schools.
MX chains: 1-D analog of CuO planes?
International Nuclear Information System (INIS)
Gammel, J.T.; Batistic, I.; Bishop, A.R.; Loh, E.Y. Jr.; Marianer, S.
1989-01-01
We study a two-band Peierls-Hubbard model for halogen-bridged mixed-valence transition metal linear chain complexes (MX chains). We include electron-electron correlations (both Hubbard and PPP-like expressions) using several techniques including calculations in the zero-hopping limit, exact diagonalization of small systems, mean field approximation, and a Gutzwiller-like Ansatz for quantum phonons. The adiabatic optical absorption and phonon spectra for both photo-excited and doping induced defects (kinks, polarons, bipolarons, and excitons) are discussed. A long period phase which occurs even at commensurate filling for certain parameter values may be related to twinning. The effect of including the electron-phonon in addition to the electron-electron interaction on the polaron/bipolaron (pairing) competition is especially interesting when this class of compounds is viewed as a 1-D analog of high-temperature superconductors. 6 refs., 4 figs
Quadratic Finite Element Method for 1D Deterministic Transport
International Nuclear Information System (INIS)
Tolar, D R Jr.; Ferguson, J M
2004-01-01
In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ((und r)) and angular ((und (Omega))) dependences on the angular flux ψ(und r),(und (Omega))are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of ψ(und r),(und (Omega)). Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable (μ) in developing the one-dimensional (1D) spherical geometry S N equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S N algorithms
Axial turbomachine modelling with a 1D axisymmetric approach
International Nuclear Information System (INIS)
Tauveron, Nicolas; Saez, Manuel; Ferrand, Pascal; Leboeuf, Francis
2007-01-01
This work concerns the design and safety analysis of direct cycle gas cooled reactor. The estimation of compressor and turbine performances in transient operations is of high importance for the designer. The first goal of this study is to provide a description of compressor behaviour in unstable conditions with a better understanding than the models based on performance maps ('traditional' 0D approach). A supplementary objective is to provide a coherent description of the turbine behaviour. The turbomachine modelling approach consists in the solution of 1D axisymmetric Navier-Stokes equations on an axial grid inside the turbomachine: mass, axial momentum, circumferential momentum and total-enthalpy balances are written. Blade forces are taken into account by using compressor or turbine blade cascade steady correlations. A particular effort has been developed to generate or test correlations in low mass flow and negative mass flow regimes, based on experimental data. The model is tested on open literature cases of the gas turbine aircraft community. For compressor and turbine, steady situations are fairly described, especially for medium and high mass flow rate. The dynamic behaviour of compressor is also quite well described, even in unstable operation (surge): qualitative tendencies (role of plenum volume and role of throttle) and some quantitative characteristics (frequency) are in a good agreement with experimental data. The application to transient simulations of gas cooled nuclear reactors is concentrated on the hypothetical 10 in. break accident. The results point out the importance of the location of the pipe rupture in a hypothetical break event. In some detailed cases, compressor surge and back flow through the circuit can occur. In order to be used in a design phase, a simplified model of surge has also been developed. This simplified model is applied to the gas fast reactor (GFR) and compared quite favourably with 1D axisymmetric simulation results
Variational Assimilation of Sparse and Uncertain Satellite Data For 1D Saint-Venant River Models
Garambois, P. A.; Brisset, P.; Monnier, J.; Roux, H.
2016-12-01
Profusion of satellites are providing increasingly accurate measurements of continental water cyle, and water bodies variations while in situ observability is declining. The future Surface Water and Ocean Topography (SWOT) mission will provide maps of river surface elevations widths and slopes with an almost global coverage and temporal revisits. This will offer the possibility to address a larger variety of inverse problems in surface hydrology. Data assimilation techniques, that are broadly used in several scientific fields, aim to optimally combine models, system observations and prior information. Variational assimilation consists in iterative minimization of a discrepency measure between model outputs and observations, here for retrieving boundary conditions and parameters of a 1D Saint Venant model. Nevertheless, inferring river discharge and hydraulic parameters thanks to the observation of river surface is not straightforward. This is particularly true in the case of sparse and uncertain observations of flow state variables since they are governed by nonlinear physical processes. This paper investigates the identifiability of hydraulic controls given sparse and uncertain satellite observations of a river. The identifiability of river discharge alone and with roughness is tested for several spatio temporal patterns of river observations, including SWOT like observations. A new 1D Shallow water model with variational data assimilation, within the DassFlow chain is presented as well as postprocessing and observation operator dedicated to the future SWOT and SWOT simulator data. In view to decrease inverse problem dimensionality discharge is represented in a reduced basis. Moreover we introduce an original and reduced parametrization of the flow resistance that can account for various flow regimes along with a cross section design dedicated to remote sensing. We show which discharge temporal frequencies can be identified w.r.t observation ones and at which
Improving 1D Site Specific Velocity Profiles for the Kik-Net Network
Holt, James; Edwards, Benjamin; Pilz, Marco; Fäh, Donat; Rietbrock, Andreas
2017-04-01
recorded data from the Kik-Net network. First, using a reliable subset of sites, the empirical surface to borehole (S/B) ratio is calculated in the frequency domain using all events recorded at that site. In a subsequent step, we use numerical simulation to produce 1D SH transfer function curves using a suite of stochastic velocity models. Comparing the resulting amplification with the empirical S/B ratio we find optimal 1D velocity models and their uncertainty. The method will be tested to determine the level of initial information required to obtain a reliable Vs profile (e.g., starting Vs model, only Vs30, site-class, H/V ratio etc.) and then applied and tested against data from other regions using site-to-reference or empirical spectral model amplification.
Comparison of elastic and inelastic analyses
International Nuclear Information System (INIS)
Ammerman, D.J.; Heinstein, M.W.; Wellman, G.W.
1992-01-01
The use of inelastic analysis methods instead of the traditional elastic analysis methods in the design of radioactive material (RAM) transport packagings leads to a better understanding of the response of the package to mechanical loadings. Thus, better assessment of the containment, thermal protection, and shielding integrity of the package after a structure accident event can be made. A more accurate prediction of the package response can lead to enhanced safety and also allow for a more efficient use of materials, possibly leading to a package with higher capacity or lower weight. This paper discusses the advantages and disadvantages of using inelastic analysis in the design of RAM shipping packages. The use of inelastic analysis presents several problems to the package designer. When using inelastic analysis the entire nonlinear response of the material must be known, including the effects of temperature changes and strain rate. Another problem is that there currently is not an acceptance criteria for this type of analysis that is approved by regulatory agencies. Inelastic analysis acceptance criteria based on failure stress, failure strain , or plastic energy density could be developed. For both elastic and inelastic analyses it is also important to include other sources of stress in the analyses, such as fabrication stresses, thermal stresses, stresses from bolt preloading, and contact stresses at material interfaces. Offsetting these added difficulties is the improved knowledge of the package behavior. This allows for incorporation of a more uniform margin of safety, which can result in weight savings and a higher level of confidence in the post-accident configuration of the package. In this paper, comparisons between elastic and inelastic analyses are made for a simple ring structure and for a package to transport a large quantity of RAM by rail (rail cask) with lead gamma shielding to illustrate the differences in the two analysis techniques
International Nuclear Information System (INIS)
Mungan, M.; Coppersmith, S.; Vinokur, V.M.
1999-01-01
We analyze the strains near threshold in 1-d charge density wave models at zero temperature and strong pinning. We show that in these models local strains diverge near the depinning threshold and characterize the scaling behavior of the phenomenon. This helps quantify when the underlying elastic description breaks down and plastic effects have to be included
Elasticity theory of ultrathin nanofilms
International Nuclear Information System (INIS)
Li, Jiangang; Yun, Guohong; Narsu, B; Yao, Haiyan
2015-01-01
A self-consistent theoretical scheme for describing the elastic behavior of ultrathin nanofilms (UTNFs) was proposed. Taking into account the lower symmetry of an UTNF compared to its bulk counterpart, additional elastic and magnetoelastic parameters were introduced to model the elasticity rigorously. The applications of current theory to several elastic and magnetoelastic systems gave excellent agreement with experiments. More importantly, the surface elastic and magnetoelastic parameters used to fit the experimental results are physically reasonable and in close agreement with those obtained from experiment and simulation. This fact suggests that the additional elastic (magnetoelastic) constants due to symmetry breaking are of great importance in theoretical description of the mechanical properties of UTNFs. And we proved that the elasticity of UTNFs should be described by a three-dimensional model just including the intrinsic surface and bulk parameters, but not the effective surface parameters. It is believed that the theory reported here is a universal strategy for elasticity and magnetoelasticity of ultrathin films. (paper)
The Application of Simulation Method in Isothermal Elastic Natural Gas Pipeline
Xing, Chunlei; Guan, Shiming; Zhao, Yue; Cao, Jinggang; Chu, Yanji
2018-02-01
This Elastic pipeline mathematic model is of crucial importance in natural gas pipeline simulation because of its compliance with the practical industrial cases. The numerical model of elastic pipeline will bring non-linear complexity to the discretized equations. Hence the Newton-Raphson method cannot achieve fast convergence in this kind of problems. Therefore A new Newton Based method with Powell-Wolfe Condition to simulate the Isothermal elastic pipeline flow is presented. The results obtained by the new method aregiven based on the defined boundary conditions. It is shown that the method converges in all cases and reduces significant computational cost.
Energy Technology Data Exchange (ETDEWEB)
Sagdeev, R Z
1984-01-01
The results of theoretical and experimental investigations of nonlinear and turbulent phenomena from a wide range of fields in physics are presented in reviews and reports. Topics examined include localized vortex formations in an ideal fluid, phase transitions in crystals, spatially nonuniform structures in condensed matter, solitons in molecular systems, the migration of quasi-particles in easily deformed crystals, bifurcations and dissipative structures in distributed kinetic systems, and structures in a nonlinear burning medium. Consideration is given to macroscopic motion generation in nonequilibrium media, the interaction of bulk and surface wave trains, near-threshold instabilities in hydrodynamics, solitons in nonlinear elastic rods with variable characteristics, the generation of solitons and vortices from chaos, and nonlinear electromagnetic-wave dissipation in an electron system.
A hyper elasticity method for interactive virtual design of hearing aids
DEFF Research Database (Denmark)
Darkner, Sune; Erleben, Kenny
2011-01-01
We present a computational efficient method for isotropic hyper elasticity based on functional analysis. By selecting a class of shape functions, we arrive at a computational scheme which yields very sparse tensors. This enables fast computations of the hyper elastic energy potential and its...... derivatives. We achieve efficiency and performance through the use of shape functions that are linear in their parameters and through rotation into the eigenspace of the right Cauchy–Green strain tensor. This makes near real time evaluation of hyper elasticity of complex meshes on CPU relatively easy...... to implement. The approach does not rely on a specific shape function or material model but offers a general framework for isotropic hyper elasticity. The method is aimed at interactive and accurate non-linear hyper elastic modeling for a wide range of industrial virtual design applications, which we exemplify...
Measurement of the elastic cross section for positive pions on carbon at 142 MeV
International Nuclear Information System (INIS)
Oyer, A.T.
1976-12-01
A measurement of the elastic cross section dsigma/dΩ was made for the reaction π + + 12 C → π + + 12 C with 142 MeV pions at ten angles ranging from 35 to 85 0 in the laboratory. This experiment was done at the Los Alamos Meson Physics Facility. A double focusing magnetic spectrometer observed a cylindrical styrofoam target. The resulting momentum spectra were recorded by an array of nineteen totally depleted surface barrier detectors located at the spectrometer's focal plane. The spectra from the styrofoam were composed of peaks representing proton elastic, carbon elastic, carbon inelastic, and carbon quasi-elastic channels. A function made of Gaussians representing the two body channels and a distribution representing the quasi-elastic channel was fit to the data using a nonlinear least squares algorithm. The ratio of the carbon elastic to proton elastic cross sections was calculated from the areas of the corresponding Gaussians and then multiplied by the proton elastic cross section of Bugg et al eliminating several sources of systematic errors such as beam normalization. The differential cross sections were found to have the usual diffraction structure with a forward peak and a minimum near 55 0 . Finally, the carbon elastic cross sections were compared to similar π - + 12 C cross sections of Binon et al using the optical model
Measurement of the elastic cross section for positive pions on carbon at 142 MeV
Energy Technology Data Exchange (ETDEWEB)
Oyer, A.T.
