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...

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.

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

Unraveling complex nonlinear elastic behaviors in rocks using dynamic acousto-elasticity

Science.gov (United States)

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.

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.

Phononic Crystal Waveguide Transducers for Nonlinear Elastic Wave Sensing.

Science.gov (United States)

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.

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

Manipulating acoustic wave reflection by a nonlinear elastic metasurface

Science.gov (United States)

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.

Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks

Science.gov (United States)

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.

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)

DYNAMICS OF VIBRATION FEEDERS WITH A NONLINEAR ELASTIC CHARACTERISTIC

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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

Nonlinear analysis of the GFRP material wheel hub

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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.

Mixing of two co-directional Rayleigh surface waves in a nonlinear elastic material.

Science.gov (United States)

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.

Adaptive, Small-Rotation-Based, Corotational Technique for Analysis of 2D Nonlinear Elastic Frames

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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.

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

A thermodynamic approach to nonlinear ultrasonics for material state awareness and prognosis

Science.gov (United States)

Chillara, Vamshi Krishna

2017-11-01

We develop a thermodynamic framework for modeling nonlinear ultrasonic damage sensing and prognosis in materials undergoing progressive damage. The framework is based on the internal variable approach and relies on the construction of a pseudo-elastic strain energy function that captures the energetics associated with the damage progression. The pseudo-elastic strain energy function is composed of two energy functions—one that describes how a material stores energy in an elastic fashion and the other describes how material dissipates energy or stores it in an inelastic fashion. Experimental motivation for the choice of the above two functionals is discussed and some specific choices pertaining to damage progression during fatigue and creep are presented. The thermodynamic framework is employed to model the nonlinear response of material undergoing stress relaxation and creep-like degradation. For each of the above cases, evolution of the nonlinearity parameter with damage as well as with macroscopic measurables like accumulated plastic strain is obtained.

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.

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...

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...

Mechanical characterization and non-linear elastic modeling of poly(glycerol sebacate) for soft tissue engineering.

Science.gov (United States)

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.

Non-linear elastic deformations

CERN Document Server

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.

Using strong nonlinearity and high-frequency vibrations to control effective properties of discrete elastic waveguides

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...

Nonlinear electroelastic deformations of dielectric elastomer composites: II - Non-Gaussian elastic dielectrics

Science.gov (United States)

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

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

A nonlinear approach of elastic reflection waveform inversion

KAUST Repository

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

KAUST Repository

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.

Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques.

Science.gov (United States)

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.

Nonlinear Elasticity

Science.gov (United States)

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.

A nonlinear theory for elastic plates with application to characterizing paper properties

Science.gov (United States)

M. W. Johnson; Thomas J. Urbanik

1984-03-01

A theory of thin plates which is physically as well as kinematically nonlinear is, developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a...

Nonlinear surface elastic modes in crystals

Science.gov (United States)

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.

Elastic reflection based waveform inversion with a nonlinear approach

KAUST Repository

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.

Elastic reflection based waveform inversion with a nonlinear approach

KAUST Repository

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.

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.

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.

Non-linear theory of elasticity and optimal design

CERN Document Server

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

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 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.

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.

A method for determination of X-ray elastic constants of materials showing non-linear sin2ψ diagrams and its application to Zn-Ni-alloy electroplate

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)

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)

On the geometrically nonlinear elastic response of class θ = 1 tensegrity prisms

Science.gov (United States)

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.

Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions

Science.gov (United States)

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

Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies

Science.gov (United States)

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.

Analysis of the elastic behaviour of nonclassical nonlinear mesoscopic materials in quasi-static experiments

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

Postbuckling of magneto-electro-elastic CNT-MT composite nanotubes resting on a nonlinear elastic medium in a non-uniform thermal environment

Science.gov (United States)

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.

Composite Beam Theory with Material Nonlinearities and Progressive Damage

Science.gov (United States)

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

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....

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...

Nonlinear elastic inclusions in isotropic solids

KAUST Repository

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.

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

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 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

A general 3-D nonlinear magnetostrictive constitutive model for soft ferromagnetic materials

International Nuclear Information System (INIS)

Zhou Haomiao; Zhou Youhe; Zheng Xiaojing; Ye Qiang; Wei Jing

2009-01-01

In this paper, a new general nonlinear magnetostrictive constitutive model is proposed for soft ferromagnetic materials, and it can predict magnetostrictive strain and magnetization curves under various pre-stresses. From the viewpoint of magnetic domain, it is based on the important physical fact that a nonlinear part of the elastic strain produced by magnetic domain wall motion under a pre-stress is responsible for the change of the maximum magnetostrictive strain in accordance with the pre-stress. Then the reduction of magnetostrictive strain from the maximum is caused by the domain rotation. Meanwhile, the magnetization under various pre-stresses in this model is introduced by magnetostrictive effect under the same pre-stress. A simplified 3-D model is put forward by means of linearizing the nonlinear function, i.e. the nonlinear part of the elastic strain produced by domain wall motion, and by using the quartic of magnetization to describe domain rotation. Besides, for the convenience of engineering applications, two-dimensional (plate or film) and one-dimensional (rod) models are also given for isotropic materials and their application ranges are discussed too. In comparison with the experimental data of Kuruzar and Jiles, it is found that this model can predict magnetostrictive strain and magnetization curves under various pre-stresses. The numerical simulation further illustrates that the new model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves. Additionally, this model can be degenerated to the existing magnetostrictive constitutive model for giant magnetostrictive materials (GMM), i.e. a special soft ferromagnetic material

Special discontinuities in nonlinearly elastic media

Science.gov (United States)

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.

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_pR = 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.

Non-linear theory of elasticity

CERN Document Server

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.

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.

Ultrasound Shear Wave Simulation of Breast Tumor Using Nonlinear Tissue Elasticity.

Science.gov (United States)

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 reflection of shock shear waves in soft elastic media.

Science.gov (United States)

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.

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, 2.799nonlinear Schroedinger equation is no longer valid. In this case, another system of equations is derived, which governs both the wave amplitudes involved in this resonance between the fundamental torsional and its second-harmonic longitudinal modes.

Geometric Structure-Preserving Discretization Schemes for Nonlinear Elasticity

Science.gov (United States)

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

Influence of quantum confinement on the carrier contribution to the elastic constants in quantum confined heavily doped non-linear optical and optoelectronic materials: simplified theory and the suggestion for experimental determination

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-linear optical measurement of the twist elastic constant in thermotropic and DNA lyotropic chiral nematics.

Science.gov (United States)

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.

Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

KAUST Repository

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

Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).

Science.gov (United States)

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.

Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution

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.

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 ...

Free-vibration acoustic resonance of a nonlinear elastic bar

Science.gov (United States)

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.

A novel nonlinear damage resonance intermodulation effect for structural health monitoring

Science.gov (United States)

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.

Experimental and theoretical studies of spectral alteration in ultrasonic waves resulting from nonlinear elastic response in rock

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.

Experimental and theoretical studies of spectral alteration in ultrasonic waves resulting from nonlinear elastic response in rock

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

Non-linear optical materials

CERN Document Server

Saravanan, R

2018-01-01

Non-linear optical materials have widespread and promising applications, but the efforts to understand the local structure, electron density distribution and bonding is still lacking. The present work explores the structural details, the electron density distribution and the local bond length distribution of some non-linear optical materials. It also gives estimation of the optical band gap, the particle size, crystallite size, and the elemental composition from UV-Visible analysis, SEM, XRD and EDS of some non-linear optical materials respectively.

Solution of problems with material nonlinearities with a coupled finite element/boundary element scheme using an iterative solver. Yucca Mountain Site Characterization Project

International Nuclear Information System (INIS)

Koteras, J.R.

1996-01-01

The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region

Geometrically Nonlinear Static Analysis of Edge Cracked Timoshenko Beams Composed of Functionally Graded Material

Directory of Open Access Journals (Sweden)

Şeref Doğuşcan Akbaş

2013-01-01

Full Text Available Geometrically nonlinear static analysis of edge cracked cantilever Timoshenko beams composed of functionally graded material (FGM subjected to a nonfollower transversal point load at the free end of the beam is studied with large displacements and large rotations. Material properties of the beam change in the height direction according to exponential distributions. The cracked beam is modeled as an assembly of two subbeams connected through a massless elastic rotational spring. In the study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The convergence study is performed for various numbers of finite elements. In the study, the effects of the location of crack, the depth of the crack, and various material distributions on the nonlinear static response of the FGM beam are investigated in detail. Also, the difference between the geometrically linear and nonlinear analysis of edge cracked FGM beam is investigated in detail.

Energy-momentum conserving higher-order time integration of nonlinear dynamics of finite elastic fiber-reinforced continua

Science.gov (United States)

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.

Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study

KAUST Repository

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

KAUST Repository

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.

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope.

Science.gov (United States)

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.

Extremal Overall Elastic Response of Polycrystalline Materials

DEFF Research Database (Denmark)

Bendsøe, Martin P; Lipton, Robert

1996-01-01

Polycrystalline materials comprised of grains obtained froma single anisotropic material are considered in the frameworkof linear elasticity. No assumptions on the symmetry of thepolycrystal are made. We subject the material to independentexternal strain and stress fields with prescribed mean...... values.We show that the extremal overall elastic response is alwaysachieved by a configuration consisting of a single properlyoriented crystal. This result is compared to results for isotropicpolycrystals....

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

Science.gov (United States)

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.

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

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

Science.gov (United States)

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.

On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation

NARCIS (Netherlands)

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

Modeling Non-Linear Material Properties in Composite Materials

Science.gov (United States)

2016-06-28

Technical Report ARWSB-TR-16013 MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS Michael F. Macri Andrew G...REPORT TYPE Technical 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS ...systems are increasingly incorporating composite materials into their design. Many of these systems subject the composites to environmental conditions

Using nonlinearity and spatiotemporal property modulation to control effective structural properties: dynamic rods

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...

The elastic response of composite materials

International Nuclear Information System (INIS)

Laws, N.

1980-01-01

The theory of linear elasticity is used to study the elastic response of composite materials. The main concern is the prediction of overall moduli. Some attention is paid to the problem of deciding upon when the idea of an overall modulus is meaningful. In addition it is shown how to calculate some rigorous bounds on the overall moduli, and some predictions of the self-consistent method are discussed. The paper mainly concentrates on isotropic dispersions of spheres, unidirectional fibre-reinforced materials and laminates. (author)

Cavity nonlinear optics with layered materials

Directory of Open Access Journals (Sweden)

Fryett Taylor

2017-12-01

Full Text Available Unprecedented material compatibility and ease of integration, in addition to the unique and diverse optoelectronic properties of layered materials, have generated significant interest in their utilization in nanophotonic devices. While initial nanophotonic experiments with layered materials primarily focused on light sources, modulators, and detectors, recent efforts have included nonlinear optical devices. In this paper, we review the current state of cavity-enhanced nonlinear optics with layered materials. Along with conventional nonlinear optics related to harmonic generation, we report on emerging directions of nonlinear optics, where layered materials can potentially play a significant role.

Fully coupled heat conduction and deformation analyses of visco-elastic solids

KAUST Repository

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.

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

On the use of elastic-plastic material characteristics for linear-elastic component assessments

International Nuclear Information System (INIS)

Kussmaul, K.; Silcher, H.; Eisele, U.

1995-01-01

In this paper the procedure of safety assessment of components by fracture mechanics analysis as recommended in TECDOC 717 is applied to two standard specimens of ductile cast iron. It is shown that the use of a pseudo-elastic K IJ -value in linear elastic safety analysis may lead to non-conservative results, when elastic-plastic material behaviour can be expected. (author)

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

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.

Nonlinear free vibration analysis of elastically supported carbon nanotube-reinforced composite beam with the thermal environment in non-deterministic framework

Directory of Open Access Journals (Sweden)

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.