1976-12-01
A measurement of the elastic cross section dsigma/d..cap omega.. was made for the reaction ..pi../sup +/ + /sup 12/C ..-->.. ..pi../sup +/ + /sup 12/C with 142 MeV pions at ten angles ranging from 35 to 85/sup 0/ in the laboratory. This experiment was done at the Los Alamos Meson Physics Facility. A double focusing magnetic spectrometer observed a cylindrical styrofoam target. The resulting momentum spectra were recorded by an array of nineteen totally depleted surface barrier detectors located at the spectrometer's focal plane. The spectra from the styrofoam were composed of peaks representing proton elastic, carbon elastic, carbon inelastic, and carbon quasi-elastic channels. A function made of Gaussians representing the two body channels and a distribution representing the quasi-elastic channel was fit to the data using a nonlinear least squares algorithm. The ratio of the carbon elastic to proton elastic cross sections was calculated from the areas of the corresponding Gaussians and then multiplied by the proton elastic cross section of Bugg et al eliminating several sources of systematic errors such as beam normalization. The differential cross sections were found to have the usual diffraction structure with a forward peak and a minimum near 55/sup 0/. Finally, the carbon elastic cross sections were compared to similar ..pi../sup -/ + /sup 12/C cross sections of Binon et al using the optical model.
Measurement of the elastic cross section for positive pions on carbon at 142 MeV
International Nuclear Information System (INIS)
Oyer, A.T.
1976-01-01
A measurement of the elastic cross section dsigma/dOMEGA was made for the reaction π + + 12 C yields π + + 12 C with 142 MeV pions at ten angles ranging from 35 to 85 0 in the laboratory. This experiment was done at the Los Alamos Meson Physics Facility. A double focusing magnetic spectrometer observed a cylindrical styrofoam target. The resulting momentum spectra were recorded by an array of nineteen totally depleted surface barrier detectors located at the spectrometers focal plane. The spectra from the styrofoam were composed of peaks representing proton elastic, carbon elastic, carbon inelastic and carbon quasi-elastic channels. A function made of Gaussians representing the two body channels and a distribution representing the quasi-elastic channel was fit to the data using a nonlinear least squares algorithm. The ratio of the carbon elastic to proton elastic cross sections was calculated from the areas of the corresponding Gaussians and then multiplied by the proton elastic cross section of Bugg et al., eliminating several sources of systematic errors such as beam normalization. The differential cross sections were found to have the usual diffraction structure with a forward peak and a minimum near 55 0 . Finally, the carbon elastic cross sections were compared to similar π - + 12 C cross sections of Binon et al., using the optical model
Cell Elasticity Determines Macrophage Function
Patel, Naimish R.; Bole, Medhavi; Chen, Cheng; Hardin, Charles C.; Kho, Alvin T.; Mih, Justin; Deng, Linhong; Butler, James; Tschumperlin, Daniel; Fredberg, Jeffrey J.; Krishnan, Ramaswamy; Koziel, Henry
2012-01-01
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. PMID:23028423
Cell elasticity determines macrophage function.
Directory of Open Access Journals (Sweden)
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.
Multipurpose hooks for elastic attachment
Directory of Open Access Journals (Sweden)
Siddharth Shashidhar Revankar
2014-01-01
Full Text Available As certain bracket systems do not include hooks on premolar brackets for elastic attachment, Kobayashi or custom made ligature hooks have proven as an alternative. However, these hooks tend to bend labially when used with heavy elastics and these elastics can even pop loose from the hooks on mouth opening. The following article describes an innovative multipurpose hook which is simple, stiff and inexpensive and can be used for engagement of class II elastics on premolars in case of missing molars as well as engagement of intermaxillary elastics for settling of occlusion in finishing stages. As the hooks can be prefabricated, this saves a lot of chair side time and is more practical for use in day-to-day orthodontic practice.
A Survey of Nonlinear Dynamics (Chaos Theory)
1991-04-01
example of an n = 1 Hamiltonian system does have separatrices. This is the 1D pendulum (Fig. 4.2): 9=p, p=-asin9;H(9,p) =p2 /2- acosO . (4-5) Phase space...method. There is no substitute for the actual labor of applying the nonlinear operator to a sum of normal modes, producing a general Galerkin vector
General solution of string inspired nonlinear equations
International Nuclear Information System (INIS)
Bandos, I.A.; Ivanov, E.; Kapustnikov, A.A.; Ulanov, S.A.
1998-07-01
We present the general solution of the system of coupled nonlinear equations describing dynamics of D-dimensional bosonic string in the geometric (or embedding) approach. The solution is parametrized in terms of two sets of the left- and right-moving Lorentz harmonic variables providing a special coset space realization of the product of two (D-2) dimensional spheres S D-2 = SO(1,D-1)/SO(1,1)xSO(D-2) contained in K D-2 . (author)
[Nonlinear magnetohydrodynamics
International Nuclear Information System (INIS)
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile
Blocky inversion of multichannel elastic impedance for elastic parameters
Mozayan, Davoud Karami; Gholami, Ali; Siahkoohi, Hamid Reza
2018-04-01
Petrophysical description of reservoirs requires proper knowledge of elastic parameters like P- and S-wave velocities (Vp and Vs) and density (ρ), which can be retrieved from pre-stack seismic data using the concept of elastic impedance (EI). We propose an inversion algorithm which recovers elastic parameters from pre-stack seismic data in two sequential steps. In the first step, using the multichannel blind seismic inversion method (exploited recently for recovering acoustic impedance from post-stack seismic data), high-resolution blocky EI models are obtained directly from partial angle-stacks. Using an efficient total-variation (TV) regularization, each angle-stack is inverted independently in a multichannel form without prior knowledge of the corresponding wavelet. The second step involves inversion of the resulting EI models for elastic parameters. Mathematically, under some assumptions, the EI's are linearly described by the elastic parameters in the logarithm domain. Thus a linear weighted least squares inversion is employed to perform this step. Accuracy of the concept of elastic impedance in predicting reflection coefficients at low and high angles of incidence is compared with that of exact Zoeppritz elastic impedance and the role of low frequency content in the problem is discussed. The performance of the proposed inversion method is tested using synthetic 2D data sets obtained from the Marmousi model and also 2D field data sets. The results confirm the efficiency and accuracy of the proposed method for inversion of pre-stack seismic data.
A new numerical treatment based on Lucas polynomials for 1D and 2D sinh-Gordon equation
Oruç, Ömer
2018-04-01
In this paper, a new mixed method based on Lucas and Fibonacci polynomials is developed for numerical solutions of 1D and 2D sinh-Gordon equations. Firstly time variable discretized by central finite difference and then unknown function and its derivatives are expanded to Lucas series. With the help of these series expansion and Fibonacci polynomials, matrices for differentiation are derived. With this approach, finding the solution of sinh-Gordon equation transformed to finding the solution of an algebraic system of equations. Lucas series coefficients are acquired by solving this system of algebraic equations. Then by plugginging these coefficients into Lucas series expansion numerical solutions can be obtained consecutively. The main objective of this paper is to demonstrate that Lucas polynomial based method is convenient for 1D and 2D nonlinear problems. By calculating L2 and L∞ error norms of some 1D and 2D test problems efficiency and performance of the proposed method is monitored. Acquired accurate results confirm the applicability of the method.
Nonlinear theory of electroelastic and magnetoelastic interactions
Dorfmann, Luis
2014-01-01
This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.
Thermalization threshold in models of 1D fermions
Mukerjee, Subroto; Modak, Ranjan; Ramswamy, Sriram
2013-03-01
The question of how isolated quantum systems thermalize is an interesting and open one. In this study we equate thermalization with non-integrability to try to answer this question. In particular, we study the effect of system size on the integrability of 1D systems of interacting fermions on a lattice. We find that for a finite-sized system, a non-zero value of an integrability breaking parameter is required to make an integrable system appear non-integrable. Using exact diagonalization and diagnostics such as energy level statistics and the Drude weight, we find that the threshold value of the integrability breaking parameter scales to zero as a power law with system size. We find the exponent to be the same for different models with its value depending on the random matrix ensemble describing the non-integrable system. We also study a simple analytical model of a non-integrable system with an integrable limit to better understand how a power law emerges.
XBWR, 1-D Xe Transients for BWR in Axial Geometry
International Nuclear Information System (INIS)
Forti, G.
1980-01-01
1 - Nature of the physical problem solved: 1-D xenon transients for BWRs in axial geometry. 2 - Method of solution: XBWR couples a two group neutron diffusion calculation in plane geometry with a two phase flow cooling channel calculation and the heat conduction in the typical fuel rod. The program allows following any given power time schedule, such as shut-down and restart, day-night power variation etc., while the reactor is being kept critical by control rod movement, variable poisoning of the core, or coolant flow recirculation rate. The xenon and iodine concentrations variation is evaluated pointwise (up to 100 points) by analytical solution for successive fixed time steps. At the end of each time step a new distribution of fluxes, power, voids and temperatures is obtained, which is consistent with the reactor critical condition as it is got by variation of the control parameter taking into account the feedbacks. The new flux distribution is used as input for xenon and iodine concentrations evolution in the next time step
The molecular spin filter constructed from 1D organic chain
International Nuclear Information System (INIS)
Chen, Wei; Xu, Ning; Wang, Baolin; Bian, Baoan
2014-01-01
We proposed a molecular spin filter, which is constructed from the 1D metallic organic chain (Fe n+1 (C 6 H 4 ) n ). The spin-polarized transport properties of the molecular spin filter are explored by combining density functional theory with nonequilibrium Green's function formalism. Theoretical results reveal that Fe n+1 (C 6 H 4 ) n molecular chain exhibits robust spin filtering effect, and only the spin-down electrons can transmit through the molecular chain. At the given bias voltage window [−1 eV,1 eV], the calculated spin filter efficiency is close to 100% in the case of n≥3. We find that the effect of spin polarization origin from both Fe n+1 and (C 6 H 4 ) n . In addition, negative difference resistance behavior appears in Fe n+1 (C 6 H 4 ) n molecular chain. The results can help us understand the spin transport properties of organic molecular chain. - Highlights: • Theoretical results reveal that Fe n+1 (C 6 H 4 ) n molecular chain exhibits robust spin filtering effect. • The effect of spin polarization origin from both of Fe n+1 and (C 6 H 4 ) n . • Negative difference resistance behavior appears in Fe n+1 (C 6 H 4 ) n molecular chain
Parallelization of elliptic solver for solving 1D Boussinesq model
Tarwidi, D.; Adytia, D.
2018-03-01
In this paper, a parallel implementation of an elliptic solver in solving 1D Boussinesq model is presented. Numerical solution of Boussinesq model is obtained by implementing a staggered grid scheme to continuity, momentum, and elliptic equation of Boussinesq model. Tridiagonal system emerging from numerical scheme of elliptic equation is solved by cyclic reduction algorithm. The parallel implementation of cyclic reduction is executed on multicore processors with shared memory architectures using OpenMP. To measure the performance of parallel program, large number of grids is varied from 28 to 214. Two test cases of numerical experiment, i.e. propagation of solitary and standing wave, are proposed to evaluate the parallel program. The numerical results are verified with analytical solution of solitary and standing wave. The best speedup of solitary and standing wave test cases is about 2.07 with 214 of grids and 1.86 with 213 of grids, respectively, which are executed by using 8 threads. Moreover, the best efficiency of parallel program is 76.2% and 73.5% for solitary and standing wave test cases, respectively.