Nonlinear elastic longitudinal strain-wave propagation in a plate with nonequilibrium laser-generated point defects

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

Elastic properties of synthetic materials for soft tissue modeling

International Nuclear Information System (INIS)

Mansy, H A; Grahe, J R; Sandler, R H

2008-01-01

Mechanical models of soft tissue are useful for studying vibro-acoustic phenomena. They may be used for validating mathematical models and for testing new equipment and techniques. The objective of this study was to measure density and visco-elastic properties of synthetic materials that can be used to build such models. Samples of nine different materials were tested under dynamic (0.5 Hz) compressive loading conditions. The modulus of elasticity of the materials was varied, whenever possible, by adding a softener during manufacturing. The modulus was measured over a nine month period to quantify the effect of ageing and softener loss on material properties. Results showed that a wide range of the compression elasticity modulus (10 to 1400 kPa) and phase (3.5 0 -16.7 0 ) between stress and strain were possible. Some materials tended to exude softener over time, resulting in a weight loss and elastic properties change. While the weight loss under normal conditions was minimal in all materials (<3% over nine months), loss under accelerated weight-loss conditions can reach 59%. In the latter case an elasticity modulus increase of up to 500% was measured. Key advantages and limitations of candidate materials were identified and discussed

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.

Fundamentals of nonlinear optical materials

Indian Academy of Sciences (India)

Nonlinear optics; nonlinear polarization; optical fiber communication; optical switch- ing. PACS Nos 42.65Tg; ... The importance of nonlinear optics is to understand the nonlinear behavior in the induced polarization and to ..... but much work in material development and characterization remains to be done. 16. Conclusion.

Continuum mechanics elasticity, plasticity, viscoelasticity

CERN Document Server

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...

Optimal determination of the elastic constants of composite materials from ultrasonic wave-speed measurements

Science.gov (United States)

Castagnède, Bernard; Jenkins, James T.; Sachse, Wolfgang; Baste, Stéphane

1990-03-01

A method is described to optimally determine the elastic constants of anisotropic solids from wave-speeds measurements in arbitrary nonprincipal planes. For such a problem, the characteristic equation is a degree-three polynomial which generally does not factorize. By developing and rearranging this polynomial, a nonlinear system of equations is obtained. The elastic constants are then recovered by minimizing a functional derived from this overdetermined system of equations. Calculations of the functional are given for two specific cases, i.e., the orthorhombic and the hexagonal symmetries. Some numerical results showing the efficiency of the algorithm are presented. A numerical method is also described for the recovery of the orientation of the principal acoustical axes. This problem is solved through a double-iterative numerical scheme. Numerical as well as experimental results are presented for a unidirectional composite material.

Modeling dynamic acousto-elastic testing experiments: validation and perspectives.

Science.gov (United States)

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.

Variational principles for nonlinear piezoelectric materials

Energy Technology Data Exchange (ETDEWEB)

Rodriguez-Ramos, R.; Guinovart-Diaz, R. [Universidad de la Habana, Facultad de Matematica y Computacion, Vedado, Habana (Cuba); Pobedria, B.E. [Moscow State University M. V. Lomonosov, Composites Department, Moscow (Russian Federation); Padilla, P. [Universidad Nacional Autonoma de Mexico, Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas (IIMAS), Cd. Universitaria, Mexico D.F. (Mexico); Bravo-Castillero, J. [Universidad de la Habana, Facultad de Matematica y Computacion, Vedado, Habana (Cuba); Campus Estado de Mexico. Division de Arquitectura e Ingenieria, Instituto Tecnologico de Estudios Superiores de Monterrey, Atizapan de Zaragoza, Estado de Mexico (Mexico); Maugin, G.A. [Universite Pierre et Marie Curie. Case 162, UMR 7607 CNRS, Laboratoire de Modelisation en Mecanique, Paris Cedex 05 (France)

2004-12-01

In the present paper, we consider the behavior of nonlinear piezoelectric materials by generalization for this case of the Hashin-Shtrikman variational principles. The new general formulation used here differs from others, because, it gives the possibility to evaluate the upper and lower Hashin-Shtrikman bounds for specific physical nonlinearities of piezoelectric materials. Geometrical nonlinearities are not considered. (orig.)

Nonlinear Modeling and Identification of an Aluminum Honeycomb Panel with Multiple Bolts

Directory of Open Access Journals (Sweden)

Yongpeng Chu

2016-01-01

Full Text Available This paper focuses on the nonlinear dynamics modeling and parameter identification of an Aluminum Honeycomb Panel (AHP with multiple bolted joints. Finite element method using eight-node solid elements is exploited to model the panel and the bolted connection interface as a homogeneous, isotropic plate and as a thin layer of nonlinear elastic-plastic material, respectively. The material properties of a thin layer are defined by a bilinear elastic plastic model, which can describe the energy dissipation and softening phenomena in the bolted joints under nonlinear states. Experimental tests at low and high excitation levels are performed to reveal the dynamic characteristics of the bolted structure. In particular, the linear material parameters of the panel are identified via experimental tests at low excitation levels, whereas the nonlinear material parameters of the thin layer are updated by using the genetic algorithm to minimize the residual error between the measured and the simulation data at a high excitation level. It is demonstrated by comparing the frequency responses of the updated FEM and the experimental system that the thin layer of bilinear elastic-plastic material is very effective for modeling the nonlinear joint interface of the assembled structure with multiple bolts.

A 2D nonlinear multiring model for blood flow in large elastic arteries

Science.gov (United States)

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.

Extremal Overall Elastic Response of Polycrystalline Materials

DEFF Research Database (Denmark)

Bendsøe, Martin P; Lipton, Robert

1997-01-01

Polycrystalline materials comprised of grains obtained from a single anisotropic material are considered in the framework of linear elasticity. No assumptions on the symmetry of the polycrystal are made. We subject the material to independent external strain and stress fields with prescribed mean...

Geometric method for stability of non-linear elastic thin shells

CERN Document Server

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...

Non-linear elasticity of extracellular matrices enables contractile cells to communicate local position and orientation.

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.

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

Electrodynamic soil plate oscillator: Modeling nonlinear mesoscopic elastic behavior and hysteresis in nonlinear acoustic landmine detection

Science.gov (United States)

Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.

2015-10-01

significant curvature when the soil particle velocity is relatively higher. An oscillator with hysteresis modeled by a distribution of parallel spring elements each with a different threshold slip condition seems to describe fairly linear backbone curve behavior [W. D. Iwan, Transactions of the ASME, J. of Applied Mech., 33,(1966), 893-900], while a single bilinear hysteresis element describes the backbone curvature results in the experiments reported here [T. K. Caughey, Transactions of the ASME, J. of Applied Mech., 27, (1960), 640-643]. When "off target" resonances have a different backbone curvature than "on the mine" backbone curves, then false alarms may be eliminated due to resonances from the natural soil layering. See [R. A. Guyer, J. TenCate, and P. Johnson, "Hysteresis and the Dynamic Elasticity of Consolidated Granular Materials," Phys. Rev. Lett., 82, 16 (1999), 3280-3283] for recent models of nonlinear mesoscopic behavior.

Elasticity of fractal materials using the continuum model with non-integer dimensional space

Science.gov (United States)

Tarasov, Vasily E.

2015-01-01

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

Nonlinear elastic properties of superconducting antiperovskites MNNi 3 (M =Zn, Cd, Mg, Al, Ga, and In) from first principles

KAUST Repository

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.

Nonlinear elastic properties of superconducting antiperovskites MNNi 3 (M =Zn, Cd, Mg, Al, Ga, and In) from first principles

KAUST Repository

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.

Observation of elastic topological states in soft materials.

Science.gov (United States)

Li, Shuaifeng; Zhao, Degang; Niu, Hao; Zhu, Xuefeng; Zang, Jianfeng

2018-04-10

Topological elastic metamaterials offer insight into classic motion law and open up opportunities in quantum and classic information processing. Theoretical modeling and numerical simulation of elastic topological states have been reported, whereas the experimental observation remains relatively unexplored. Here we present an experimental observation and numerical simulation of tunable topological states in soft elastic metamaterials. The on-demand reversible switch in topological phase has been achieved by changing filling ratio, tension, and/or compression of the elastic metamaterials. By combining two elastic metamaterials with distinct topological invariants, we further demonstrate the formation and dynamic tunability of topological interface states by mechanical deformation, and the manipulation of elastic wave propagation. Moreover, we provide a topological phase diagram of elastic metamaterials under deformation. Our approach to dynamically control interface states in soft materials paves the way to various phononic systems involving thermal management and soft robotics requiring better use of energy.

Nonlinear and Nonequilibrium Dynamics in Geomaterials

OpenAIRE

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...

Introduction to nonlinear finite element analysis

CERN Document Server

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 ·    ...

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

Radiation processed composite materials of wood and elastic polyester resins

International Nuclear Information System (INIS)

Tapolcai, I.; Czvikovszky, T.

1983-01-01

The radiation polymerization of multifunctional unsaturated polyester-monomer mixtures in wood forms interpenetrating network system. The mechanical resistance (compression, abrasion, hardness, etc.) of these composite materials are generally well over the original wood, however the impact strength is almost the same or even reduced, in comparison to the wood itself. An attempt is made using elastic polyester resins to produced wood-polyester composite materials with improved modulus of elasticity and impact properties. For the impregnation of European beech wood two types of elastic unsaturated polyester resins were used. The exothermic effect of radiation copolymerization of these resins in wood has been measured and the dose rate effects as well as hardening dose was determined. Felxural strength and impact properties were examined. Elastic unsaturated polyester resins improved the impact strength of wood composite materials. (author)

Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

KAUST Repository

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.

A Study of Nonlinear Elasticity Effects on Permeability of Stress Sensitive Shale Rocks Using an Improved Coupled Flow and Geomechanics Model: A Case Study of the Longmaxi Shale in China

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.

Nonlinear ultrasonics for material state awareness

Science.gov (United States)

Jacobs, L. J.

2014-02-01

Predictive health monitoring of structural components will require the development of advanced sensing techniques capable of providing quantitative information on the damage state of structural materials. By focusing on nonlinear acoustic techniques, it is possible to measure absolute, strength based material parameters that can then be coupled with uncertainty models to enable accurate and quantitative life prediction. Starting at the material level, this review will present current research that involves a combination of sensing techniques and physics-based models to characterize damage in metallic materials. In metals, these nonlinear ultrasonic measurements can sense material state, before the formation of micro- and macro-cracks. Typically, cracks of a measurable size appear quite late in a component's total life, while the material's integrity in terms of toughness and strength gradually decreases due to the microplasticity (dislocations) and associated change in the material's microstructure. This review focuses on second harmonic generation techniques. Since these nonlinear acoustic techniques are acoustic wave based, component interrogation can be performed with bulk, surface and guided waves using the same underlying material physics; these nonlinear ultrasonic techniques provide results which are independent of the wave type used. Recent physics-based models consider the evolution of damage due to dislocations, slip bands, interstitials, and precipitates in the lattice structure, which can lead to localized damage.

Interface effects on effective elastic moduli of nanocrystalline materials

International Nuclear Information System (INIS)

Wang Gangfeng; Feng Xiqiao; Yu Shouwen; Nan Cewen

2003-01-01

Interfaces often play a significant role in many physical properties and phenomena of nanocrystalline materials (NcMs). In the present paper, the interface effects on the effective elastic property of NcMs are investigated. First, an atomic potential method is suggested for estimating the effective elastic modulus of an interface phase. Then, the Mori-Tanaka effective field method is employed to determine the overall effective elastic moduli of a nanocrystalline material, which is regarded as a binary composite consisting of a crystal or inclusion phase with regular lattice connected by an amorphous-like interface or matrix phase. Finally, the stiffening effects of strain gradients are examined on the effective elastic property by using the strain gradient theory to analyze a representative unit cell. Our analysis shows two physical mechanisms of interfaces that influence the effective stiffness and other mechanical properties of materials. One is the softening effect due to the distorted atomic structures and the increased atomic spacings in interface regions, and another is the baffling effect due to the existence of boundary layers between the interface phase and the crystalline phase

Development of a Tomography Technique for Assessment of the Material Condition of Concrete Using Optimized Elastic Wave Parameters

Directory of Open Access Journals (Sweden)

Hwa Kian Chai

2016-04-01

Full Text Available Concrete is the most ubiquitous construction material. Apart from the fresh and early age properties of concrete material, its condition during the structure life span affects the overall structural performance. Therefore, development of techniques such as non-destructive testing which enable the investigation of the material condition, are in great demand. Tomography technique has become an increasingly popular non-destructive evaluation technique for civil engineers to assess the condition of concrete structures. In the present study, this technique is investigated by developing reconstruction procedures utilizing different parameters of elastic waves, namely the travel time, wave amplitude, wave frequency, and Q-value. In the development of algorithms, a ray tracing feature was adopted to take into account the actual non-linear propagation of elastic waves in concrete containing defects. Numerical simulation accompanied by experimental verifications of wave motion were conducted to obtain wave propagation profiles in concrete containing honeycomb as a defect and in assessing the tendon duct filling of pre-stressed concrete (PC elements. The detection of defects by the developed tomography reconstruction procedures was evaluated and discussed.

Compatible-strain mixed finite element methods for incompressible nonlinear elasticity

Science.gov (United States)

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.

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)

Application of Nonlinear Elastic Resonance Spectroscopy For Damage Detection In Concrete: An Interesting Story

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.

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

Formulation of stiffness equation for a three-dimensional isoparametric element with elastic-plastic material and large deformation

International Nuclear Information System (INIS)

Chang, T.Y.; Prachuktam, S.; Reich, M.

1975-01-01

The formulation of the stiffness equation for an 8 to 21 node isoparametric element with elastic-plastic material and large deformation is presented. The formulation has been implemented in a nonlinear finite element program for the analysis of three-dimensional continuums. To demonstrate the utility of the formulation, a thick-walled cylinder was analyzed and the results are compared favorably with a known solution. The element type presented can be applied not only to 3-D continuums, but also to plate or shell structures, for which degenerated isoparametric elements may be used

Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

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.

Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

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

Non-linear waves in heterogeneous elastic rods via homogenization

KAUST Repository

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.

Method of determining elastic and plastic mechanical properties of ceramic materials using spherical indenters

Science.gov (United States)

Adler, Thomas A.

1996-01-01

The invention pertains a method of determining elastic and plastic mechanical properties of ceramics, intermetallics, metals, plastics and other hard, brittle materials which fracture prior to plastically deforming when loads are applied. Elastic and plastic mechanical properties of ceramic materials are determined using spherical indenters. The method is most useful for measuring and calculating the plastic and elastic deformation of hard, brittle materials with low values of elastic modulus to hardness.

Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

KAUST Repository

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.

Propagation law of impact elastic wave based on specific materials

Directory of Open Access Journals (Sweden)

Chunmin CHEN

2017-02-01

Full Text Available In order to explore the propagation law of the impact elastic wave on the platform, the experimental platform is built by using the specific isotropic materials and anisotropic materials. The glass cloth epoxy laminated plate is used for anisotropic material, and an organic glass plate is used for isotropic material. The PVDF sensors adhered on the specific materials are utilized to collect data, and the elastic wave propagation law of different thick plates and laminated plates under impact conditions is analyzed. The Experimental results show that in anisotropic material, transverse wave propagation speed along the fiber arrangement direction is the fastest, while longitudinal wave propagation speed is the slowest. The longitudinal wave propagation speed in anisotropic laminates is much slower than that in the laminated thick plates. In the test channel arranged along a particular angle away from the central region of the material, transverse wave propagation speed is larger. Based on the experimental results, this paper proposes a material combination mode which is advantageous to elastic wave propagation and diffusion in shock-isolating materials. It is proposed to design a composite material with high acoustic velocity by adding regularly arranged fibrous materials. The overall design of the barrier material is a layered structure and a certain number of 90°zigzag structure.

FRICTION ANALYSIS ON SCRATCH DEFORMATION MODES OF VISCO-ELASTIC-PLASTIC MATERIALS

Directory of Open Access Journals (Sweden)

Budi Setiyana

2013-11-01

Full Text Available Understanding of abrasion resistance and associated surfaces deformation mechanisms is of primary importance in materials engineering and design. Instrumented scratch testing has proven to be a useful tool for characterizing the abrasion resistance of materials. Using a conical indenter in a scratch test may result in different deformation modes, like as elastic deformation, ironing, ductile ploughing and cutting. This paper presents the friction analysis of some deformation modes of visco-elastic-plastic behaving polymer materials, especially PEEK (poly ether ether ketone.In general, it is accepted that the friction consist of an adhesion and a deformation component, which can be assumed to be independent to each others. During a scratch test, the friction coefficient is influenced by some parameters, such as the sharpness of indenter, the deformation modes and the degree of elastic recovery. Results show that the adhesion component strongly influences the friction in the elastic and ironing deformation mode (scratching with a blunt cone, friction for the cutting deformation mode (scratching with a sharp cone is dominantly influenced by the deformation component. From the analysis, it can be concluded that the adhesion friction model is suitable for ironing - elastic deformation mode and the deformation friction model with elastic recovery is good for cutting mode. Moreover, the ductile ploughing mode is combination of the adhesion and plastic deformation friction model. ANALISIS FRIKSI PADA BENTUK DEFORMASI AKIBAT GORESAN PADA MATERIAL VISKO-ELASTIK-PLASTIK. Pemahaman tentang ketahanan abrasi dan deformasi permukaan  yang  menyertainya merupakan hal yang penting dalam rekayasa dan disain material. Peralatan uji gores terbukti ampuh untuk menyatakan ketahanan abrasi dari material. Pemakaian indenter kerucut dalam uji gores akan menghasilkan beberapa bentuk deformasi seperti halnya deformasi elastik, penyetrikaan, plowing dan pemotongan

Nonlinear optics of liquid crystalline materials

International Nuclear Information System (INIS)

Khoo, Iam Choon

2009-01-01

Liquid crystals occupy an important niche in nonlinear optics as a result of their unique physical and optical properties. Besides their broadband birefringence and transparency, abilities to self-assemble into various crystalline phases and to conform to various flexible forms and shapes, liquid crystals are compatible with almost all other optoelectronic materials and technology platforms. In both isotropic and ordered phases, liquid crystals possess extraordinarily large optical nonlinearities that stretch over multiple time scales. To date, almost all conceivable nonlinear optical phenomena have been observed in a very broad spectrum spanning the entire visible to infrared and beyond. In this review, we present a self-contained complete discussion of the optical nonlinearities of liquid crystals, and a thorough review of a wide range of nonlinear optical processes and phenomena enabled by these unique properties. Starting with a brief historical account of the development of nonlinear optical studies of the mesophases of liquid crystals, we then review various liquid crystalline materials and structures, and their nonlinear optical properties. Emphasis is placed on the nematic phase, which best exemplifies the dual nature of liquid crystals, although frequent references to other phases are also made. We also delve into recent work on novel structures such as photonic crystals, metamaterials and nanostructures and their special characteristics and emergent properties. The mechanisms and complex nonlocal dynamics of optical nonlinearities associated with laser induced director axis reorientation, thermal, density, and order parameter fluctuations, space charge field formation and photorefractivity are critically reviewed as a foundation for the discussions of various nonlinear optical processes detailed in this paper

Nonlinear Waves In A Stenosed Elastic Tube Filled With Viscous Fluid: Forced Perturbed Korteweg-De Vries Equation

Science.gov (United States)

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.

All-optical signal processing in quadratic nonlinear materials

DEFF Research Database (Denmark)

Johansen, Steffen Kjær

2002-01-01

of materials with a second order nonlinearity, the so-called X(2) materials, is faster and stronger than that of more conventional materials with a cubic nonlinearity. The X(2) materials support spatial solitons consisting of two coupled components, the fundamental wave (FW) and its second harmonic (SH......). During this project the interaction between such spatial solitons has been investigated theoretically through perturbation theory and experimentally via numerical simulations. The outcome of this research isnew theoretical tools for quantitatively predicting the escape angle, i.e. the angle of incidence...... are dedicated to this part of the research. In chapter 4 the generality of the theoretical approach is emphasised with the derivation and verification of equivalent tools for media with a saturable nonlinearity. The strength of the X(2) nonlinearity strongly depends on the phase mismatch between the FW...

A comparative study on the elastic modulus of polyvinyl alcohol sponge using different stress-strain definitions.

Science.gov (United States)

Karimi, Alireza; Navidbakhsh, Mahdi; Alizadeh, Mansour; Razaghi, Reza

2014-10-01

There have been different stress-strain definitions to measure the elastic modulus of spongy materials, especially polyvinyl alcohol (PVA) sponge. However, there is no agreement as to which stress-strain definition should be implemented. This study was aimed to show how different results are given by the various definitions of stress-strain used, and to recommend a specific definition when testing spongy materials. A fabricated PVA sponge was subjected to a series of tensile tests in order to measure its mechanical properties. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were used to determine the elastic modulus. The results revealed that the Almansi-Hamel strain definition exhibited the highest non-linear stress-strain relation and, as a result, may overestimate the elastic modulus at different stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress). The Green-St. Venant strain definition failed to address the non-linear stress-strain relation using different definitions of stress and invoked an underestimation of the elastic modulus values. Engineering stress and strain definitions were only valid for small strains and displacements, which make them impractical when analyzing spongy materials. The results showed that the effect of varying the stress definition on the maximum stress measurements was significant but not when calculating the elastic modulus. It is important to consider which stress-strain definition is employed when characterizing the mechanical properties of spongy materials. Although the true stress-true strain definition exhibits a non-linear relation, we favor it in spongy materials mechanics as it gives more accurate measurements of the material's response using the instantaneous values.

Nonlinear theory of electroelastic and magnetoelastic interactions

CERN Document Server

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.

Geometrically and material non-linear analysis of bubble condenser steel structure

International Nuclear Information System (INIS)

Gyoergyi, J.; Lenkei, P.

2003-01-01

In frame of the project funded by the European Commission (EC) through the Phare and Tacis Programmes experimentally investigate the behaviour of the bubble condenser system (BCS) during phenomena induced by postulated design basis accidents (DBA). The bubble condenser steel structure consists of 12 trays. To enable the Bubble Condenser Test Prototype to be representative of the majority of trays and sections, it was decided to model a typical tray. The test results demonstrate the integrity of the standard tray pressure retaining boundary (side wall, face wall, ceiling and bottom) against a differential pressure (30 kPa). The stability of the side wall and the face wall of tray level 12 was not assured for this differential pressure. The thermal-hydraulic tests demonstrate that the maximum differential pressure across the tray walls in the case of Large Break Loss of Coolant Accident (LBLOCA) is 20 kPa. We have got from the experiences the differential pressure in function of time. The results of the approximate calculations showed the effect of nonlinearly. In case of calculation by FEM model we have done the elastic and linear analyses, and calculated with the geometrically and material non-linearity. (author)

Dynamic frictional contact for elastic viscoplastic material

Directory of Open Access Journals (Sweden)

Kenneth L. Kuttler

2007-05-01

Full Text Available Using a general theory for evolution inclusions, existence and uniqueness theorems are obtained for weak solutions to a frictional dynamic contact problem for elastic visco-plastic material. An existence theorem in the case where the friction coefficient is discontinuous is also presented.

An analysis of hypercritical states in elastic and inelastic systems

Science.gov (United States)

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.

Non-Linear Optical Phenomena in Detecting Materials as a Possibility for Fast Timing in Detectors of Ionizing Radiation

CERN Document Server

Korjik, M. V.; Buganov, O.; Fedorov, A. A.; Emelianchik, I.; Griesmayer, E.; Mechinsky, V.; Nargelas, S.; Sidletskiy, O.; Tamulaitis, G.; Tikhomirov, S. N.; Vaitkevicius, A.

2016-01-01

The time resolution of the detectors currently in use is limited by 50-70 ps due to the spontaneous processes involved in the development of the response signal, which forms after the relaxation of carriers generated during the interaction. In this study, we investigate the feasibility of exploiting sub-picosecond phenomena occurring after the interaction of scintillator material with ionizing radiation by probing the material with ultra-short laser pulses. One of the phenomena is the elastic polarization due to the local lattice distortion caused by the displacement of electrons and holes generated by ionization. The key feature of the elastic polarization is its short response time, which makes it prospective for using as an optically detectable time mark. The nonlinear optical absorption of femtosecond light pulses of appropriate wavelength is demonstrated to be a prospective tool to form the mark. This study was aimed at searching for inorganic crystalline media combining scintillation properties and non-...

Nonlinear elastic wave spectroscopy in symbiosis with time reversal for localization of defects: TR-NEWS

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

Riemann-Cartan geometry of nonlinear disclination mechanics

KAUST Repository

Yavari, A.

2012-03-23

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 the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan\\'s method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).

Probabilistic analysis of a materially nonlinear structure

Science.gov (United States)

Millwater, H. R.; Wu, Y.-T.; Fossum, A. F.