Giant magnons in the D1-D5 system
International Nuclear Information System (INIS)
David, Justin R.; Sahoo, Bindusar
2008-01-01
We study giant magnons in the the D1-D5 system from both the boundary CFT and as classical solutions of the string sigma model in AdS 3 x S 3 x T 4 . Re-examining earlier studies of the symmetric product conformal field theory we argue that giant magnons in the symmetric product are BPS states in a centrally extended SU(1|1) x SU(1|1) superalgebra with two more additional central charges. The magnons carry these additional central charges locally but globally they vanish. Using a spin chain description of these magnons and the extended superalgebra we show that these magnons obey a dispersion relation which is periodic in momentum. We then identify these states on the string theory side and show that here too they are BPS in the same centrally extended algebra and obey the same dispersion relation which is periodic in momentum. This dispersion relation arises as the BPS condition for the extended algebra and is similar to that of magnons in N = 4 Yang-Mills
Cellular reprogramming dynamics follow a simple 1D reaction coordinate
Teja Pusuluri, Sai; Lang, Alex H.; Mehta, Pankaj; Castillo, Horacio E.
2018-01-01
Cellular reprogramming, the conversion of one cell type to another, induces global changes in gene expression involving thousands of genes, and understanding how cells globally alter their gene expression profile during reprogramming is an ongoing problem. Here we reanalyze time-course data on cellular reprogramming from differentiated cell types to induced pluripotent stem cells (iPSCs) and show that gene expression dynamics during reprogramming follow a simple 1D reaction coordinate. This reaction coordinate is independent of both the time it takes to reach the iPSC state as well as the details of the experimental protocol used. Using Monte-Carlo simulations, we show that such a reaction coordinate emerges from epigenetic landscape models where cellular reprogramming is viewed as a ‘barrier-crossing’ process between cell fates. Overall, our analysis and model suggest that gene expression dynamics during reprogramming follow a canonical trajectory consistent with the idea of an ‘optimal path’ in gene expression space for reprogramming.
Modeling of 1D Anomalous Diffusion in Fractured Nanoporous Media
Directory of Open Access Journals (Sweden)
Albinali Ali
2016-07-01
Full Text Available Fractured nanoporous reservoirs include multi-scale and discontinuous fractures coupled with a complex nanoporous matrix. Such systems cannot be described by the conventional dual-porosity (or multi-porosity idealizations due to the presence of different flow mechanisms at multiple scales. More detailed modeling approaches, such as Discrete Fracture Network (DFN models, similarly suffer from the extensive data requirements dictated by the intricacy of the flow scales, which eventually deter the utility of these models. This paper discusses the utility and construction of 1D analytical and numerical anomalous diffusion models for heterogeneous, nanoporous media, which is commonly encountered in oil and gas production from tight, unconventional reservoirs with fractured horizontal wells. A fractional form of Darcy’s law, which incorporates the non-local and hereditary nature of flow, is coupled with the classical mass conservation equation to derive a fractional diffusion equation in space and time. Results show excellent agreement with established solutions under asymptotic conditions and are consistent with the physical intuitions.
Effective theory of black holes in the 1/D expansion
International Nuclear Information System (INIS)
Emparan, Roberto; Shiromizu, Tetsuya; Suzuki, Ryotaku; Tanabe, Kentaro; Tanaka, Takahiro
2015-01-01
The gravitational field of a black hole is strongly localized near its horizon when the number of dimensions D is very large. In this limit, we can effectively replace the black hole with a surface in a background geometry (e.g. Minkowski or Anti-deSitter space). The Einstein equations determine the effective equations that this ‘black hole surface’ (or membrane) must satisfy. We obtain them up to next-to-leading order in 1/D for static black holes of the Einstein-(A)dS theory. To leading order, and also to next order in Minkowski backgrounds, the equations of the effective theory are the same as soap-film equations, possibly up to a redshift factor. In particular, the Schwarzschild black hole is recovered as a spherical soap bubble. Less trivially, we find solutions for ‘black droplets’, i.e. black holes localized at the boundary of AdS, and for non-uniform black strings.
An analysis of hypercritical states in elastic and inelastic systems
Kowalczk, Maciej
The author raises a wide range of problems whose common characteristic is an analysis of hypercritical states in elastic and inelastic systems. the article consists of two basic parts. The first part primarily discusses problems of modelling hypercritical states, while the second analyzes numerical methods (so-called continuation methods) used to solve non-linear problems. The original approaches for modelling hypercritical states found in this article include the combination of plasticity theory and an energy condition for cracking, accounting for the variability and cyclical nature of the forms of fracture of a brittle material under a die, and the combination of plasticity theory and a simplified description of the phenomenon of localization along a discontinuity line. The author presents analytical solutions of three non-linear problems for systems made of elastic/brittle/plastic and elastic/ideally plastic materials. The author proceeds to discuss the analytical basics of continuation methods and analyzes the significance of the parameterization of non-linear problems, provides a method for selecting control parameters based on an analysis of the rank of a rectangular matrix of a uniform system of increment equations, and also provides a new method for selecting an equilibrium path originating from a bifurcation point. The author provides a general outline of continuation methods based on an analysis of the rank of a matrix of a corrective system of equations. The author supplements his theoretical solutions with numerical solutions of non-linear problems for rod systems and problems of the plastic disintegration of a notched rectangular plastic plate.
Becker, K.; Shapiro, S.; Stanchits, S.; Dresen, G.; Kaselow, A.; Vinciguerra, S.
2005-12-01
Elastic properties of rocks are sensitive to changes of the in-situ stress and damage state. In particular, seismic velocities are strongly affected by stress-induced formation and deformation of cracks or shear-enhanced pore collapse. The effect of stress on seismic velocities as a result of pore space deformation in isotropic rock at isostatic compression may be expressed by the equation: A+K*P-B*exp (-D*P) (1), where P=Pc-Pp is the effective pressure, the pure difference between confining pressure and pore pressure. The parameter A, K, B and D describe material constants determined using experimental data. The physical meaning of the parameters is given by Shapiro (2003, in Geophysics Vol.68(Nr.2)). Parameter D is related to the stress sensitivity of the rock. A similar relation was derived by Shapiro and Kaselow (2005, in Geophysics in press) for weak anisotropic rocks under arbitrary load. They describe the stress dependent anisotropy in terms of Thomson's (1986, in Geophysics, Vol. 51(Nr.10)) anisotropy parameters ɛ and γ as a function of stress in the case of an initially isotropic rock: ɛ ∝ E2-E3, γ ∝ E3-E2 (2) with Ei=exp (D*Pi). The exponential terms Ei are controlled by the effective stress components Pi. To test this relation, we have conducted a series of triaxial compression tests on dry samples of initially isotropic Etnean Basalt in a servo-controlled MTS loading frame equipped with a pressure cell. Confining pressure was 60, 40 and 20 MPa. Samples were 5 cm in diameter and 10 cm in length. Elastic anisotropy was induced by axial compression of the samples through opening and growth of microcracks predominantly oriented parallel to the sample axis. Ultrasonic P- and S- wave velocities were monitored parallel and normal to the sample axis by an array of 20 piezoceramic transducers glued to the surface. Preamplified full waveform signals were stored in two 12 channel transient recorders. According to equation 2 the anisotropy parameters are
Variable-range hopping in 2D quasi-1D electronic systems
International Nuclear Information System (INIS)
Teber, S.
2005-12-01
A semi-phenomenological theory of variable-range hopping (VRH) is developed for two-dimensional (2D) quasi-one-dimensional (quasi-1D) systems such as arrays of quantum wires in the Wigner crystal regime. The theory follows the phenomenology of Efros, Mott and Shklovskii allied with microscopic arguments. We first derive the Coulomb gap in the single-particle density of states, g(ε), where ε is the energy of the charge excitation. We then derive the main exponential dependence of the electron conductivity in the linear (L), i.e. σ(T) ∼ exp [-(T L /T) γL ], and current in the non-linear (NL), i.e. j(E) ∼ [-(E NL /E) γNL ], response regimes (E is the applied electric field). Due to the strong anisotropy of the system and its peculiar dielectric properties we show that unusual, with respect to known results, Coulomb gaps open followed by unusual VRH laws, i.e. with respect to the disorder-dependence of T L and E NL and the values of γ L and γ NL . (author)
Treebak, Jonas T; Pehmøller, Christian; Kristensen, Jonas M; Kjøbsted, Rasmus; Birk, Jesper B; Schjerling, Peter; Richter, Erik A; Goodyear, Laurie J; Wojtaszewski, Jørgen F P
2014-01-15
We investigated the phosphorylation signatures of two Rab-GTPase activating proteins TBC1D1 and TBC1D4 in human skeletal muscle in response to physical exercise and physiological insulin levels induced by a carbohydrate rich meal using a paired experimental design. Eight healthy male volunteers exercised in the fasted or fed state and muscle biopsies were taken before and immediately after exercise. We identified TBC1D1/4 phospho-sites that (1) did not respond to exercise or postprandial increase in insulin (TBC1D4: S666), (2) responded to insulin only (TBC1D4: S318), (3) responded to exercise only (TBC1D1: S237, S660, S700; TBC1D4: S588, S751), and (4) responded to both insulin and exercise (TBC1D1: T596; TBC1D4: S341, T642, S704). In the insulin-stimulated leg, Akt phosphorylation of both T308 and S473 correlated significantly with multiple sites on both TBC1D1 (T596) and TBC1D4 (S318, S341, S704). Interestingly, in the exercised leg in the fasted state TBC1D1 phosphorylation (S237, T596) correlated significantly with the activity of the α2/β2/γ3 AMPK trimer, whereas TBC1D4 phosphorylation (S341, S704) correlated with the activity of the α2/β2/γ1 AMPK trimer. Our data show differential phosphorylation of TBC1D1 and TBC1D4 in response to physiological stimuli in human skeletal muscle and support the idea that Akt and AMPK are upstream kinases. TBC1D1 phosphorylation signatures were comparable between in vitro contracted mouse skeletal muscle and exercised human muscle, and we show that AMPK regulated phosphorylation of these sites in mouse muscle. Contraction and exercise elicited a different phosphorylation pattern of TBC1D4 in mouse compared with human muscle, and although different circumstances in our experimental setup may contribute to this difference, the observation exemplifies that transferring findings between species is problematic.
Li, M. P.; Sun, Q. P.
2018-01-01
We investigate the roles of grain size (lg) and grain boundary thickness (lb) on the stress-induced phase transition (PT) behaviors of nanocrystalline shape memory alloys (SMAs) by using a Core-shell type "crystallite-amorphous composite" model. A non-dimensionalized length scale lbarg(=lg /lb) is identified as the governing parameter which is indicative of the energy competition between the crystallite and the grain boundary. Closed form analytical solutions of a reduced effective 1D model with embedded microstructure length scales of lg and lb are presented in this paper. It is shown that, with lbarg reduction, the energy of the elastic non-transformable grain boundary will gradually become dominant in the phase transition process, and eventually bring fundamental changes of the deformation behaviors: breakdown of two-phase coexistence and vanishing of superelastic hysteresis. The predictions are supported by experimental data of nanocrystalline NiTi SMAs.
bessel functions for axisymmetric elasticity problems of the elastic
African Journals Online (AJOL)
HOD
2, 3DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF NIGERIA, NSUKKA. ENUGU STATE. ... theory of elasticity and in the case of vertical applied loads, was first ... partial differential equations in bodies having cylindrical symmetry.
Nonlinear wave propagation studies, dispersion modeling, and signal parameters correction
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk
..: ..., 2004, 00. [European Workshop on FP6-AERONEWS /1./. Naples (IT), 13.09.2004-16.09.2004] EU Projects: European Commission(XE) 502927 - AERO-NEWS Institutional research plan: CEZ:AV0Z2076919 Keywords : nodestructive testing * nonlinear elastic wave spectroscopy Subject RIV: BI - Acoustics
Strain fluctuations and elastic constants
Energy Technology Data Exchange (ETDEWEB)
Parrinello, M.; Rahman, A.