1990-01-01

A probabilistic finite element program is used to perform probabilistic analysis of a materially nonlinear structure. The program used in this study is NESSUS (Numerical Evaluation of Stochastic Structure Under Stress), under development at Southwest Research Institute. The cumulative distribution function (CDF) of the radial stress of a thick-walled cylinder under internal pressure is computed and compared with the analytical solution. In addition, sensitivity factors showing the relative importance of the input random variables are calculated. Significant plasticity is present in this problem and has a pronounced effect on the probabilistic results. The random input variables are the material yield stress and internal pressure with Weibull and normal distributions, respectively. The results verify the ability of NESSUS to compute the CDF and sensitivity factors of a materially nonlinear structure. In addition, the ability of the Advanced Mean Value (AMV) procedure to assess the probabilistic behavior of structures which exhibit a highly nonlinear response is shown. Thus, the AMV procedure can be applied with confidence to other structures which exhibit nonlinear behavior.

Extrinsic contribution to the non-linearity in a PZT disc

Energy Technology Data Exchange (ETDEWEB)

Perez, Rafel [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Albareda, Alfons [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Garcia, Jose E [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Tiana, Jordi [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Ringgaard, Erling [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark); Wolny, Wanda W [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark)

2004-10-07

Non-linear increases in elastic, piezoelectric (direct and reverse) and dielectric coefficients have been measured under a high electrical field or under high mechanical stress. The permittivity and reverse piezoelectric coefficient can be measured by applying a high voltage at a low frequency, while the elastic compliance and direct piezoelectric coefficient can be measured at the first radial resonance frequency in order to apply a high stress. The non-linear behaviour has been analysed at the radial resonance of a disc. In all the materials tested, the results show that there is a close relation between the non-linear increments of the different coefficients. An empirical model has been proposed in order to describe and understand these relations. It is assumed that either the strain or the electrical displacement is produced by intrinsic and extrinsic processes, but only the latter, which consist mainly in the motion of domain walls, contribute to the non-linearity. The model enables us to find the domain wall contribution to elastic, piezoelectric and dielectric non-linearities, and allows us to compare the amplitudes of the fields and stresses that produce the same displacement of domain walls.

Contribution to research on the elastic and elastoplastic behavior of porous materials

International Nuclear Information System (INIS)

Frappier, J.-C.

1979-11-01

This three-part study concerns the mechanical behavior of porous materials. Part one, a bibliographical survey on the mechanical properties of porous materials, deals in turn with the following subjects: elastic properties, elasto-plastic boundary, plastic flow laws, fracture behavior and characterization methods. Part two is devoted to elastic behavior, giving the results of an experimental study on the elastic properties of a sintered nickel within a wide porosity range (5% to 55%) and establishing a theoretical law for the prediction of such characteristics; apart from the total porosity fraction and the elastic properties of the matrix this law can integrate parameters which represent the morphology of the material and may be determined empirically or by a modelisation, also proposed, of the structure of the material. Part three describes elastoplastic, behavior and includes experimental results obtained on sintered nickel in cases of simple mechanical stress, the demonstration - based on energy considerations of a theoretical plasticity criterion accounting for the substance, a theoretical definition of the plastic Poisson's ratio and the establishment of flow laws associated with this criterion [fr

Elastic-Plastic J-Integral Solutions or Surface Cracks in Tension Using an Interpolation Methodology

Science.gov (United States)

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.

Elastic-plastic analysis of high speed rotors with no plane of symmetry

International Nuclear Information System (INIS)

Anantha Ramu, S.

1981-01-01

A general method of analysis of elastic plastic shells has been developed. The material of the shell is assumed to obey von Mises yield condition and a stress strain law on the basis of deformation theory of plasticity. The method permits an easy iterative solution of the complete set of coupled nonlinear differential equations. The iterative procedure is essentially the solution of the elastic problem several times with different sets of loads. The solution finally yields among other things, the location of the elastic-plastic boundary in the shell wall. The second approach suggested is a three-dimensional hexahedral isoparametric solid element. The computer program developed is capable of modelling perfectly plastic, bilinear as well as nonlinear strain hardening behaviour of materials. As an example, a radial impeller is analysed by both the approaches by idealizing it as a rotating conical shell. The complete history of plastification of the shell wall as the speed increases is determined. The results of both approaches are found to be in good agreement with each other. (orig./HP)

New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity

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 elasticity in resonance experiments

Science.gov (United States)

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.

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.

Sapphire: A kinking nonlinear elastic solid

Science.gov (United States)

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 the solvability of asymmetric quasilinear finite element approximate problems in nonlinear incompressible elasticity

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

Study of a Piezo-Thermo-Elastic Materials Console

Directory of Open Access Journals (Sweden)

hamza madjid berrabah

2015-09-01

Full Text Available In the first part of this work, analytical expressions were determined for the stresses through the thickness of a composite beam submitted to electrical excitation. In the second part of this study we are interested in the theory of elasticity, which is used to obtain exact solutions of piezo-thermo-elastic consoles gradually coupled evaluated under different loads. These solutions are used to identify the piezoelectric parameter and thermal coefficients of the materials. In addition, numerical results are obtained for the analysis of the loaded console by two different types of loading. In this study we show also that changing the linear thermal parameters of the material does not affect the distribution of the stress and the induction of the beam. However it affetcs the components of the deformation, electric field, the displacement and the electric potential of the console.

Nonlinear morphoelastic plates II: Exodus to buckled states

KAUST Repository

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

KAUST Repository

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.

Time history nonlinear earthquake response analysis considering materials and geometrical nonlinearity

International Nuclear Information System (INIS)

Kobayashi, T.; Yoshikawa, K.; Takaoka, E.; Nakazawa, M.; Shikama, Y.

2002-01-01

A time history nonlinear earthquake response analysis method was proposed and applied to earthquake response prediction analysis for a Large Scale Seismic Test (LSST) Program in Hualien, Taiwan, in which a 1/4 scale model of a nuclear reactor containment structure was constructed on sandy gravel layer. In the analysis both of strain-dependent material nonlinearity, and geometrical nonlinearity by base mat uplift, were considered. The 'Lattice Model' for the soil-structure interaction model was employed. An earthquake record on soil surface at the site was used as control motion, and deconvoluted to the input motion of the analysis model at GL-52 m with 300 Gal of maximum acceleration. The following two analyses were considered: (A) time history nonlinear, (B) equivalent linear, and the advantage of time history nonlinear earthquake response analysis method is discussed

Weyl geometry and the nonlinear mechanics of distributed point defects

KAUST Repository

Yavari, A.

2012-09-05

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-where the body is stress-free-is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan\\'s moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby\\'s celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid. © 2012 The Royal Society.

Elastic-plastic transition on rotating spherical shells in dependence of compressibility

Directory of Open Access Journals (Sweden)

Thakur Pankaj

2017-01-01

Full Text Available The purpose of this paper is to establish the mathematical model on the elastic-plastic transitions occurring in the rotating spherical shells based on compressibility of materials. The paper investigates the elastic-plastic stresses and angular speed required to start yielding in rotating shells for compressible and incompressible materials. The paper is based on the non-linear transition theory of elastic-plastic shells given by B.R. Seth. The elastic-plastic transition obtained is treated as an asymptotic phenomenon at critical points & the solution obtained at these points generates stresses. The solution obtained does not require the use of semi-empirical yield condition like Tresca or Von Mises or other certain laws. Results are obtained numerically and depicted graphically. It has been observed that Rotating shells made of the incompressible material are on the safer side of the design as compared to rotating shells made of compressible material. The effect of density variation has been discussed numerically on the stresses. With the effect of density variation parameter, rotating spherical shells start yielding at the internal surface with the lower values of the angular speed for incompressible/compressible materials.

Nonlinear time reversal signal processing techniques applied to acousto-mechanical imaging of complex materials

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

Weyl geometry and the nonlinear mechanics of distributed point defects

KAUST Repository

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

Effective material parameter retrieval of anisotropic elastic metamaterials with inherent nonlocality

Science.gov (United States)

Lee, Hyung Jin; Lee, Heung Son; Ma, Pyung Sik; Kim, Yoon Young

2016-09-01

In this paper, the scattering (S-) parameter retrieval method is presented specifically for anisotropic elastic metamaterials; so far, no retrieval has been accomplished when elastic metamaterials exhibit fully anisotropic behavior. Complex constitutive property and intrinsic scattering behavior of elastic metamaterials make their characterization far more complicated than that for acoustic and electromagnetic metamaterials. In particular, elastic metamaterials generally exhibit anisotropic scattering behavior due to higher scattering modes associated with shear deformation. They also exhibit nonlocal responses to some degrees, which originate from strong multiple scattering interactions even in the long wavelength limit. Accordingly, the conventional S-parameter retrieval methods cannot be directly used for elastic metamaterials, because they determine only the diagonal components in effective tensor property. Also, the conventional methods simply use the analytic inversion formulae for the material characterization so that inherent nonlocality cannot be taken into account. To establish a retrieval method applicable to anisotropic elastic metamaterials, we propose an alternative S-parameter method to deal with full anisotropy of elastic metamaterials. To retrieve the whole effective anisotropic parameter, we utilize not only normal but also oblique wave incidences. For the retrieval, we first retrieve the ratio of the effective stiffness tensor to effective density and then determine the effective density. The proposed retrieval method is validated by characterizing the effective material parameters of various types of non-resonant anisotropic metamaterials. It is found that the whole effective parameters are retrieved consistently regardless of used retrieval conditions in spite of inherent nonlocality.

Nonlinear dynamic characterization of two-dimensional materials

NARCIS (Netherlands)

Davidovikj, D.; Alijani, F.; Cartamil Bueno, S.J.; van der Zant, H.S.J.; Amabili, M.; Steeneken, P.G.

2017-01-01

Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator's

Nanoparticle amount, and not size, determines chain alignment and nonlinear hardening in polymer nanocomposites

Science.gov (United States)

Varol, H. Samet; Meng, Fanlong; Hosseinkhani, Babak; Malm, Christian; Bonn, Daniel; Bonn, Mischa; Zaccone, Alessio

2017-01-01

Polymer nanocomposites—materials in which a polymer matrix is blended with nanoparticles (or fillers)—strengthen under sufficiently large strains. Such strain hardening is critical to their function, especially for materials that bear large cyclic loads such as car tires or bearing sealants. Although the reinforcement (i.e., the increase in the linear elasticity) by the addition of filler particles is phenomenologically understood, considerably less is known about strain hardening (the nonlinear elasticity). Here, we elucidate the molecular origin of strain hardening using uniaxial tensile loading, microspectroscopy of polymer chain alignment, and theory. The strain-hardening behavior and chain alignment are found to depend on the volume fraction, but not on the size of nanofillers. This contrasts with reinforcement, which depends on both volume fraction and size of nanofillers, potentially allowing linear and nonlinear elasticity of nanocomposites to be tuned independently. PMID:28377517

Design and optimization of carbon-nanotube-material/dielectric hybrid nonlinear optical waveguides

International Nuclear Information System (INIS)

Zhao, Xin; Zheng, Zheng; Lu, Zhiting; Zhu, Jinsong; Zhou, Tao

2011-01-01

The nonlinear optical characteristics of highly nonlinear waveguides utilizing carbon nanotube composite materials are investigated theoretically. The extremely high nonlinearity and relatively high loss of the carbon nanotube materials are shown to greatly affect the performance of such waveguides for nonlinear optical applications, in contrast to waveguides using conventional nonlinear materials. Different configurations based on applying the carbon nanotube materials to the popular ridge and buried waveguides are thoroughly studied, and the optimal geometries are derived through simulations. It is shown that, though the nonlinear coefficient is often huge for these waveguides, the loss characteristics can significantly limit the maximum achievable accumulated nonlinearity, e.g. the maximum nonlinear phase shift. Our results suggest that SOI-based high-index-contrast, carbon nanotube cladding waveguides, rather than the currently demonstrated low-contrast waveguides, could hold the promise of achieving significantly higher accumulated nonlinearity

Energy nonlinearity in radiation detection materials: Causes and consequences

International Nuclear Information System (INIS)

Jaffe, J.E.; Jordan, D.V.; Peurrung, A.J.

2007-01-01

The phenomenology and present theoretical understanding of energy nonlinearity (nonproportionality) in radiation detection materials is reviewed, with emphasis on gamma-ray spectroscopy. Scintillators display varying degrees and patterns of nonlinearity, while semiconductor detectors are extremely linear, and gas detectors show a characteristic form of nonproportionality associated with core levels. The relation between nonlinear response (to both primary particles and secondary electrons) and spectrometer resolution is also discussed. We review the qualitative ideas about the origin of nonlinearity in scintillators that have been proposed to date, with emphasis on transport and recombination of electronic excitations. Recent computational and experimental work on the basic physics of scintillators is leading towards a better understanding of energy nonlinearity and should result in new, more linear scintillator materials in the near future

Optimal determination of the elastic constants of woven 2D SiC/SiC composite materials

International Nuclear Information System (INIS)

Mouchtachi, A; Guerjouma, R El; Baboux, J C; Rouby, D; Bouami, D

2004-01-01

For homogeneous materials, the ultrasonic immersion method, associated with a numerical optimization process mostly based on Newton's algorithm, allows the determination of elastic constants for various synthetic and natural composite materials. Nevertheless, a principal limitation of the existing optimization procedure occurs when the considered material is at the limit of the homogeneous hypothesis. Such is the case of the woven bidirectional SiC matrix and SiC fibre composite material. In this study, we have developed two numerical methods for the determination of the elastic constants of the 2D SiC/SiC composite material (2D SiC/SiC). The first one is based on Newton's algorithm: the elastic constants are obtained by minimizing the square deviation between experimental and calculated velocities. The second method is based on the Levenberg-Marquardt algorithm. We show that these algorithms give the same results in the case of homogeneous anisotropic composite materials. For the 2D SiC/SiC composite material, the two methods, using the same measured velocities, give different sets of elastic constants. We then note that the Levenberg-Marquardt algorithm enables a better convergence towards a global set of elastic constants in good agreement with the elastic properties, which can be measured using classical quasi-static methods

Modeling Pseudo-elastic Behavior of Springback

International Nuclear Information System (INIS)

Xia, Z. Cedric

2005-01-01

One of the principal foundations of mathematical theory of conventional plasticity for rate-independent metals is that there exists a well-defined yield surface in stress space for any material point under deformation. A material point can undergo further plastic deformation if the applied stresses are beyond current yield surface which is generally referred as 'plastic loading'. On the other hand, if the applied stress state falls within or on the yield surface, the metal will deform elastically only and is said to be undergoing 'elastic unloading'. Although it has been always recognized throughout the history of development of plasticity theory that there is indeed inelastic deformation accompanying elastic unloading, which leads to metal's hysteresis behavior, its effects were thought to be negligible and were largely ignored in the mathematical treatment.Recently there have been renewed interests in the study of unloading behavior of sheet metals upon large plastic deformation and its implications on springback prediction. Springback is essentially an elastic recovery process of a formed sheet metal blank when it is released from the forming dies. Its magnitude depends on the stress states and compliances of the deformed sheet metal if no further plastic loading occurs during the relaxation process. Therefore the accurate determination of material compliances during springback and its effective incorporation into simulation software are important aspects for springback calculation. Some of the studies suggest that the unloading curve might deviate from linearity, and suggestions were made that a reduced elastic modulus be used for springback simulation.The aim of this study is NOT to take a position on the debate of whether elastic moduli are changed during sheet metal forming process. Instead we propose an approach of modeling observed psuedoelastic behavior within the context of mathematical theory of plasticity, where elastic moduli are treated to be

Geometrically nonlinear dynamic and static analysis of shallow spherical shell resting on two-parameters elastic foundations

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

A nonlinear boundary integral equations method for the solving of quasistatic elastic contact problem with Coulomb friction

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.

Sound Transmission Through Multi-Panel Structures Lined with Elastic Porous Materials

Science.gov (United States)

Bolton, J. S.; Shiau, N.-M.; Kang, Y. J.

1996-04-01

Theory and measurements related to sound transmission through double panels lined with elastic porous media are presented. The information has application to the design of noise control barriers and to the optimization of aircraft fuselage transmission loss, for example. The major difference between the work described here and earlier research in this field relates to the treatment of the porous material that is used to line the cavity between the two panels of the double panel structure. Here we have used the porous material theory proposed by Biot since it takes explicit account of all the wave types known to propagate in elastic porous materials. As a result, it is possible to use the theory presented here to calculate the transmission loss of lined double panels at arbitrary angles of incidence; results calculated over a range of incidence angles may then be combined to yield the random incidence transmission loss. In this paper, the equations governing wave propagation in an elastic porous material are first considered briefly and then the general forms for the stresses and displacements within the porous material are given. Those solutions are expressed in terms of a number of constants that can be determined by application of appropriate boundary conditions. The boundary conditions required to model double panels having linings that are either directly attached to the facing panels or separated?!from them by air gaps are presented and discussed. Measurements of the random incidence transmission loss of aluminium double-panel structures lined with polyurethane foam are presented and have been found to be in good agreement with theoretical predictions. Both the theoretical predictions and the measured results have shown that the method by which an elastic porous lining material is attached to the facing panels can have a profound influence on the transmission loss of the panel system. It has been found, for example, that treatments in which the lining material

Elastic properties of zinc, cadmium, bismuth, thallium, tin, lead and their binary alloys with indium

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

Dependence of the frequency spectrum of small amplitude vibrations superimposed on finite deformations of a nonlinear, cylindrical elastic body on residual stress

KAUST Repository

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

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...

Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods

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

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...

Nonlinear analysis of reinforced concrete beam with/without tension stiffening effect

International Nuclear Information System (INIS)

Dede, T.; Ayvaz, Y.

2009-01-01

The aim of this paper is to do materially nonlinear failure analysis of RC beam by using finite element method. In the finite element modeling, two different approaches and different tension stress-strain models with/without tension stiffening effect are used by considering two different mesh sizes. In the first approach, the material matrices of concrete and reinforcement are constructed separately, and then superimposed to obtain the element stiffness matrix. In the second approach, the reinforcement is assumed to be uniformly distributed throughout the beam. So, the beam is modeled as a single composite element with increasing the modulus of elasticity of concrete by considering the reinforcement ratio. For these two approaches, elastic-perfectly plastic stress-strain relationship is used for concrete in compression. For the concrete in tension, a stress-strain relationship with/without tension stiffening is used. It is concluded that the approaches and the models considered in this study can be effectively used in the materially nonlinear analysis of RC beams.

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

Mathematical model predicts the elastic behavior of composite materials

Directory of Open Access Journals (Sweden)

Zoroastro de Miranda Boari

2005-03-01

Full Text Available Several studies have found that the non-uniform distribution of reinforcing elements in a composite material can markedly influence its characteristics of elastic and plastic deformation and that a composite's overall response is influenced by the physical and geometrical properties of its reinforcing phases. The finite element method, Eshelby's method and dislocation mechanisms are usually employed in formulating a composite's constitutive response. This paper discusses a composite material containing SiC particles in an aluminum matrix. The purpose of this study was to find the correlation between a composite material's particle distribution and its resistance, and to come up with a mathematical model to predict the material's elastic behavior. The proposed formulation was applied to establish the thermal stress field in the aluminum-SiC composite resulting from its fabrication process, whereby the mixture is prepared at 600 °C and the composite material is used at room temperature. The analytical results, which are presented as stress probabilities, were obtained from the mathematical model proposed herein. These results were compared with the numerical ones obtained by the FEM method. A comparison of the results of the two methods, analytical and numerical, reveals very similar average thermal stress values. It is also shown that Maxwell-Boltzmann's distribution law can be applied to identify the correlation between the material's particle distribution and its resistance, using Eshelby's thermal stresses.

The application of nonlinear dynamics in the study of ferroelectric materials

International Nuclear Information System (INIS)

Blochwitz, S.; Habel, R.; Diestelhorst, M.; Beige, H.

1996-01-01

It is well known that the structural phase transitions in ferroelectric materials are connected with strong nonlinear properties. So we can expect all features of nonlinear dynamical systems such as period-doubling cascades and chaos in a dynamical system that contains ferroelectric materials. Therefore we can apply nonlinear dynamics to these ferroelectric materials and we are doing it in two directions: (i) We study the structural phase transitions by analyzing the large signal behaviour with means of nonlinear dynamics. (ii) We control the chaotic behaviour of the system with the method proposed by Ott, Grebogi and Yorke. (authors)

Nonlinear continuum mechanics and large inelastic deformations

CERN Document Server

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...

Poromechanical approach describing the moisture influence on the non-linear quasi-static and dynamic behaviour of porous building materials

NARCIS (Netherlands)

Carmeliet, J.; Abeele, van den K.E.A.

2004-01-01

The non-linear quasi-static and dynamic elastic behaviour of Berea sandstone has been experimentally analysed showing hysteresis and a strong influence of moisture especially in the lower saturation range. It is shown that non-linear hysteretic response originates within the "bond system" of the

Elastic constants of stressed and unstressed materials in the phase-field crystal model

Science.gov (United States)

Wang, Zi-Le; Huang, Zhi-Feng; Liu, Zhirong

2018-04-01

A general procedure is developed to investigate the elastic response and calculate the elastic constants of stressed and unstressed materials through continuum field modeling, particularly the phase-field crystal (PFC) models. It is found that for a complete description of system response to elastic deformation, the variations of all the quantities of lattice wave vectors, their density amplitudes (including the corresponding anisotropic variation and degeneracy breaking), the average atomic density, and system volume should be incorporated. The quantitative and qualitative results of elastic constant calculations highly depend on the physical interpretation of the density field used in the model, and also importantly, on the intrinsic pressure that usually pre-exists in the model system. A formulation based on thermodynamics is constructed to account for the effects caused by constant pre-existing stress during the homogeneous elastic deformation, through the introducing of a generalized Gibbs free energy and an effective finite strain tensor used for determining the elastic constants. The elastic properties of both solid and liquid states can be well produced by this unified approach, as demonstrated by an analysis for the liquid state and numerical evaluations for the bcc solid phase. The numerical calculations of bcc elastic constants and Poisson's ratio through this method generate results that are consistent with experimental conditions, and better match the data of bcc Fe given by molecular dynamics simulations as compared to previous work. The general theory developed here is applicable to the study of different types of stressed or unstressed material systems under elastic deformation.

New organic materials for optics: optical storage and nonlinear optics

International Nuclear Information System (INIS)

Gan, F.

1996-01-01

New organic materials have received considerable attention recently, due to their easy preparation and different variety. The most application fields in optics are optical storage and nonlinear optics. In optical storage the organic dyes have been used for example, in record able and erasable compact disks (CD-R, CD-E) nonlinear optical effects, such as nonlinear optical absorption, second and third order optical absorption, second and third order optical nonlinearities, can be applied for making optical limiters, optical modulators, as well as laser second and third harmonic generations. Due to high value of optical absorption and optical nonlinearity organic materials are always used as thin films in optical integration. In this paper the new experimental results have been presented, and future development has been also discussed. (author)

Morphoelasticity: A theory of elastic growth

KAUST Repository

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

KAUST Repository

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.

Nonlinear coherent structures in granular crystals

Science.gov (United States)

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.

Design of steel-liners and their anchorage with regard to non-linear behaviour of liner-material and anchorage

International Nuclear Information System (INIS)

Oberpichler, R.

1979-01-01

The thin steel liner attached by studs or rib-type anchors to the interior wall of a Prestressed Concrete Reactor Pressure Vessel (PCRV) or a Concrete Containment Vessel (PCCV) has to provide the leak-tightness of the vessel. The liner also may serve as internal shuttering for placing concrete as well as a support for the cooling system or thermal isolation. Mainly strained by self-limited loads imposed on the liner by deformations of the vessel-wall or by heatup inside the vessel the liner predominantly will function in a compressive biaxially strained state like a membrane. The vessel-wall is assumed to be a rigid boundary without reactions caused by the liner-anchor-restraints. Furthermore it is assumed that the liner supported in a close-spaced pattern to the concrete with respect to self-limited loads and all effects of non-linear behaviour of liner-material and non-linear anchor-characteristics will not fail by instability, especially not by an effect of snapthrough. Only one essential mode of failure, the shear connector failure is assumed to be basis for all liner investigations. Design of the liner and its anchorage therefore is based on the analysis of large deformations with regard to elastic-plastic behaviour of liner-material and non-linear anchor characteristics. By this method both economical and safe sizing and spacing of the anchors can be calculated. (orig.)