1982-03-01
It is shown that the elastic strain fluctuations are a direct measure of elastic compliances in a general anisotropic medium; depending on the ensemble in which the fluctuation is measured either the isothermal or the adiabatic compliances are obtained. These fluctuations can now be calculated in a constant enthalpy and pressure, and hence, constant entropy, ensemble due to recent develpments in the molecular dynamics techniques. A calculation for a Ni single crystal under uniform uniaxial 100 tensile or compressive load is presented as an illustration of the relationships derived between various strain fluctuations and the elastic modulii. The Born stability criteria and the behavior of strain fluctuations are shown to be related.
High energy elastic hadron scattering
International Nuclear Information System (INIS)
Fearnly, T.A.
1986-04-01
The paper deals with the WA7 experiment at the CERN super proton synchrotron (SPS). The elastic differential cross sections of pion-proton, kaon-proton, antiproton-proton, and proton-proton at lower SPS energies over a wide range of momentum transfer were measured. Some theoretical models in the light of the experimental results are reviewed, and a comprehensive impact parameter analysis of antiproton-proton elastic scattering over a wide energy range is presented. A nucleon valence core model for high energy proton-proton and antiproton-proton elastic scattering is described
Westra, H.J.R.
2012-01-01
In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like
CONCERNING THE ELASTIC ORTHOTROPIC MODEL APPLIED TO WOOD ELASTIC PROPERTIES
Tadeu Mascia,Nilson
2003-01-01
Among the construction materials, wood reveals an orthotropic pattern, because of unique characteristics in its internal structure with three axes of wood biological directions (longitudinal, tangential and radial). elastic symmetry: longitudinal, tangential and radial, reveals an orthotropic pattern. The effect of grain angle orientation onin the elastic modulus constitutes the fundamental cause forof wood anisotropy. It is responsible for the greatest changes in the values of the constituti...
Spectral dimension of elastic Sierpinski gaskets with general elastic forces
International Nuclear Information System (INIS)
Liu, S.H.; Liu, A.J.
1985-01-01
The spectral dimension is calculated for a Sierpinski gasket with the most general elastic restoring forces allowed by symmetry. The elastic forces consist of bond-stretching and angle-bending components. The spectral dimension is the same as that for the bond-stretching-force (central-force) model. This demonstrates that on the Sierpinski gasket the two types of forces belong to the same universality class
Synthesis, characterization, and physical properties of 1D nanostructures
Marley, Peter Mchael
The roster of materials exhibiting metal---insulator transitions with sharply discontinuous switching of electrical conductivity close to room temperature remains rather sparse despite the fundamental interest in the electronic instabilities manifested in such materials and the plethora of potential technological applications, ranging from frequency-agile metamaterials to electrochromic coatings and Mott field-effect transistors. Vanadium oxide bronzes with the general formula MxV2O 5, provide a wealth of compositions and frameworks where strong electron correlation can be systematically (albeit thus far only empirically) tuned. Charge fluctuations along the quasi-1D frameworks of MxV 2O5 bronzes have evinced much recent interest owing to the manifestation of colossal metal---insulator transitions and superconductivity. We start with a general review on the phase transitions, both electronic and structural, of vanadium oxide bronzes in Chapter 1. In Chapter 2, we demonstrate an unprecedented reversible transformation between double-layered (delta) and tunnel (beta) quasi-1D geometries for nanowires of a divalent vanadium bronze CaxV2O5 (x ˜0.23) upon annealing-induced dehydration and hydrothermally-induced hydration. Such a facile hydration/dehydration-induced interconversion between two prominent quasi-1D structures (accompanied by a change in charge ordering motifs) has not been observed in the bulk and is posited to result from the ease of propagation of crystallographic slip processes across the confined nanowire widths for the delta→beta conversion and the facile diffusion of water molecules within the tunnel geometries for the beta→delta reversion. We demonstrate in Chapter 3 unprecedented pronounced metal-insulator transitions induced by application of a voltage for nanowires of a vanadium oxide bronze with intercalated divalent cations, beta-PbxV 2O5 (x ˜0.33). The induction of the phase transition through application of an electric field at room
Astronomical optics and elasticity theory
Lemaitre, Gerard Rene
2008-01-01
Astronomical Optics and Elasticity Theory provides a very thorough and comprehensive account of what is known in this field. After an extensive introduction to optics and elasticity, the book discusses variable curvature and multimode deformable mirrors, as well as, in depth, active optics, its theory and applications. Further, optical design utilizing the Schmidt concept and various types of Schmidt correctors, as well as the elasticity theory of thin plates and shells are elaborated upon. Several active optics methods are developed for obtaining aberration corrected diffraction gratings. Further, a weakly conical shell theory of elasticity is elaborated for the aspherization of grazing incidence telescope mirrors. The very didactic and fairly easy-to-read presentation of the topic will enable PhD students and young researchers to actively participate in challenging astronomical optics and instrumentation projects.
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...
Wrinkling of Pressurized Elastic Shells
Vella, Dominic; Ajdari, Amin; Vaziri, Ashkan; Boudaoud, Arezki
2011-01-01
We study the formation of localized structures formed by the point loading of an internally pressurized elastic shell. While unpressurized shells (such as a ping-pong ball) buckle into polygonal structures, we show that pressurized shells
NONLINEAR DYNAMICS OF A ROTOR WITH CANTILEVERED DISK RESTING ON ANGULAR CONTACT BALL BEARINGS
Directory of Open Access Journals (Sweden)
S. Filipkovskyi
2016-06-01
Full Text Available The mathematical model of nonlinear oscillations of the rotor resting on angular contact ball bearings is developed. The disc is fixed on the console end of the shaft. The deflection of the shaft, and the elastic deformation of the bearings have the same order. Analysis of free oscillations is carried out, using nonlinear normal modes. The modes and backbone curves of rotor nonlinear oscillations are calculated. The system has soft characteristics.
Tian, Yuxing; Yu, Zhentao; Ong, Chun Yee Aaron; Kent, Damon; Wang, Gui
2015-05-01
Cold-deformability and mechanical compatibility of the biomedical β-type titanium alloy are the foremost considerations for their application in stents, because the lower ductility restricts the cold-forming of thin-tube and unsatisfactory mechanical performance causes a failed tissue repair. In this paper, β-type titanium alloy (Ti-25Nb-3Zr-3Mo-2Sn, wt%) thin-tube fabricated by routine cold rolling is reported for the first time, and its elastic behavior and mechanical properties are discussed for the various microstructures. The as cold-rolled tube exhibits nonlinear elastic behavior with large recoverable strain of 2.3%. After annealing and aging, a nonlinear elasticity, considered as the intermediate stage between "double yielding" and normal linear elasticity, is attributable to a moderate precipitation of α phase. Quantitive relationships are established between volume fraction of α phase (Vα) and elastic modulus, strength as well as maximal recoverable strain (εmax-R), where the εmax-R of above 2.0% corresponds to the Vα range of 3-10%. It is considered that the "mechanical" stabilization of the (α+β) microstructure is a possible elastic mechanism for explaining the nonlinear elastic behavior. Copyright © 2015 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Arkoprovo Biswas
2011-07-01
Full Text Available In the presence of conducting inhomogeneities in near-surface structures, apparent resistivity data in magnetotelluric sounding can be severely distorted. This is due to electric fields generated from boundary charges on surficial inhomogeneities. Such distortion persists throughout the entire recording range and is known as static shift in magnetotellurics. Frequency-independent static shifts manifest as vertical, parallel shifts that occur in plots of the dual logarithmic scale of apparent resistivity versus time period. The phase of magnetotelluric sounding data remains unaffected by the static shift and can be used to remove the static shift to some extent. However, individual inversion of phase data yields highly nonunique results, and alone it will not work to correctly remove the static shift. Inversions of uncorrected magnetotelluric data yield erroneous and unreliable estimations, while static-shift-corrected magnetotelluric data provide better and reliable estimations of the resistivities and thicknesses of subsurface structures. In the present study, static shift (a frequency-independent real constant is also considered as one of the model parameters and is optimized together with other model parameters (resistivity and thickness using the very fast simulated annealing global inversion technique. This implies that model parameters are determined simultaneously with the estimate of the static shift in the data. Synthetic and noisy data generated for a number of models are interpreted, to demonstrate the efficacy of the approach to yield reliable estimates of subsurface structures when the apparent resistivity data are affected by static shift. Individual inversions of static-shift-affected apparent resistivity data and phase data yield unreliable estimations of the model parameters. Furthermore, the estimated model parameters after individual data inversions do not show any systematic correlations with the amount of static shift in the data. The present study shows that only joint inversion of the apparent resistivity and phase data, without or with optimizing of the static shift, yields models that show good fits between the observed and the model data. Joint inversion results also reveal a systematic relationship between the estimated model parameters and the static shift in the data. The proposed approach also shows that estimated resistivities are ‘S’ (the static shift parameter times the actual resistivities, and that estimated thicknesses are √S times the actual thicknesses without optimization of the static shift. This result is in good agreement with the existing relationship in the literature. Therefore, the global optimization procedure developed can be effectively used to optimize the static shifts in data, to obtain reliable estimations of model parameters. Subsequently, joint inversion of the apparent resistivity and phase data, with optimization of the static shift, is performed, which yields accurate estimates of subsurface structures. It is demonstrated that this approach can also be used when the data is not affected by the static shift. In such cases, the estimated static shift parameter ‘S’ will be close to unity. The efficacy of the approach is demonstrated with a field example from Singhbhum craton, eastern India, by providing an accurate estimation of the craton thickness and the conducting structure that lies below the craton.
From nonfinite to finite 1D arrays of origami tiles.
Wu, Tsai Chin; Rahman, Masudur; Norton, Michael L
2014-06-17
average solution structures for blocks is more readily achieved using computer models than using direct imaging methods. The development of scalable 1D-origami arrays composed of uniquely addressable components is a logical, if not necessary, step in the evolution of higher order fully addressable structures. Our research into the fabrication of arrays has led us to generate a listing of several important areas of future endeavor. Of high importance is the re-enforcement of the mechanical properties of the building blocks and the organization of multiple arrays on a surface of technological importance. While addressing this short list of barriers to progress will prove challenging, coherent development along each of these lines of inquiry will accelerate the appearance of commercial scale molecular manufacturing.
CONFERENCE: Elastic and diffractive scattering
Energy Technology Data Exchange (ETDEWEB)
White, Alan
1989-09-15
Elastic scattering, when particles appear to 'bounce' off each other, and the related phenomena of diffractive scattering are currently less fashionable than the study of hard scattering processes. However this could change rapidly if unexpected results from the UA4 experiment at the CERN Collider are confirmed and their implications tested. These questions were highlighted at the third 'Blois Workshop' on Elastic and Diffractive Scattering, held early in May on the Evanston campus of Northwestern University, near Chicago.
A Labor Supply Elasticity Accord?
Lars Ljungqvist; Thomas J. Sargent
2011-01-01
A dispute about the size of the aggregate labor supply elasticity has been fortified by a contentious aggregation theory used by real business cycle theorists. The replacement of that aggregation theory with one more congenial to microeconomic observations opens possibilities for an accord about the aggregate labor supply elasticity. The new aggregation theory drops features to which empirical microeconomists objected and replaces them with life-cycle choices. Whether the new aggregation theo...
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.
Mathematical theory of elastic and elasto-plastic bodies an introduction
Necas, J
2013-01-01
The book acquaints the reader with the basic concepts and relations of elasticity and plasticity, and also with the contemporary state of the theory, covering such aspects as the nonlinear models of elasto-plastic bodies and of large deflections of plates, unilateral boundary value problems, variational principles, the finite element method, and so on.