Material-Point Method Analysis of Bending in Elastic Beams

DEFF Research Database (Denmark)

Andersen, Søren Mikkel; Andersen, Lars

2007-01-01

The aim of this paper is to test different types of spatial interpolation for the material-point method. The interpolations include quadratic elements and cubic splines. A brief introduction to the material-point method is given. Simple liner-elastic problems are tested, including the classical...... cantilevered beam problem. As shown in the paper, the use of negative shape functions is not consistent with the material-point method in its current form, necessitating other types of interpolation such as cubic splines in order to obtain smoother representations of field quantities. It is shown...

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

Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties

Science.gov (United States)

Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon

2012-01-01

Purpose: The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F[subscript 0]) during anterior-posterior stretching. Method: Three materially linear and 3 materially nonlinear models were…

Analysis of nonlinear elastic behavior in miniature pneumatic artificial muscles

Science.gov (United States)

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)

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.

Simplified method for elastic plastic analysis of material presenting bilinear kinematic hardening

International Nuclear Information System (INIS)

Roche, R.

1983-12-01

A simplified method for elastic plastic analysis is presented. Material behavior is assumed to be elastic plastic with bilinear kinematic hardening. The proposed method give a strain-stress field fullfilling material constitutive equations, equations of equilibrium and continuity conditions. This strain-stress is obtained through two linear computations. The first one is the conventional elastic analysis of the body submitted to the applied load. The second one use tangent matrix (tangent Young's modulus and Poisson's ratio) for the determination of an additional stress due to imposed initial strain. Such a method suits finite elements computer codes, the most useful result being plastic strains resulting from the applied loading (load control or deformation control). Obviously, there is not unique solution, for stress-strain field is not depending only of the applied load, but of the load history. Therefore, less pessimistic solutions can be got by one or two additional linear computations [fr

X-ray elastic constants in textured Zr-base materials

International Nuclear Information System (INIS)

Ortiz, M.; Pochettino, A.A.; Lebrun, J.L.; Maeder, G.

1993-01-01

A general method for the calculation of the X-ray elastic constants (XREC) for textured hexagonal close-packed (hcp) materials was developed by using the orientation distribution function (ODF) and the Reuss hypothesis. This method was applied to textured zirconium (Zr) sheets and zircaloy 4 (Zry 4) extruded tubes. For these samples, where the elastic anisotropy is not very strong, an 'isotropic approximation' method is proposed using the ODF data. In that case, the classical XREC 1/2S 2 and S, values are calculated and experimentally verified for (10 bar 14) diffracting planes. Theoretical XREC values are also given for different (hkil) that could be chosen according to the experimental conditions, considering texture effects on diffracting peak intensities

Temperature dependence of the elastic constant of Borassus Flabellifier 'BF' material by acoustic response

International Nuclear Information System (INIS)

Phadke, Sushil; DShrivastava, B; Dagaonkar, N; Mishra, Ashutosh

2012-01-01

The homogeneous continuous materials are widely used for many structural applications. Migrations of atoms or molecules are the mechanism of mechanical and kinetic processes in materials for their synthesis processing as well as for their structural evolutions. The elastic constant of solids provides valuable information on their mechanical and dynamical properties. In particular, they provide information on the stability and stiffness of materials. In the present study author investigated relation between elastic constant and temperature in Borassus Flabellifier 'BF' wood part. Determination of elastic properties of material is based on the longitudinal wave's velocities via ultrasonic methods. The resonant frequencies of the specimens were measured by Ultrasonic Interferometer (for solids) dual frequency using longitudinal cubic piezoelectric crystal of quartz of frequency 123.62 KHz. The temperature variations from room temperature were done by PID control unit, Mittal Enterprises, New Delhi, India. Characterization of the samples was done by scanning electron microscope (SEM) Model JEOL JSM5400 at 5.0kvx750, 10 μm.

Elastic properties

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

Non-linear extension of FFT-based methods accelerated by conjugate gradients to evaluate the mechanical behavior of composite materials

International Nuclear Information System (INIS)

Gelebart, Lionel; Mondon-Cancel, Romain

2013-01-01

FFT-based methods are used to solve the problem of a heterogeneous unit-cell submitted to periodic boundary conditions, which is of a great interest in the context of numerical homogenization. Recently (in 2010), Brisard and Zeman proposed simultaneously to use Conjugate Gradient based solvers in order to improve the convergence properties (when compared to the basic scheme, proposed initially in 1994). The purpose of the paper is to extend this idea to the case of non-linear behaviors. The proposed method is based on a Newton-Raphson algorithm and can be applied to various kinds of behaviors (time dependant or independent, with or without internal variables) through a conventional integration procedure as used in finite element codes. It must be pointed out that this approach is fundamentally different from the traditional FFT-based approaches which rely on a fixed-point algorithm (e.g. basic scheme, Eyre and Milton accelerated scheme, Augmented Lagrangian scheme, etc.). The method is compared to the basic scheme on the basis of a simple application (a linear elastic spherical inclusion within a non-linear elastic matrix): a low sensitivity to the reference material and an improved efficiency, for a soft or a stiff inclusion, are observed. At first proposed for a prescribed macroscopic strain, the method is then extended to mixed loadings. (authors)

An improved energy conserving implicit time integration algorithm for nonlinear dynamic structural analysis

International Nuclear Information System (INIS)

Haug, E.; Rouvray, A.L. de; Nguyen, Q.S.

1977-01-01

This study proposes a general nonlinear algorithm stability criterion; it introduces a nonlinear algorithm, easily implemented in existing incremental/iterative codes, and it applies the new scheme beneficially to problems of linear elastic dynamic snap buckling. Based on the concept of energy conservation, the paper outlines an algorithm which degenerates into the trapezoidal rule, if applied to linear systems. The new algorithm conserves energy in systems having elastic potentials up to the fourth order in the displacements. This is true in the important case of nonlinear total Lagrange formulations where linear elastic material properties are substituted. The scheme is easily implemented in existing incremental-iterative codes with provisions for stiffness reformation and containing the basic Newmark scheme. Numerical analyses of dynamic stability can be dramatically sensitive to amplitude errors, because damping algorithms may mask, and overestimating schemes may numerically trigger, the physical instability. The newly proposed scheme has been applied with larger time steps and less cost to the dynamic snap buckling of simple one and multi degree-of-freedom structures for various initial conditions

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

Negative stiffness honeycombs as tunable elastic metamaterials

Science.gov (United States)

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.

Utilizing strongly absorbing materials for low-loss surface-wave nonlinear optics

Science.gov (United States)

Grosse, Nicolai B.; Franz, Philipp; Heckmann, Jan; Pufahl, Karsten; Woggon, Ulrike

2018-04-01

Optical media endowed with large nonlinear susceptibilities are highly prized for their employment in frequency conversion and the generation of nonclassical states of light. Although the presence of an optical resonance can greatly increase the nonlinear response (e.g., in epsilon-near-zero materials), the non-negligible increase in linear absorption often precludes the application of such materials in nonlinear optics. Absorbing materials prepared as thin films, however, can support a low-loss surface wave: the long-range surface exciton polariton (LRSEP). Its propagation lifetime increases with greater intrinsic absorption and reduced film thickness, provided that the film is embedded in a transparent medium (symmetric cladding). We explore LRSEP propagation in a molybdenum film by way of a prism-coupling configuration. Our observations show that excitation of the LRSEP mode leads to a dramatic increase in the yield of second-harmonic generation. This implies that the LRSEP mode is an effective vehicle for utilizing the nonlinear response of absorbing materials.

Dynamics of pre-strained bi-material elastic systems linearized three-dimensional approach

CERN Document Server

Akbarov, Surkay D

2015-01-01

This book deals with dynamics of pre-stressed or pre-strained bi-material elastic systems consisting of stack of pre-stressed layers, stack of pre-stressed layers and pre-stressed half space (or half plane), stack of pre-stressed layers as well as absolute rigid foundation, pre-stressed compound solid and hollow cylinders and pre-stressed sandwich hollow cylinders. The problems considered in the book relate to the dynamics of a moving and oscillating moving load, forced vibration caused by linearly located or point located time-harmonic forces acting to the foregoing systems. Moreover, a considerable part of the book relate to the problems regarding the near surface, torsional and axisymmetric longitudinal waves propagation and dispersion in the noted above bi-material elastic systems. The book carries out the investigations within the framework of the piecewise homogeneous body model with the use of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies.

Modeling complicated rheological behaviors in encapsulating shells of lipid-coated microbubbles accounting for nonlinear changes of both shell viscosity and elasticity.

Science.gov (United States)

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.

Modeling complicated rheological behaviors in encapsulating shells of lipid-coated microbubbles accounting for nonlinear changes of both shell viscosity and elasticity

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)

Mesoscopic approach to modeling elastic-plastic polycrystalline material behaviour

International Nuclear Information System (INIS)

Kovac, M.; Cizelj, L.

2001-01-01

Extreme loadings during severe accident conditions might cause failure or rupture of the pressure boundary of a reactor coolant system. Reliable estimation of the extreme deformations can be crucial to determine the consequences of such an accident. One of important drawbacks of classical continuum mechanics is idealization of inhomogenous microstructure of materials. This paper discusses the mesoscopic approach to modeling the elastic-plastic behavior of a polycrystalline material. The main idea is to divide the continuum (e.g., polycrystalline aggregate) into a set of sub-continua (grains). The overall properties of the polycrystalline aggregate are therefore determined by the number of grains in the aggregate and properties of randomly shaped and oriented grains. The random grain structure is modeled with Voronoi tessellation and random orientations of crystal lattices are assumed. The elastic behavior of monocrystal grains is assumed to be anisotropic. Crystal plasticity is used to describe plastic response of monocrystal grains. Finite element method is used to obtain numerical solutions of strain and stress fields. The analysis is limited to two-dimensional models.(author)

The variation in elastic modulus throughout the compression of foam materials

International Nuclear Information System (INIS)

Sun, Yongle; Amirrasouli, B.; Razavi, S.B.; Li, Q.M.; Lowe, T.; Withers, P.J.

2016-01-01

We present a comprehensive experimental study of the variation in apparent unloading elastic modulus of polymer (largely elastic), aluminium (largely plastic) and fibre-reinforced cement (quasi-brittle) closed-cell foams throughout uniaxial compression. The results show a characteristic “zero-yield-stress” response and thereafter a rapid increase in unloading modulus during the supposedly “elastic” regime of the compressive stress–strain curve. The unloading modulus then falls with strain due to the localised cell-wall yielding or failure in the pre-collapse stage and the progressive cell crushing in the plateau stage, before rising sharply during the densification stage which is associated with global cell crushing and foam compaction. A finite element model based on the actual 3D cell structure of the aluminium foam imaged by X-ray computed tomography (CT) predicts an approximately linear fall of elastic modulus from zero strain until a band of collapsed cells forms. It shows that the subsequent gradual decrease in modulus is caused by the progressive collapse of cells. The elastic modulus rises sharply after the densification initiation strain has been reached. However, the elastic modulus is still well below that of the constituent material even when the “fully” dense state is approached. This work highlights the fact that the unloading elastic modulus varies throughout compression and challenges the idea that a constant elastic modulus can be applied in a homogenised foam model. It is suggested that the most representative value of elastic modulus may be obtained by extrapolating the measured unloading modulus to zero strain.

Material selection for elastic energy absorption in origami-inspired compliant corrugations

International Nuclear Information System (INIS)

Tolman, Sean S; Delimont, Isaac L; Howell, Larry L; Fullwood, David T

2014-01-01

Elastic absorption of kinetic energy and distribution of impact forces are required in many applications. Recent attention to the potential for using origami in engineering may provide new methods for energy absorption and force distribution. A three-stage strategy is presented for selecting materials for such origami-inspired designs that can deform to achieve a desired motion without yielding, absorb elastic strain energy, and be lightweight or cost effective. Two material indices are derived to meet these requirements based on compliant mechanism theory. Finite element analysis is used to investigate the effects of the material stiffness in the Miura-ori tessellation on its energy absorption and force distribution characteristics compared with a triangular wave corrugation. An example is presented of how the method can be used to select a material for a general energy absorption application of the Miura-ori. Whereas the focus of this study is the Miura-ori tessellation, the methods developed can be applied to other tessellated patterns used in energy absorbing or force distribution applications. (paper)

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

Science.gov (United States)

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.