Shaping through buckling in elastic gridshells: from camping tents to architectural roofs
Reis, Pedro
Elastic gridshells comprise an initially planar network of elastic rods that is actuated into a 3D shell-like structure by loading its extremities. This shaping results from elastic buckling and the subsequent geometrically nonlinear deformation of the grid structure. Architectural elastic gridshells first appeared in the 1970's. However, to date, only a limited number of examples have been constructed around the world, primarily due to the challenges involved in their structural design. Yet, elastic gridshells are highly appealing: they can cover wide spans with low self-weight, they allow for aesthetically pleasing shapes and their construction is typically simple and rapid. We study the mechanics of elastic gridshells by combining precision model experiments that explore their scale invariance, together with computer simulations that employ the Discrete Elastic Rods method. Excellent agreement is found between the two. Upon validation, the numerics are then used to systematically explore parameter space and identify general design principles for specific target final shapes. Our findings are rationalized using the theory of discrete Chebyshev nets, together with the group theory for crystals. Higher buckling modes occur for some configurations due to geometric incompatibility at the boundary and result in symmetry breaking. Along with the systematic classification of the various possible modes of deformation, we provide a reduced model that rationalizes form-finding in elastic gridshells. This work was done in collaboration with Changyeob Baek, Khalid Jawed and Andrew Sageman-Furnas. We are grateful to the NSF for funding (CAREER, CMMI-1351449).
In Situ elastic property sensors
International Nuclear Information System (INIS)
Olness, D.; Hirschfeld, T.; Kishiyama, K.; Steinhaus, R.
1987-01-01
Elasticity is an important property of many materials. Loss of elasticity can have serious consequences, such as when a gasket deteriorates and permits leakage of an expensive or hazardous material, or when a damping system begins to go awry. Loss of elasticity can also provide information related to an ancillary activity such as degradation of electrical insulation, loss of plasticizer in a plastic, or changes in permeability of a thin film. In fact, the mechanical properties of most organic compounds are altered when the compound degrades. Thus, a sensor for the mechanical properties can be used to monitor associated characteristics as well. A piezoelectric material in contact with an elastomer forms an oscillating system that can provide real-time elasticity monitoring. This combination constitutes a forced harmonic oscillator with damping provided by the elastomer. A ceramic oscillator with a total volume of a few mm 3 was used as an elasticity sensor. It was placed in intimate contact with an elastomer and then monitored remotely with a simple oscillator circuit and standard frequency counting electronics. Resonant frequency shifts and changes in Q value were observed corresponding to changes in ambient temperature and/or changes in pressure applied to the sample. Elastomer samples pretreated with ozone (to simulate aging) showed changes in Q value and frequency response, even though there were no visible changes in the elastic samples
DEFF Research Database (Denmark)
Thomsen, Jon Juel; Blekhman, Iliya I.
2007-01-01
What are the effective properties of a generally nonlinear material or structure, whose local properties are modulated in both space and time? It has been suggested to use spatiotemporal modulation of structural properties to create materials and structures with adjustable effective properties......, and to call these dynamic materials or spatiotemporal composites. Also, according to theoretical predictions, structural nonlinearity enhances the possibilities of achieving specific effective properties. For example, with an elastic rod having cubical elastic nonlinearities, it seems possible to control......, and exemplified. Then simple approximate analytical expressions are derived for the effective wave speed and natural frequencies for one-dimensional wave propagation in a nonlinear elastic rod, where the spatiotemporal modulation is imposed as a high-frequency standing wave, supposed to be given. Finally the more...
DEFF Research Database (Denmark)
Jacque, C M; Baumann, N A; Bock, E
1976-01-01
Seven antigens specific to the nervous tissue were measured in both Jimpy and control mice. The D5 and the GFA protein, both components of the glia, are strongly increased in the mutant while the neuronal components 14-3-2, synaptin C1, D1, D2 and D3 are unchanged....
DEFF Research Database (Denmark)
Treebak, Jonas Thue; Pehmøller, Christian; Kristensen, Jonas Møller
2014-01-01
We investigated the phosphorylation signatures of two Rab GTPase activating proteins TBC1D1 and TBC1D4 in human skeletal muscle in response to physical exercise and physiological insulin levels induced by a carbohydrate rich meal using a paired experimental design. Eight healthy male volunteers e...
Nonlinear acoustic/seismic waves in earthquake processes
International Nuclear Information System (INIS)
Johnson, Paul A.
2012-01-01
Nonlinear dynamics induced by seismic sources and seismic waves are common in Earth. Observations range from seismic strong ground motion (the most damaging aspect of earthquakes), intense near-source effects, and distant nonlinear effects from the source that have important consequences. The distant effects include dynamic earthquake triggering—one of the most fascinating topics in seismology today—which may be elastically nonlinearly driven. Dynamic earthquake triggering is the phenomenon whereby seismic waves generated from one earthquake trigger slip events on a nearby or distant fault. Dynamic triggering may take place at distances thousands of kilometers from the triggering earthquake, and includes triggering of the entire spectrum of slip behaviors currently identified. These include triggered earthquakes and triggered slow, silent-slip during which little seismic energy is radiated. It appears that the elasticity of the fault gouge—the granular material located between the fault blocks—is key to the triggering phenomenon.
Elastic-Plastic Calculation of a Dilatation Compensation Component
Atanasiu, Costică; Iliescu, Nicolae; Sorohan, Ștefan
2017-12-01
Compensators are elastic structures that have the role of taking over the axial displacements that occur in the junction areas of the technological equipment (pipelines or containers) through which the fluids circulate at pressures and high temperatures. These elastic structures, realized in a very wide range of shapes and sizes, are sujected by the inner pressure and an axial force produced by dilatation of structures in which they are mounted. The calculation of the expansion compensators raises many problems caused by the working regimes of the technological equipments they belong to. Following previous studies, undertaken by calculus and experimental, by the authors of this paper, it was found that in operation the state of stress in these elastic structures exceeds the flow limit of the material from which they are manufacturated. For this reason, in the present paper, the authors present the results of a calculus study, by FEM, on the stress and strain state, in the elasto-plastic regime of a leticular compensator. The calculation was made for two loading modes, separately applied and superimposed. The nonlinear mechanical behavior of this compensator is analyzed and discussed comparatively to the results of previous studies performed in elastic regime on the same type of compensator.
Elastic and Mechanical Properties of the MAX Phases
Barsoum, Michel W.; Radovic, Miladin
2011-08-01
The more than 60 ternary carbides and nitrides, with the general formula Mn+1AXn—where n = 1, 2, or 3; M is an early transition metal; A is an A-group element (a subset of groups 13-16); and X is C and/or N—represent a new class of layered solids, where Mn+1Xn layers are interleaved with pure A-group element layers. The growing interest in the Mn+1AXn phases lies in their unusual, and sometimes unique, set of properties that can be traced back to their layered nature and the fact that basal dislocations multiply and are mobile at room temperature. Because of their chemical and structural similarities, the MAX phases and their corresponding MX phases share many physical and chemical properties. In this paper we review our current understanding of the elastic and mechanical properties of bulk MAX phases where they differ significantly from their MX counterparts. Elastically the MAX phases are in general quite stiff and elastically isotropic. The MAX phases are relatively soft (2-8 GPa), are most readily machinable, and are damage tolerant. Some of them are also lightweight and resistant to thermal shock, oxidation, fatigue, and creep. In addition, they behave as nonlinear elastic solids, dissipating 25% of the mechanical energy during compressive cycling loading of up to 1 GPa at room temperature. At higher temperatures, they undergo a brittle-to-plastic transition, and their mechanical behavior is a strong function of deformation rate.
Mansoori Kermani, Maryam; Dehestani, Maryam
2018-06-01
We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell-Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.
Mansoori Kermani, Maryam; Dehestani, Maryam
2018-03-01
We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell-Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.
Janssen, E.J.G.; Milosevic, D.; Baltus, P.G.M.
2010-01-01
All RF circuits that incorporate active devices exhibit nonlinear behavior. Nonlinearities result in signal distortion, and therefore state the upper limit of the dynamic range of the circuits. A measure for linearity used quite commonly in RF is the P1dB and/or IP3 point. These quantities are
Temperature dependence of elastic properties of paratellurite
International Nuclear Information System (INIS)
Silvestrova, I.M.; Pisarevskii, Y.V.; Senyushenkov, P.A.; Krupny, A.I.
1987-01-01
New data are presented on the temperature dependence of the elastic wave velocities, elastic stiffness constants, and thermal expansion of paratellurite. It is shown that the external pressure appreciably influences the elastic properties of TeO 2 , especially the temperature dependence of the elastic modulus connected with the crystal soft mode. (author)
Nonlinear analysis of the GFRP material wheel hub
Directory of Open Access Journals (Sweden)
Dong Yun-Feng
2015-01-01
Full Text Available In this paper, the current bicycle wheel was replaced by the ones which composed by the wheel hub with Glassfiber Reinforced Plastic (alkali free thin-walled cylinder material, hereinafter referred to as GFRP material and the protective components made up of rubber outer pneumatic pad. With the help of the basic theory of elastic-plastic mechanics, the finite element “Nonlinear buckling” analysis of the wheel was carried out. The results show that the maximum elastic deformation of the wheel hub and the critical value of buckling failure load were restricted by the elasticity under the condition of external loads. Considering with the tensile strength and elastic modulus of the GFRP value of the material, it is demonstrated that the material is feasible to be used for wheel hub.
Nonlinearity in structural and electronic materials
International Nuclear Information System (INIS)
Bishop, A.R.; Beardmore, K.M.; Ben-Naim, E.
1997-01-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The project strengthens a nonlinear technology base relevant to a variety of problems arising in condensed matter and materials science, and applies this technology to those problems. In this way the controlled synthesis of, and experiments on, novel electronic and structural materials provide an important focus for nonlinear science, while nonlinear techniques help advance the understanding of the scientific principles underlying the control of microstructure and dynamics in complex materials. This research is primarily focused on four topics: (1) materials microstructure: growth and evolution, and porous media; (2) textures in elastic/martensitic materials; (3) electro- and photo-active polymers; and (4) ultrafast photophysics in complex electronic materials. Accomplishments included the following: organization of a ''Nonlinear Materials'' seminar series and international conferences including ''Fracture, Friction and Deformation,'' ''Nonequilibrium Phase Transitions,'' and ''Landscape Paradigms in Physics and Biology''; invited talks at international conference on ''Synthetic Metals,'' ''Quantum Phase Transitions,'' ''1996 CECAM Euroconference,'' and the 1995 Fall Meeting of the Materials Research Society; large-scale simulations and microscopic modeling of nonlinear coherent energy storage at crack tips and sliding interfaces; large-scale simulation and microscopic elasticity theory for precursor microstructure and dynamics at solid-solid diffusionless phase transformations; large-scale simulation of self-assembling organic thin films on inorganic substrates; analysis and simulation of smoothing of rough atomic surfaces; and modeling and analysis of flux pattern formation in equilibrium and nonequilibrium Josephson junction arrays and layered superconductors
Compact titanium dioxide waveguides with high nonlinearity at telecommunication wavelengths
DEFF Research Database (Denmark)
Guan, Xiaowei; Hu, Hao; Oxenløwe, Leif Katsuo
2018-01-01
.43 mu m(2)) and a low loss (5.4 +/- 1 dB/cm) at telecommunication wavelengths around 1550 nm have been fabricated and measured. A microring resonator having a 50 mu m radius has been measured to have a loaded quality factor of 53500. Four-wave mixing experiments reveal a nonlinear parameter...
Nonlinear amplitude dynamics in flagellar beating.
Oriola, David; Gadêlha, Hermes; Casademunt, Jaume
2017-03-01
The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.
Elastic-plastic transition: A universal law
Directory of Open Access Journals (Sweden)
Chen Zhong
2016-01-01
Full Text Available Although the initial stress-strain behavior in a tensile test is often characterized as linear elastic up to a yield stress and nonlinear plastic thereafter, the pre-yield transition region is known to exhibit significant curvature and hysteresis. Hundreds of high-precision loading-unloading-loading tensile tests were performed using 26 commercial sheet alloys exhibiting a wide range of strength, ductility and crystal structure. Analysis of the results reveals the following: 1.There is no significant linear elastic region; the proportional limit is ~0 MPa when measured with sufficient sensitivity. 2.Each of the hundreds of measured transitional stress-strain curves can be characterized by a single parameter, here called the “modulus reduction rate.”The corresponding equation captures ~80% of the observed variation, a factor of 3 to 6 better than a one-parameter linear approximation. 3.Most interestingly, the transitional behavior for all alloys follows a “Universal Law” requiring no fit parameters. The law depends only upon the strength of the material and its Young’s modulus, both of which are can be measured by independent tests or adopted from handbooks. The Universal Law captures ~90% of the variation represented by the one-parameter representation and eliminates the need for mechanical testing to implement and apply. The practical and theoretical implications of these results are discussed. The results provide a simple path to significantly improving applied constitutive models in the transitional regime. The consistency of the effect for such a wide range of metals and suggests that the origin of the behavior lies in the pile-up and relaxation of dislocation arrays.
The Morishima Gross elasticity of substitution
Blackorby, Charles; Primont, Daniel; Russell, R. Robert
2007-01-01
We show that the Hotelling-Lau elasticity of substitution, an extension of the Allen-Uzawa elasticity to allow for optimal output-quantity (or utility) responses to changes in factor prices, inherits all of the failings of the Allen-Uzawa elasticity identified by Blackorby and Russell [1989 AER]. An analogous extension of the Morishima elasticity of substitution to allow for output quantity changes preserves the salient properties of the original Hicksian notion of elasticity of substitution.
Nonlinear damage detection in composite structures using bispectral analysis
Ciampa, Francesco; Pickering, Simon; Scarselli, Gennaro; Meo, Michele
2014-03-01
Literature offers a quantitative number of diagnostic methods that can continuously provide detailed information of the material defects and damages in aerospace and civil engineering applications. Indeed, low velocity impact damages can considerably degrade the integrity of structural components and, if not detected, they can result in catastrophic failure conditions. This paper presents a nonlinear Structural Health Monitoring (SHM) method, based on ultrasonic guided waves (GW), for the detection of the nonlinear signature in a damaged composite structure. The proposed technique, based on a bispectral analysis of ultrasonic input waveforms, allows for the evaluation of the nonlinear response due to the presence of cracks and delaminations. Indeed, such a methodology was used to characterize the nonlinear behaviour of the structure, by exploiting the frequency mixing of the original waveform acquired from a sparse array of sensors. The robustness of bispectral analysis was experimentally demonstrated on a damaged carbon fibre reinforce plastic (CFRP) composite panel, and the nonlinear source was retrieved with a high level of accuracy. Unlike other linear and nonlinear ultrasonic methods for damage detection, this methodology does not require any baseline with the undamaged structure for the evaluation of the nonlinear source, nor a priori knowledge of the mechanical properties of the specimen. Moreover, bispectral analysis can be considered as a nonlinear elastic wave spectroscopy (NEWS) technique for materials showing either classical or non-classical nonlinear behaviour.
Analysis of elastic-plastic dynamic response of reinforced concrete frame structure
International Nuclear Information System (INIS)
Li Zhongcheng
2009-01-01
Based on a set of data from seismic response test on an R/C frame, a force-based R/C beam fibre model with non-linear material properties and bond-slip effects are presented firstly in this paper, and then the applications to the tested R/C frame are presented to illustrate the model characteristics and to show the accuracy of seismic analysis including consideration of non-linear factors. It can be concluded that the elastic-plastic analysis is a potential step toward the accurate modelling for the dynamic analyses of R/C structures. Especially for the seismic safety re-evaluation of the existing NPPs, the elastic-plastic methodology with consideration of different non-linearities should be involved. (author)
On the buckling of an elastic rotating beam
DEFF Research Database (Denmark)
Furta, Stanislaw D.; Kliem, Wolfhard; Pommer, Christian
1997-01-01
problem is integrated and this results in a second order differential equation of the Fuchs type, which allows an asymptotic expansion of the buckling equation. By means of Lyapunov and Chetaev functions, a rigorous proof is given that the loss of stability of the trivial equilibrium shape occurs for any......A nonlinear model is developed, which describes the buckling phenomena of an elastic beam clamped to the interior of a rotating wheel. We use a power series method to obtain an approximate expression of the buckling equation and compare this with previous results in the literature. The linearized...
Fully digital 1-D, 2-D and 3-D multiscroll chaos as hardware pseudo random number generators
Mansingka, Abhinav S.
2012-10-07
This paper introduces the first fully digital implementation of 1-D, 2-D and 3-D multiscroll chaos using the sawtooth nonlinearity in a 3rd order ODE with the Euler approximation. Systems indicate chaotic behaviour through phase space boundedness and positive Lyapunov exponent. Low-significance bits form a PRNG and pass all tests in the NIST SP. 800-22 suite without post-processing. Real-time control of the number of scrolls allows distinct output streams with 2-D and 3-D multiscroll chaos enabling greater controllability. The proposed PRNGs are experimentally verified on a Xilinx Virtex 4 FPGA with logic utilization less than 1.25%, throughput up to 5.25 Gbits/s and up to 512 distinct output streams with low cross-correlation.
Boundary modes in quasiperiodic elastic structures
Rosa, Matheus I. N.; Pal, Raj K.; Arruda, José R. F.; Ruzzene, Massimo
2018-03-01
Topological metamaterials are a new class of materials that support topological modes such as edge modes and interface modes, which are commonly immune to scattering and imperfections. This novelty has been the subject of extensive research in many branches of physics such as electronics, photonics, phononics, and acoustics. The nontrivial topological properties related to the presence of topological modes are tipically found in periodic media. However, it was recently demonstrated that structures called quasicrystals may also exhibit nontrivial topological behavior attributed to dimensions higher than that of the quasicrystal. While quasiperiodicity has received a lot of attention in the fields of crystallography and photonics, research into quasiperiodic elastic structures has been scarce. In this paper, we show how the concepts of quasiperiodicity may be applied to the design of topological mechanical metamaterials. We start by investigating the boundary modes present in quasiperiodic 1D phononic lattices. These modes have the interesting property of being localized at either one of the two different boundaries depending on the value of an additional parameter, which is remnant of the higher dimension. A smooth variation of this parameter in either time or a spatial dimension can lead to a robust transfer of energy between two sites of the structure. We present an idealized mechanical system composed by an array of coupled rods that may be used as a platform for realizing this kind of robust transfer of energy. These are preliminary investigations into a entirely new class of structures which may lead to novel engineering applications.
On Poisson Nonlinear Transformations
Directory of Open Access Journals (Sweden)
Nasir Ganikhodjaev
2014-01-01
Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.
A comparison of time-history elastic plastic piping analysis with measurement
International Nuclear Information System (INIS)
Scavuzzo, R.J.; Sansalone, K.H.
1992-01-01
The GE/ETEC Green piping system was subjected to high seismic inputs from hydraulic sleds at each pipe foundation. These inputs were high enough to force bending stresses into the plastic regime. Strain gages recorded the pipe response at various positions within the system. The ABAQUS finite element code was used to model this piping system and the dynamic input. Problems associated with the dynamic input are discussed. Various types of finite elements were evaluated for accurancy. Both an elastic time-history analysis and an elastic-plastic time-history analysis of the system were conducted. Results of these analyses are compared to each other and the experimental data. These comparisons indicated that elastic analysis of dynamic strains are conservative at all points of comparison and that there is good agreement between the nonlinear elastic-plastic analysis and experimental data. (orig.)
Elastic-wave generation in the evolution of displacement peaks
International Nuclear Information System (INIS)
Zhukov, V.P.; Boldin, A.A.
1988-01-01
This paper investigated the character of elastic shock wave generation and damping in irradiated materials along with the possibility of their long-range influence on the structure of the irradiated materials. Dispersion at the elastoplastic stage of atomic displacement peak development was taken into account. The three-dimensional nonlinear wave was described by an equation in the approximation of weak nonlinearity and weak spatial dispersion. Numerical modeling of the propagation of a plane shock wave in a crystal lattice was conducted. The distribution of the density and mass velocity of the material at the instant of complete damping of the plastic shock-wave component was determined. The appearance of solitary waves (solitons) at large amplitudes, localized in space, which propagate without distortion to arbitrary distances and retain their amplitude and form in interacting with one another, was investigated. Some physical consequences of the influence of solitary waves on the irradiated materials were considered
Phason elasticity and surface roughening
International Nuclear Information System (INIS)
Tang Leihan; Jaric, M.V.
1990-01-01
The phason elasticity of two-dimensional (2D) equilibrium quasicrystals is discussed in analogy with surface roughening phenomena. Taking a Penrose tiling model as an example, we show that the phason elastic energy is linear in the phason strain at zero temperature (T = 0), but becomes quadratic at any T > 0 and sufficiently small strain. Heuristic and real-space renormalization group arguments are given for the thermal roughening of the hyper-surface which represents quasicrystal tiling. Monte Carlo method is applied to illustrate the logarithmically diverging phason fluctuations and power-law diffraction intensities at T > 0. For three-dimensional systems, we present arguments which suggest a finite temperature transition between two quasicrystal phases, characterized by linear and quadratic phason elastic energy, respectively. (author). 17 refs, 12 figs
Appraisal of elastic follow up
International Nuclear Information System (INIS)
Roche, R.L.
1981-08-01
The aim of this paper is to provide indications to choose what fraction of a self limiting stress can be considered as secondary. At first, considerations are given to a simple structure which could be called ''creep relaxation tensile test''. A bar (with constant cross section) is loaded by an elastic spring in order to obtain a given elongation of the assembly. The stress evolution is studied. Then the creep damage is computed, and compared to the damage corresponding to the elastic computed stress. This comparison gives the fraction of the self limiting stress which must be considered as primary. This involve the structural parameter 0 which is the initial value of the ratio of elastic energy to dissipating power. Extension of the rule is made with the help of KACHANOV approximation. As a conclusion a procedure is described which determines what fraction of a self limiting stress must be considered as primary
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Investor response to consumer elasticity
International Nuclear Information System (INIS)
Grenaa Jensen, Stine; Meibom, Peter; Ravn, H.F.; Straarup, Sarah
2004-01-01
In the Nordic electricity system there is considerable uncertainty with respect to the long-term development in production capacity. The process towards liberalisation of the electricity sector started in a situation with a large reserve margin, but this margin is gradually vanishing. Since the potential investors in new production capacity are unaccustomed with investments under the new regime it is unknown if and when investments will take place. The electricity price is the key market signal to potential investors. The price is settled as a balance between supply and demand, and it is generally assumed that the demand side has an important role in this, and increasingly so. However, since consumers have not earlier had the incentive to respond to electricity prices, no reliable estimate of demand elasticity is known. The purpose of the present study is to analyse the role of electricity demand elasticity for investments in new electricity production capacity. Electricity price scenarios generated with a partial equilibrium model (Balmorel) are combined with a model of investment decisions. In this, various scenarios concerning the development in the demand elasticity are used. The simulated investment decisions are taken in a stochastic, dynamic setting, where a key point is the timing of the investment decision in relation to the gathering of new information relative to the stochastic elements. Based on this, the consequences of the development in consumer price elasticity for investments in a base load and a peak load plant are investigated. The main result of the analysis is that peak load investments can be made unprofitable by the development in consumer price elasticity, such that an investor will tend to wait with his peak load investment, until the development in consumer price elasticity has been revealed. (au)
CONFERENCE: Elastic and diffractive scattering
International Nuclear Information System (INIS)
White, Alan
1989-01-01
Elastic scattering, when particles appear to 'bounce' off each other, and the related phenomena of diffractive scattering are currently less fashionable than the study of hard scattering processes. However this could change rapidly if unexpected results from the UA4 experiment at the CERN Collider are confirmed and their implications tested. These questions were highlighted at the third 'Blois Workshop' on Elastic and Diffractive Scattering, held early in May on the Evanston campus of Northwestern University, near Chicago
International Nuclear Information System (INIS)
Gale, J.; Tiselj, I.