A 3D Orthotropic Elastic Continuum Damage Material Model

Energy Technology Data Exchange (ETDEWEB)

English, Shawn Allen [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Brown, Arthur A. [Sandia National Lab. (SNL-CA), Livermore, CA (United States)

2013-08-01

A three dimensional orthotropic elastic constitutive model with continuum damage is implemented for polymer matrix composite lamina. Damage evolves based on a quadratic homogeneous function of thermodynamic forces in the orthotropic planes. A small strain formulation is used to assess damage. In order to account for large deformations, a Kirchhoff material formulation is implemented and coded for numerical simulation in Sandia’s Sierra Finite Element code suite. The theoretical formulation is described in detail. An example of material parameter determination is given and an example is presented.

Modeling of nonlinear responses for reciprocal transducers involving polarization switching

DEFF Research Database (Denmark)

Willatzen, Morten; Wang, Linxiang

2007-01-01

Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled...... by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled...... intrinsically. The time-dependent Ginzburg-Landau theory is used in the parameter identification involving hysteresis effects. We use the Chebyshev collocation method in the numerical simulations. The elastic field is assumed to be coupled linearly with other fields, and the nonlinearity is in the E-D coupling...

Elastic-Plastic Nonlinear Response of a Space Shuttle External Tank Stringer. Part 2; Thermal and Mechanical Loadings

Science.gov (United States)

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.

Equivalence between short-time biphasic and incompressible elastic material responses.

Science.gov (United States)

Ateshian, Gerard A; Ellis, Benjamin J; Weiss, Jeffrey A

2007-06-01

Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response deltatelasticity tensor, and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components.

Nonlinear piezoelectricity in epitaxial ferroelectrics at high electric fields.

Science.gov (United States)

Grigoriev, Alexei; Sichel, Rebecca; Lee, Ho Nyung; Landahl, Eric C; Adams, Bernhard; Dufresne, Eric M; Evans, Paul G

2008-01-18

Nonlinear effects in the coupling of polarization with elastic strain have been predicted to occur in ferroelectric materials subjected to high electric fields. Such predictions are tested here for a PbZr0.2Ti0.8O3 ferroelectric thin film at electric fields in the range of several hundred MV/m and strains reaching up to 2.7%. The piezoelectric strain exceeds predictions based on constant piezoelectric coefficients at electric fields from approximately 200 to 400 MV/m, which is consistent with a nonlinear effect predicted to occur at corresponding piezoelectric distortions.

Coupled electrostatic-elastic analysis for topology optimization using material interpolation

International Nuclear Information System (INIS)

Alwan, A; Ananthasuresh, G K

2006-01-01

In this paper, we present a novel analytical formulation for the coupled partial differential equations governing electrostatically actuated constrained elastic structures of inhomogeneous material composition. We also present a computationally efficient numerical framework for solving the coupled equations over a reference domain with a fixed finiteelement mesh. This serves two purposes: (i) a series of problems with varying geometries and piece-wise homogeneous and/or inhomogeneous material distribution can be solved with a single pre-processing step (ii) topology optimization methods can be easily implemented by interpolating the material at each point in the reference domain from a void to a dielectric or a conductor. This is attained by considering the steady-state electrical current conduction equation with a 'leaky capacitor' model instead of the usual electrostatic equation. This formulation is amenable for both static and transient problems in the elastic domain coupled with the quasi-electrostatic electric field. The procedure is numerically implemented on the COMSOL Multiphysics (registered) platform using the weak variational form of the governing equations. Examples have been presented to show the accuracy and versatility of the scheme. The accuracy of the scheme is validated for the special case of piece-wise homogeneous material in the limit of the leaky-capacitor model approaching the ideal case

Ultrasonic nondestructive materials characterization

Science.gov (United States)

Green, R. E., Jr.

1986-01-01

A brief review of ultrasonic wave propagation in solid materials is presented with consideration of the altered behavior in anisotropic and nonlinear elastic materials in comparison with isotropic and linear elastic materials. Some experimental results are described in which ultrasonic velocity and attenuation measurements give insight into materials microstructure and associated mechanical properties. Recent developments with laser beam non-contact generation and detection of ultrasound are presented. The results of several years of experimental measurements using high-power ultrasound are discussed, which provide substantial evidence of the inability of presently accepted theories to fully explain the interaction of ultrasound with solid materials. Finally, a special synchrotron X-ray topographic system is described which affords the possibility of observing direct interaction of ultrasonic waves with the microstructural features of real crystalline solid materials for the first time.

Design considerations for multi component molecular-polymeric nonlinear optical materials

Energy Technology Data Exchange (ETDEWEB)

Singer, K.D. (Case Western Reserve Univ., Cleveland, OH (USA). Dept. of Physics); Kuzyk, M.G. (Washington State Univ., Pullman, WA (USA). Dept. of Physics); Fang, T.; Holland, W.R. (AT and T Bell Labs., Princeton, NJ (USA)); Cahill, P.A. (Sandia National Labs., Albuquerque, NM (USA))

1990-01-01

We review our work on multi component polymeric nonlinear optical materials. These materials consist of nonlinear optical molecules incorporated in a polymeric host. A cross-linked triazine polymer incorporating a dicyanovinyl terminated azo dye was found to be relatively stable at 85{degree} and posses an electro-optic coefficient of 11pm/V. We have also observed the zero dispersion condition in a new anomalous dispersion dye for phase matched second harmonic generation, and expect efficient conversion to the blue. A squarylium dye, ISQ, has been found to posses a large third order nonlinearity, and may display two-level behavior. 24 refs., 11 figs.

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.

Science.gov (United States)

Kourakis, I; Shukla, P K

2005-07-01

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

Using the ultrasound and instrumented indentation techniques to measure the elastic modulus of engineering materials

International Nuclear Information System (INIS)

Meza, J. M.; Franco, E. E.; Farias, M. C. M.; Buiochi, F.; Souza, R. M.; Cruz, J.

2008-01-01

Currently, the acoustic and nano indentation techniques are two of the most used techniques for materials elastic modulus measurement. In this article fundamental principles and limitations of both techniques are shown and discussed. Last advances in nano indentation technique are also reviewed. an experimental study in ceramic, metallic, composite and single crystals was also done. Results shown that ultrasonic technique is capable to provide results in agreement with those reported in literature. However, ultrasonic technique does not allow measuring the elastic modulus of some small samples and single crystals. On the other hand, the nano indentation technique estimates the elastic modulus values in reasonable agreement with those measured by acoustic methods, particularly in amorphous materials, while in some policristaline materials some deviation from expected values was obtained. (Author) 29 refs

Material-point Method Analysis of Bending in Elastic Beams

DEFF Research Database (Denmark)

Andersen, Søren Mikkel; Andersen, Lars

The aim of this paper is to test different types of spatial interpolation for the materialpoint method. The interpolations include quadratic elements and cubic splines. A brief introduction to the material-point method is given. Simple liner-elastic problems are tested, including the classical...... cantilevered beam problem. As shown in the paper, the use of negative shape functions is not consistent with the material-point method in its current form, necessitating other types of interpolation such as cubic splines in order to obtain smoother representations of field quantities. It is shown...

Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis.

Science.gov (United States)

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.

Nonlinear Optics with 2D Layered Materials.

Science.gov (United States)

Autere, Anton; Jussila, Henri; Dai, Yunyun; Wang, Yadong; Lipsanen, Harri; Sun, Zhipei

2018-03-25

2D layered materials (2DLMs) are a subject of intense research for a wide variety of applications (e.g., electronics, photonics, and optoelectronics) due to their unique physical properties. Most recently, increasing research efforts on 2DLMs are projected toward the nonlinear optical properties of 2DLMs, which are not only fascinating from the fundamental science point of view but also intriguing for various potential applications. Here, the current state of the art in the field of nonlinear optics based on 2DLMs and their hybrid structures (e.g., mixed-dimensional heterostructures, plasmonic structures, and silicon/fiber integrated structures) is reviewed. Several potential perspectives and possible future research directions of these promising nanomaterials for nonlinear optics are also presented. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Thermomechanical theory of materials undergoing large elastic and viscoplastic deformation (AWBA development program)

International Nuclear Information System (INIS)

Martin, S.E.; Newman, J.B.

1980-11-01

A thermomechanical theory of large deformation elastic-inelastic material behavior is developed which is based on a multiplicative decomposition of the strain. Very general assumptions are made for the elastic and inelastic constitutive relations and effects such as thermally-activated creep, fast-neutron-flux-induced creep and growth, annealing, and strain recovery are compatible with the theory. Reduced forms of the constitutive equations are derived by use of the second law of thermodynamics in the form of the Clausius-Duhem inequality. Observer invariant equations are derived by use of an invariance principle which is a generalization of the principle of material frame indifference

Study of critical behavior in concrete during curing by application of dynamic linear and nonlinear means.

Science.gov (United States)

Lacouture, Jean-Christoph; Johnson, Paul A; Cohen-Tenoudji, Frederic

2003-03-01

The monitoring of both linear and nonlinear elastic properties of a high performance concrete during curing is presented by application of compressional and shear waves. To follow the linear elastic behavior, both compressional and shear waves are used in wide band pulse echo mode. Through the value of the complex reflection coefficient between the cell material (Lucite) and the concrete within the cell, the elastic moduli are calculated. Simultaneously, the transmission of a continuous compressional sine wave at progressively increasing drive levels permits us to calculate the nonlinear properties by extracting the harmonics amplitudes of the signal. Information regarding the chemical evolution of the concrete based upon the reaction of hydration of cement is obtained by monitoring the temperature inside the sample. These different types of measurements are linked together to interpret the critical behavior.

The Quest for the Ultimate Nonlinear Optical Material

Science.gov (United States)

Dagenais, M.

1990-10-01

The following sections are included: * Introduction * From Infancy to the Real World * Highly Efficient Nonlinear Optical Materials for Switching and Processing * The Era of Pragmatism * Conclusion * References

Elastic interaction of hydrogen atoms on graphene: A multiscale approach from first principles to continuum elasticity

Science.gov (United States)

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.

A new nonlinear parameter in the developed strain-to-applied strain of the soft tissues and its application in ultrasound elasticity imaging.

Science.gov (United States)

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

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.

Study on the Unsteady Creep of Composite Beams with an Irregular Laminar Fibrous Structure Made from Nonlinear Hereditary Materials

Science.gov (United States)

Yankovskii, A. P.

2017-09-01

The creep of homogenous and hybrid composite beams of an irregular laminar fibrous structure is investigated. The beams consist of thin walls and flanges (load-carrying layers). The walls may be reinforced longitudinally or crosswise in the plane, and the load-carrying layers are reinforced in the longitudinal direction. The mechanical behavior of phase materials is described by the Rabotnov nonlinear hereditary theory of creep taking into account their possible different resistance to tension and compression. On the basis of hypotheses of the Timoshenko theory, with using the method of time steps, a problem is formulated for the inelastic bending deformation of such beams with account of the weakened resistance of their walls to the transverse shear. It is shown that, at discrete instants of time, the mechanical behavior of such structures can formally be described by the governing relations for composite beams made of nonlinear elastic anisotropic materials with a known initial stress state. The method of successive iterations, similar to the method of variable parameters of elasticity, is used to linearize the boundary-value problem at each instant of time. The bending deformation is investigated for homogeneous and reinforced cantilever and simply supported beams in creep under the action of a uniformly distributed transverse load. The cross sections of the beams considered are I-shaped. It is found that the use of the classical theory for such beams leads to the prediction of indefensibly underestimated flexibility, especially in long-term loading. It is shown that, in beams with reinforced load-carrying layers, the creep mainly develops due to the shear strains of walls. It is found that, in short- and long-term loadings of composite beams, the reinforcement structures rational by the criterion of minimum flexibility are different.

Elastic and plastic characteristics of a model Cu–Zr amorphous alloy

International Nuclear Information System (INIS)

Nakamura, Akiho; Kamimura, Yasushi; Edagawa, Keiichi; Takeuchi, Shin

2014-01-01

Athermal quasistatic simulation of shear deformation has been conducted for a realistic model Cu–Zr amorphous alloy to investigate characteristic features of elasticity and plasticity of the material. Significant reduction of the shear modulus by nonaffine atomic displacements and appreciable nonlinearity of elasticity have been observed. The fourth-order elastic constant in shear deformation and the ideal shear strength have been evaluated. Plastic deformation has been observed to start with isolated local shear transformations (LSTs) followed by collective LSTs leading to the formation of a shear band. Participation-ratio analysis (PRA) has demonstrated how the nonaffine displacement field converges as the system approaches the critical point of losing structural stability. PRA has also evaluated quantitatively the numbers of atoms participating in LSTs – the average number is about 30. Spatially anisotropic development of nascent shear band on a plane has been shown, attributable to anisotropic internal stress field induced by an LST. The evaluated stresses for the shear-band nucleation and for its propagation have indicated that the yielding in real materials is controlled by the shear-band propagation, as previously pointed out

Topology optimization for elastic base under rectangular plate subjected to moving load

Directory of Open Access Journals (Sweden)

Jilavyan Samvel H.