2002-01-01
One dimensional two-fluid six-equation model of two-phase flow, that can be found in computer codes like RELAP5, TRAC, and CATHARE, was upgraded with additional terms, which enable modelling of the pressure waves in elastic pipes. It is known that pipe elasticity reduces the propagation velocity of the shock and other pressure waves in the piping systems. Equations that include the pipe elasticty terms are used in WAHA code, which is being developed within the WAHALoads project of 5't'h EU research program.(author)
Subrahmanyam, Priyanka B; Carey, Gregory B; Webb, Tonya J
2014-09-01
NKT cells are a unique subset of T cells that recognize glycolipid Ags presented in the context of CD1d molecules. NKT cells mount strong antitumor responses and are a major focus in developing effective cancer immunotherapy. It is known that CD1d molecules are constantly internalized from the cell surface, recycled through the endocytic compartments, and re-expressed on the cell surface. However, little is known about the regulation of CD1d-mediated Ag processing and presentation in B cell lymphoma. Prosurvival factors of the Bcl-2 family, such as Bcl-xL, are often upregulated in B cell lymphomas and are intimately linked to sphingolipid metabolism, as well as the endocytic compartments. We hypothesized that Bcl-xL can regulate CD1d-mediated Ag presentation to NKT cells. We found that overexpression or induction of Bcl-xL led to increased Ag presentation to NKT cells. Conversely, the inhibition or knockdown of Bcl-xL led to decreased NKT cell activation. Furthermore, knockdown of Bcl-xL resulted in the loss of CD1d trafficking to lysosome-associated membrane protein 1(+) compartments. Rab7, a late endosomal protein, was upregulated and CD1d molecules accumulated in the Rab7(+) late endosomal compartment. These results demonstrate that Bcl-xL regulates CD1d-mediated Ag processing and presentation to NKT cells by altering the late endosomal compartment and changing the intracellular localization of CD1d. Copyright © 2014 by The American Association of Immunologists, Inc.
Hanamura, Eiichi; Yamanaka, Akio
2007-01-01
This graduate-level textbook gives an introductory overview of the fundamentals of quantum nonlinear optics. Based on the quantum theory of radiation, Quantum Nonlinear Optics incorporates the exciting developments in novel nonlinear responses of materials (plus laser oscillation and superradiance) developed over the past decade. It deals with the organization of radiation field, interaction between electronic system and radiation field, statistics of light, mutual manipulation of light and matter, laser oscillation, dynamics of light, nonlinear optical response, and nonlinear spectroscopy, as well as ultrashort and ultrastrong laser pulse. Also considered are Q-switching, mode locking and pulse compression. Experimental and theoretical aspects are intertwined throughout.
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Perturbation analysis of nonlinear matrix population models
Directory of Open Access Journals (Sweden)
Hal Caswell
2008-03-01
Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.
Bifurcation of elastic solids with sliding interfaces
Bigoni, D.; Bordignon, N.; Piccolroaz, A.; Stupkiewicz, S.
2018-01-01
Lubricated sliding contact between soft solids is an interesting topic in biomechanics and for the design of small-scale engineering devices. As a model of this mechanical set-up, two elastic nonlinear solids are considered jointed through a frictionless and bilateral surface, so that continuity of the normal component of the Cauchy traction holds across the surface, but the tangential component is null. Moreover, the displacement can develop only in a way that the bodies in contact do neither detach, nor overlap. Surprisingly, this finite strain problem has not been correctly formulated until now, so this formulation is the objective of the present paper. The incremental equations are shown to be non-trivial and different from previously (and erroneously) employed conditions. In particular, an exclusion condition for bifurcation is derived to show that previous formulations based on frictionless contact or `spring-type' interfacial conditions are not able to predict bifurcations in tension, while experiments-one of which, ad hoc designed, is reported-show that these bifurcations are a reality and become possible when the correct sliding interface model is used. The presented results introduce a methodology for the determination of bifurcations and instabilities occurring during lubricated sliding between soft bodies in contact.
Variation of nonlinearity parameter at low fundamental amplitudes
Barnard, Daniel J.
1999-04-01
Recent harmonic generation measurements of the nonlinearity parameter β in polycrystalline Cu-Al alloys have shown a transition to lower values at low fundamental amplitude levels. Values for β at high (>10 Å) fundamental levels are in the range predicted by single-crystal second- and third-order elastic constants while lower fundamental levels (alloy by others. The source of the effect is unclear but initial results may require a reexamination of current methods for measurement of third-order elastic constants.
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....
On the evaluation of elastic follow-up of a high temperature discontinuous structure
International Nuclear Information System (INIS)
Lee, J. M.; Kim, J. B.; Lee, H. Y.; Lee, J. H.
2003-01-01
While high temperature structures of LMR experience inelastic deformation such as plasticity and creep due to high temperature operating temperature of 530∼550 .deg. C, geometric nonlinear structures may undergo elastic follow-up behavior due to the interaction between stiff region and weak region. Thus, careful consideration should be given to the design and analysis of high temperature geometric nonlinear structure. In this study, the elastic follow-up behavior of geometric nonlinear structure has been investigated and the current status of design method implemented in the ASME-NH, Japanese BDS, French RCC-MR, and UK R-5 codes to consider elastic follow-up behavior has been reviewed. It has been shown that the ratio of the stiff region and the weak region and the type of loading affect the elastic follow-up behavior greatly from the detailed inelastic analyses of two bar model and L-shaped structure subjected to various loading situation. The applicability and the conservatism of simplified analysis methods implemented among various design codes need to be studied further
Elastic-plastic analysis using an efficient formulation of the finite element method
International Nuclear Information System (INIS)
Aamodt, B.; Mo, O.
1975-01-01
Based on the flow theory of plasticity, the von Mises or the Tresca yield criterion and the isotropic hardening law, an incremental stiffness relationship can be established for a finite element model of the elasto-plastic structure. However, instead of including all degrees of freedom and all finite elements of the total model in a nonlinear solution process, a separation of elastic and plastic parts of the structure can be carried out. Such a separation can be obtained by identifying elastic parts of the structure as 'elastic' superelements and elasto-plastic parts of the structure as 'elasto-plastic' superelements. Also, it may be of advantage to use several levels of superelements in modelling the elastic parts of the structure. For the 'elasto-plastic' superelements the specific plastic computations such as updating of the incremental stiffness matrix and subsequent reduction (i.e. static condensation of all degrees of freedom being local to the superelements) have to be carried out repeatedly during the nonlinear solution process. The solution of the nonlinear equations is performed utilizing a combination of load incrementation and equilibrium interations. The present method of analysis is demonstrated for two larger examples of elasto-plastic analysis. (Auth.)
Elastic-Plastic J-Integral Solutions or Surface Cracks in Tension Using an Interpolation Methodology
Allen, P. A.; Wells, D. N.
2013-01-01
No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear, three-dimensional nature of the problem. Traditionally, each surface crack must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 less than or equal to a/c less than or equal to 1, depth: 0.2 less than or equal to a/B less than or equal to 0.8) and material flow properties (elastic modulus-to-yield ratio: 100 less than or equal to E/ys less than or equal to 1,000, and hardening: 3 less than or equal to n less than or equal to 20). The authors have developed a methodology for interpolating between the goemetric and material property variables that allows the user to reliably evaluate the full elastic-plastic J-integral and force versus crack mouth opening displacement solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format.
Forming a complex with MHC class I molecules interferes with mouse CD1d functional expression.
Directory of Open Access Journals (Sweden)
Renukaradhya J Gourapura
Full Text Available CD1d molecules are structurally similar to MHC class I, but present lipid antigens as opposed to peptides. Here, we show that MHC class I molecules physically associate with (and regulate the functional expression of mouse CD1d on the surface of cells. Low pH (3.0 acid stripping of MHC class I molecules resulted in increased surface expression of murine CD1d on antigen presenting cells as well as augmented CD1d-mediated antigen presentation to NKT cells. Consistent with the above results, TAP1-/- mice were found to have a higher percentage of type I NKT cells as compared to wild type mice. Moreover, bone marrow-derived dendritic cells from TAP1-/- mice showed increased antigen presentation by CD1d compared to wild type mice. Together, these results suggest that MHC class I molecules can regulate NKT cell function, in part, by masking CD1d.
Directory of Open Access Journals (Sweden)
Lagerev I.A.
2016-03-01
Full Text Available The article considers the problems of designing an original damping devices worn for cylindrical hinges in crane-manipulating installations of mobile machines. These devices can significantly reduce the additional impact load on a steel structure manipulators due to the presence of increased gaps in the hinges. Formulated the general formulation of nonlinear constrained optimization of the sizes of the elastic elements of the damping devices. Considered a promising design variants of elastic elements. For circular and arc elastic elements with circular and rectangular cross-section for-mulated the problems of optimal design including criterion functions and systems of geometric, technological, stiffness and strength penalty constraints. Analysis of the impact of various operating and design parameters on the results of optimal design of elastic elements was performed. Were set to the recommended the use of the constructive types of elastic elements to generate the required stiffness of the damper devices.
Contraction regulates site-specific phosphorylation of TBC1D1 in skeletal muscle.
Vichaiwong, Kanokwan; Purohit, Suneet; An, Ding; Toyoda, Taro; Jessen, Niels; Hirshman, Michael F; Goodyear, Laurie J
2010-10-15
TBC1D1 (tre-2/USP6, BUB2, cdc16 domain family member 1) is a Rab-GAP (GTPase-activating protein) that is highly expressed in skeletal muscle, but little is known about TBC1D1 regulation and function. We studied TBC1D1 phosphorylation on three predicted AMPK (AMP-activated protein kinase) phosphorylation sites (Ser231, Ser660 and Ser700) and one predicted Akt phosphorylation site (Thr590) in control mice, AMPKα2 inactive transgenic mice (AMPKα2i TG) and Akt2-knockout mice (Akt2 KO). Muscle contraction significantly increased TBC1D1 phosphorylation on Ser231 and Ser660, tended to increase Ser700 phosphorylation, but had no effect on Thr590. AICAR (5-aminoimidazole-4-carboxyamide ribonucleoside) also increased phosphorylation on Ser231, Ser660 and Ser700, but not Thr590, whereas insulin only increased Thr590 phosphorylation. Basal and contraction-stimulated TBC1D1 Ser231, Ser660 and Ser700 phosphorylation were greatly reduced in AMPKα2i TG mice, although contraction still elicited a small increase in phosphorylation. Akt2 KO mice had blunted insulin-stimulated TBC1D1 Thr590 phosphorylation. Contraction-stimulated TBC1D1 Ser231 and Ser660 phosphorylation were normal in high-fat-fed mice. Glucose uptake in vivo was significantly decreased in tibialis anterior muscles overexpressing TBC1D1 mutated on four predicted AMPK phosphorylation sites. In conclusion, contraction causes site-specific phosphorylation of TBC1D1 in skeletal muscle, and TBC1D1 phosphorylation on AMPK sites regulates contraction-stimulated glucose uptake. AMPK and Akt regulate TBC1D1 phosphorylation, but there must be additional upstream kinases that mediate TBC1D1 phosphorylation in skeletal muscle.
Heart transplantation and arterial elasticity
Directory of Open Access Journals (Sweden)
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
Numerical determination of elastic positron- and electron-atom scattering phaseshifts
International Nuclear Information System (INIS)
Page, B.A.P.
1976-01-01
Numerical investigations of both the positron- and electron-hydrogen systems in the elastic scattering energy region are presented. For the positron-hydrogen system, modifications of the Kohn variational method are used in which the quantities etasub(v) and etasub(Q) are related to the trial wavefunction PSIsub(t) through integral expressions using approximations to the target wavefunction psi. The quantities etasub(v) and etasub(Q) become the Kohn elastic phaseshifts when the exact target wavefunction is used. From the results obtained for the positron-hydrogen system it is conjectured that if the values of either etasub(v) or etasub(Q) display a local maximum when all the nonlinear parameters of PSIsub(t) are varied, then this local maximum value is a good approximation to the Kohn elastic phaseshifts that would be obtained by replacing the approximate psi with the exact psi in the particular PSIsub(t) used in the calculations. Application of this procedure to the positron-helium elastic scattering system is given using Hylleraas-type approximations to the helium ground-state wavefunction. Both the positron- and electron-hydrogen systems are analysed in the elastic scattering energy region using a modified optical potential method. The results suggest that the local maximum value of the modified optical potential phaseshift when all the nonlinear parameters of PSIsub(t) are varied, is reasonably close to the normal optical potential phaseshift obtained when the exact psi is used. (author)
Exercise increases TBC1D1 phosphorylation in human skeletal muscle
Jessen, Niels; An, Ding; Lihn, Aina S.; Nygren, Jonas; Hirshman, Michael F.; Thorell, Anders
2011-01-01
Exercise and weight loss are cornerstones in the treatment and prevention of type 2 diabetes, and both interventions function to increase insulin sensitivity and glucose uptake into skeletal muscle. Studies in rodents demonstrate that the underlying mechanism for glucose uptake in muscle involves site-specific phosphorylation of the Rab-GTPase-activating proteins AS160 (TBC1D4) and TBC1D1. Multiple kinases, including Akt and AMPK, phosphorylate TBC1D1 and AS160 on distinct residues, regulating their activity and allowing for GLUT4 translocation. In contrast to extensive rodent-based studies, the regulation of AS160 and TBC1D1 in human skeletal muscle is not well understood. In this study, we determined the effects of dietary intervention and a single bout of exercise on TBC1D1 and AS160 site-specific phosphorylation in human skeletal muscle. Ten obese (BMI 33.4 ± 2.4, M-value 4.3 ± 0.5) subjects were studied at baseline and after a 2-wk dietary intervention. Muscle biopsies were obtained from the subjects in the resting (basal) state and immediately following a 30-min exercise bout (70% V̇o2 max). Muscle lysates were analyzed for AMPK activity and Akt phosphorylation and for TBC1D1 and AS160 phosphorylation on known or putative AMPK and Akt sites as follows: AS160 Ser711 (AMPK), TBC1D1 Ser231 (AMPK), TBC1D1 Ser660 (AMPK), TBC1D1 Ser700 (AMPK), and TBC1D1 Thr590 (Akt). The diet intervention that consisted of a major shift in the macronutrient composition resulted in a 4.2 ± 0.4 kg weight loss (P < 0.001) and a significant increase in insulin sensitivity (M value 5.6 ± 0.6), but surprisingly, there was no effect on expression or phosphorylation of any of the muscle-signaling proteins. Exercise increased muscle AMPKα2 activity but did not increase Akt phosphorylation. Exercise increased phosphorylation on AS160 Ser711, TBC1D1 Ser231, and TBC1D1 Ser660 but had no effect on TBC1D1 Ser700. Exercise did not increase TBC1D1 Thr590 phosphorylation or TBC1D1/AS160 PAS
The Planar Sandwich and Other 1D Planar Heat Flow Test Problems in ExactPack
Energy Technology Data Exchange (ETDEWEB)
Singleton, Jr., Robert [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-01-24
This report documents the implementation of several related 1D heat flow problems in the verification package ExactPack [1]. In particular, the planar sandwich class defined in Ref. [2], as well as the classes PlanarSandwichHot, PlanarSandwichHalf, and other generalizations of the planar sandwich problem, are defined and documented here. A rather general treatment of 1D heat flow is presented, whose main results have been implemented in the class Rod1D. All planar sandwich classes are derived from the parent class Rod1D.
A model of nonlinear strain and damage accumulation in polymer composites
Directory of Open Access Journals (Sweden)
A. N. Ruslantsev
2014-01-01
Full Text Available This paper presents a model to predict a nonlinear strain of the carbon laminate; the model is based on the relations between the theory of laminated plates and the non-linear approximation of deformation curve of unidirectional layer at the shear in the layer plane. The explicit expressions of stiffness and compliance matrices were obtained via multiplying the matrices that correspond to the elastic characteristics by the matrices, considering the non-linear properties of the laminate. The paper suggests an approximation option for the non-linear properties of the layer at the shear using an exponential function. Some considerations on damage accumulation in carbon laminates were made.
Dudar, O. I.; Dudar, E. S.
2017-11-01
The features of application of the 1D dimensional finite element method (FEM) in combination with the laminar solutions method (LSM) for the calculation of underground ventilating networks are considered. In this case the processes of heat and mass transfer change the properties of a fluid (binary vapour-air mix). Under the action of gravitational forces it leads to such phenomena as natural draft, local circulation, etc. The FEM relations considering the action of gravity, the mass conservation law, the dependence of vapour-air mix properties on the thermodynamic parameters are derived so that it allows one to model the mentioned phenomena. The analogy of the elastic and plastic rod deformation processes to the processes of laminar and turbulent flow in a pipe is described. Owing to this analogy, the guaranteed convergence of the elastic solutions method for the materials of plastic type means the guaranteed convergence of the LSM for any regime of a turbulent flow in a rough pipe. By means of numerical experiments the convergence rate of the FEM - LSM is investigated. This convergence rate appeared much higher than the convergence rate of the Cross - Andriyashev method. Data of other authors on the convergence rate comparison for the finite element method, the Newton method and the method of gradient are provided. These data allow one to conclude that the FEM in combination with the LSM is one of the most effective methods of calculation of hydraulic and ventilating networks. The FEM - LSM has been used for creation of the research application programme package “MineClimate” allowing to calculate the microclimate parameters in the underground ventilating networks.
Design of advanced materials for linear and nonlinear dynamics
DEFF Research Database (Denmark)
Frandsen, Niels Morten Marslev
to reveal the fundamental dynamic characteristics and thus the relevant design parameters.The thesis is built around the characterization of two one-dimensional, periodic material systems. The first is a nonlinear mass-spring chain with periodically varying material properties, representing a simple......The primary catalyst of this PhD project has been an ambition to design advanced materials and structural systems including, and possibly even exploiting, nonlinear phenomena such as nonlinear modal interaction leading to energy conversion between modes. An important prerequisite for efficient...... but general model of inhomogeneous structural materials with nonlinear material characteristics. The second material system is an “engineered” material in the sense that a classical structural element, a linear elastic and homogeneous rod, is “enhanced” by applying a mechanism on its surface, amplifying...
Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics
Yavari, Arash
2012-03-09
We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold-where the body is stress free-is a Weitzenböck manifold, that is, a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan\\'s moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields, assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance. © 2012 Springer-Verlag.
Nonlinear coherent structures in granular crystals
Chong, C.; Porter, Mason A.; Kevrekidis, P. G.; Daraio, C.
2017-10-01
The study of granular crystals, which are nonlinear metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures—which include traveling solitary waves, dispersive shock waves, and discrete breathers—have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research to date has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.
Fully coupled heat conduction and deformation analyses of visco-elastic solids
Khan, Kamran
2012-04-21
Visco-elastic materials are known for their capability of dissipating energy. This energy is converted into heat and thus changes the temperature of the materials. In addition to the dissipation effect, an external thermal stimulus can also alter the temperature in a viscoelastic body. The rate of stress relaxation (or the rate of creep) and the mechanical and physical properties of visco-elastic materials, such as polymers, vary with temperature. This study aims at understanding the effect of coupling between the thermal and mechanical response that is attributed to the dissipation of energy, heat conduction, and temperature-dependent material parameters on the overall response of visco-elastic solids. The non-linearly viscoelastic constitutive model proposed by Schapery (Further development of a thermodynamic constitutive theory: stress formulation, 1969,Mech. Time-Depend. Mater. 1:209-240, 1997) is used and modified to incorporate temperature- and stress-dependent material properties. This study also formulates a non-linear energy equation along with a dissipation function based on the Gibbs potential of Schapery (Mech. Time-Depend. Mater. 1:209-240, 1997). A numerical algorithm is formulated for analyzing a fully coupled thermo-visco-elastic response and implemented it in a general finite-element (FE) code. The non-linear stress- and temperature-dependent material parameters are found to have significant effects on the coupled thermo-visco-elastic response of polymers considered in this study. In order to obtain a realistic temperature field within the polymer visco-elastic bodies undergoing a non-uniform heat generation, the role of heat conduction cannot be ignored. © Springer Science+Business Media, B. V. 2012.
Hydro-elastic complementarity in black branes at large D
Energy Technology Data Exchange (ETDEWEB)
Emparan, Roberto [ICREA, Passeig Lluís Companys 23, E-08010 Barcelona (Spain); Departament de Física Fonamental, Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, E-08028 Barcelona (Spain); Izumi, Keisuke; Luna, Raimon [Departament de Física Fonamental, Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, E-08028 Barcelona (Spain); Suzuki, Ryotaku [Department of Physics, Osaka City University, Osaka 558-8585 (Japan); Tanabe, Kentaro [Theory Center, Institute of Particles and Nuclear Studies, KEK,Tsukuba, Ibaraki, 305-0801 (Japan)
2016-06-21
We obtain the effective theory for the non-linear dynamics of black branes — both neutral and charged, in asymptotically flat or Anti-deSitter spacetimes — to leading order in the inverse-dimensional expansion. We find that black branes evolve as viscous fluids, but when they settle down they are more naturally viewed as solutions of an elastic soap-bubble theory. The two views are complementary: the same variable is regarded in one case as the energy density of the fluid, in the other as the deformation of the elastic membrane. The large-D theory captures finite-wavelength phenomena beyond the conventional reach of hydrodynamics. For asymptotically flat charged black branes (either Reissner-Nordstrom or p-brane-charged black branes) it yields the non-linear evolution of the Gregory-Laflamme instability at large D and its endpoint at stable non-uniform black branes. For Reissner-Nordstrom AdS black branes we find that sound perturbations do not propagate (have purely imaginary frequency) when their wavelength is below a certain charge-dependent value. We also study the polarization of black branes induced by an external electric field.
Estimation of parameters of constant elasticity of substitution production functional model
Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi
2017-11-01
Nonlinear model building has become an increasing important powerful tool in mathematical economics. In recent years the popularity of applications of nonlinear models has dramatically been rising up. Several researchers in econometrics are very often interested in the inferential aspects of nonlinear regression models [6]. The present research study gives a distinct method of estimation of more complicated and highly nonlinear model viz Constant Elasticity of Substitution (CES) production functional model. Henningen et.al [5] proposed three solutions to avoid serious problems when estimating CES functions in 2012 and they are i) removing discontinuities by using the limits of the CES function and its derivative. ii) Circumventing large rounding errors by local linear approximations iii) Handling ill-behaved objective functions by a multi-dimensional grid search. Joel Chongeh et.al [7] discussed the estimation of the impact of capital and labour inputs to the gris output agri-food products using constant elasticity of substitution production function in Tanzanian context. Pol Antras [8] presented new estimates of the elasticity of substitution between capital and labour using data from the private sector of the U.S. economy for the period 1948-1998.
Collusion and the elasticity of demand
David Collie
2004-01-01
The analysis of collusion in infinitely repeated Cournot oligopoly games has generally assumed that demand is linear, but this note uses constant-elasticity demand functions to investigate how the elasticity of demand affects the sustainability of collusion.
Mechanical behaviour of nanoparticles: Elasticity and plastic ...
Indian Academy of Sciences (India)
2015-06-03
Jun 3, 2015 ... Mechanical behaviour of nanoparticles: Elasticity and plastic deformation mechanisms ... The main results in terms of elasticity and plastic deformation mechanisms are then reported ... Pramana – Journal of Physics | News.