2015-09-01

Full Text Available Distribution optimization of elastic material under elastic isotropic rectangular thin plate subjected to concentrated moving load is investigated in the present paper. The aim of optimization is to damp its vibrations in finite (fixed time. Accepting Kirchhoff hypothesis with respect to the plate and Winkler hypothesis with respect to the base, the mathematical model of the problem is constructed as two-dimensional bilinear equation, i.e. linear in state and control function. The maximal quantity of the base material is taken as optimality criterion to be minimized. The Fourier distributional transform and the Bubnov-Galerkin procedures are used to reduce the problem to integral equality type constraints. The explicit solution in terms of two- dimensional Heaviside‘s function is obtained, describing piecewise-continuous distribution of the material. The determination of the switching points is reduced to a problem of nonlinear programming. Data from numerical analysis are presented.

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.

PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual

Science.gov (United States)

Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.

1977-01-01

The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.

Parameter estimation of a nonlinear Burger's model using nanoindentation and finite element-based inverse analysis

Science.gov (United States)

Hamim, Salah Uddin Ahmed

Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain behavior. Thus, theoretically it is possible to extract mechanical properties of a material through nanoindentation. However, due to various nonlinearities associated with nanoindentation the process of interpreting load-displacement data into material properties is difficult. Although, simple elastic behavior can be characterized easily, a method to characterize complicated material behavior such as nonlinear viscoelasticity is still lacking. In this study, a nanoindentation-based material characterization technique is developed to characterize soft materials exhibiting nonlinear viscoelasticity. Nanoindentation experiment was modeled in finite element analysis software (ABAQUS), where a nonlinear viscoelastic behavior was incorporated using user-defined subroutine (UMAT). The model parameters were calibrated using a process called inverse analysis. In this study, a surrogate model-based approach was used for the inverse analysis. The different factors affecting the surrogate model performance are analyzed in order to optimize the performance with respect to the computational cost.

Quasi-static incremental behavior of granular materials: Elastic-plastic coupling and micro-scale dissipation

Science.gov (United States)

Kuhn, Matthew R.; Daouadji, Ali

2018-05-01

The paper addresses a common assumption of elastoplastic modeling: that the recoverable, elastic strain increment is unaffected by alterations of the elastic moduli that accompany loading. This assumption is found to be false for a granular material, and discrete element (DEM) simulations demonstrate that granular materials are coupled materials at both micro- and macro-scales. Elasto-plastic coupling at the macro-scale is placed in the context of thermomechanics framework of Tomasz Hueckel and Hans Ziegler, in which the elastic moduli are altered by irreversible processes during loading. This complex behavior is explored for multi-directional loading probes that follow an initial monotonic loading. An advanced DEM model is used in the study, with non-convex non-spherical particles and two different contact models: a conventional linear-frictional model and an exact implementation of the Hertz-like Cattaneo-Mindlin model. Orthotropic true-triaxial probes were used in the study (i.e., no direct shear strain), with tiny strain increments of 2 ×10-6 . At the micro-scale, contact movements were monitored during small increments of loading and load-reversal, and results show that these movements are not reversed by a reversal of strain direction, and some contacts that were sliding during a loading increment continue to slide during reversal. The probes show that the coupled part of a strain increment, the difference between the recoverable (elastic) increment and its reversible part, must be considered when partitioning strain increments into elastic and plastic parts. Small increments of irreversible (and plastic) strain and contact slipping and frictional dissipation occur for all directions of loading, and an elastic domain, if it exists at all, is smaller than the strain increment used in the simulations.

Nonlinear damage detection in composite structures using bispectral analysis

Science.gov (United States)

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.

Numerical simulation of the interaction between a nonlinear elastic structure and compressible flow by the discontinuous Galerkin method

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

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.

Nonlinear Wave Mixing Technique for Nondestructive Assessment of Infrastructure Materials

Science.gov (United States)

Ju, Taeho

To operate safely, structures and components need to be inspected or monitored either periodically or in real time for potential failure. For this purpose, ultrasonic nondestructive evaluation (NDE) techniques have been used extensively. Most of these ultrasonic NDE techniques utilize only the linear behavior of the ultrasound. These linear techniques are effective in detecting discontinuities in materials such as cracks, voids, interfaces, inclusions, etc. However, in many engineering materials, it is the accumulation of microdamage that leads to degradation and eventual failure of a component. Unfortunately, it is difficult for linear ultrasonic NDE techniques to characterize or quantify such damage. On the other hand, the acoustic nonlinearity parameter (ANLP) of a material is often positively correlated with such damage in a material. Thus, nonlinear ultrasonic NDE methods have been used in recently years to characterize cumulative damage such as fatigue in metallic materials, aging in polymeric materials, and degradation of cement-based materials due to chemical reactions. In this thesis, we focus on developing a suit of novel nonlinear ultrasonic NDE techniques based on the interactions of nonlinear ultrasonic waves, namely wave mixing. First, a noncollinear wave mixing technique is developed to detect localized damage in a homogeneous material by using a pair of noncollinear a longitudinal wave (L-wave) and a shear wave (S-wave). This pair of incident waves make it possible to conduct NDE from a single side of the component, a condition that is often encountered in practical applications. The proposed noncollinear wave mixing technique is verified experimentally by carrying out measurements on aluminum alloy (AA 6061) samples. Numerical simulations using the Finite Element Method (FEM) are also conducted to further demonstrate the potential of the proposed technique to detect localized damage in structural components. Second, the aforementioned nonlinear

JAC2D: A two-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method

International Nuclear Information System (INIS)

Biffle, J.H.; Blanford, M.L.

1994-05-01

JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere

JAC3D -- A three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method

International Nuclear Information System (INIS)

Biffle, J.H.

1993-02-01

JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere

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

X-Ray Elastic Constants for Cubic Materials

Energy Technology Data Exchange (ETDEWEB)

Malen, K.

1974-10-15

The stress-strain relation to be used in X-ray stress measurements in anisotropic texture-free media is studied. The method for evaluation of appropriate elastic constants for a cubic medium is described. Some illustrative numerical examples have been worked out including line broadening due to elastic anisotropy. The elastic stress and strain compatibility at grain boundaries is taken into account using Kroner's method. These elastic constants obviously only apply when no internal stresses due to plastic deformation are present. The case of reorientation of free interstitials in the stress field can be taken into account

X-Ray Elastic Constants for Cubic Materials

International Nuclear Information System (INIS)

Malen, K.

1974-10-01

The stress-strain relation to be used in X-ray stress measurements in anisotropic texture-free media is studied. The method for evaluation of appropriate elastic constants for a cubic medium is described. Some illustrative numerical examples have been worked out including line broadening due to elastic anisotropy. The elastic stress and strain compatibility at grain boundaries is taken into account using Kroner's method. These elastic constants obviously only apply when no internal stresses due to plastic deformation are present. The case of reorientation of free interstitials in the stress field can be taken into account

X-Ray Elastic Constants for Cubic Materials

Energy Technology Data Exchange (ETDEWEB)

Malen, K

1974-10-15

The stress-strain relation to be used in X-ray stress measurements in anisotropic texture-free media is studied. The method for evaluation of appropriate elastic constants for a cubic medium is described. Some illustrative numerical examples have been worked out including line broadening due to elastic anisotropy. The elastic stress and strain compatibility at grain boundaries is taken into account using Kroner's method. These elastic constants obviously only apply when no internal stresses due to plastic deformation are present. The case of reorientation of free interstitials in the stress field can be taken into account

Nonlinear Ballistic Transport in an Atomically Thin Material.

Science.gov (United States)

Boland, Mathias J; Sundararajan, Abhishek; Farrokhi, M Javad; Strachan, Douglas R

2016-01-26

Ultrashort devices that incorporate atomically thin components have the potential to be the smallest electronics. Such extremely scaled atomically thin devices are expected to show ballistic nonlinear behavior that could make them tremendously useful for ultrafast applications. While nonlinear diffusive electron transport has been widely reported, clear evidence for intrinsic nonlinear ballistic transport in the growing array of atomically thin conductors has so far been elusive. Here we report nonlinear electron transport of an ultrashort single-layer graphene channel that shows quantitative agreement with intrinsic ballistic transport. This behavior is shown to be distinctly different than that observed in similarly prepared ultrashort devices consisting, instead, of bilayer graphene channels. These results suggest that the addition of only one extra layer of an atomically thin material can make a significant impact on the nonlinear ballistic behavior of ultrashort devices, which is possibly due to the very different chiral tunneling of their charge carriers. The fact that we observe the nonlinear ballistic response at room temperature, with zero applied magnetic field, in non-ultrahigh vacuum conditions and directly on a readily accessible oxide substrate makes the nanogap technology we utilize of great potential for achieving extremely scaled high-speed atomically thin devices.

Integration of Geometrical and Material Nonlinear Energy Sink with Piezoelectric Material Energy Harvester

Directory of Open Access Journals (Sweden)

Ye-Wei Zhang

2017-01-01

Full Text Available This paper presents a novel design by integrating geometrical and material nonlinear energy sink (NES with a piezoelectric-based vibration energy harvester under shock excitation, which can realize vibration control and energy harvesting. The nonlinear spring and hysteresis behavior of the NES could reflect geometrical and material nonlinearity, respectively. Two configurations of the piezoelectric device, including the piezoelectric element embedded between the NES mass and the single-degree-of-freedom system or ground, are utilised to examine the energy dissipated by damper and hysteresis behavior of NES and the energy harvested by the piezoelectric element. Similar numerical research methods of Runge-Kutta algorithm are used to investigate the two configurations. The energy transaction measure (ETM is adopted to examine the instantaneous energy transaction between the primary and the NES-piezoelectricity system. And it demonstrates that the dissipated and harvested energy transaction is transferred from the primary system to the NES-piezoelectricity system and the instantaneous transaction of mechanical energy occupies a major part of the energy of transaction. Both figurations could realize vibration control efficiently.

Detecting closing delaminations in laminated composite plates using nonlinear structural intensity and time reversal mirrors

International Nuclear Information System (INIS)

Lamberti, Alfredo; Semperlotti, Fabio

2013-01-01

Closing delaminations in composite laminated structures exhibit a nonlinear dynamic response when excited by high frequency elastic waves. The contact acoustic nonlinear effects taking place at the damage interface act as a mechanism of energy redistribution from the driving frequency to the nonlinear harmonic frequencies. In this paper, we extend the concept of nonlinear structural intensity (NSI) to the analysis of closing delaminations in composite laminated plates. NSI is calculated using a method based on a combination of finite element and finite difference techniques, which is suitable for processing both numerical and experimental data. NSI is proven to be an effective metric to identify the presence and location of closing delaminations. The highly directional nature of orthotropic composites results in vibrational energy propagating in a different direction from that of the initial elastic wave. This aspect reduces the ability to effectively interrogate the damage and, therefore, the sensitivity to the damage. The time reversal mirror technique is explored as a possible approach to overcome the effect of the material directionality and increase the ability to interrogate the damage. Numerical simulations show that this technique is able to overcome the material directionality and to drastically enhance the ability to interrogate the damage. (paper)

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

Investigation of nonlinear optical properties of various organic materials by the Z-scan method

Science.gov (United States)

Ganeev, R. A.; Boltaev, G. S.; Tugushev, R. I.; Usmanov, T.

2012-06-01

We have studied the nonlinear optical properties of various organic materials (vegetable oil, juice, wine, cognac, Coca-Cola and Fanta drinks, Nescafé coffee, tea, gasoline, clock oil, glycerol, and polyphenyl ether) that are used in everyday life. Their nonlinearities have been studied by the Z-scan method in the near-IR and visible spectral ranges. We have shown that the majority of samples possess a nonlinear absorption; however, some of the studied materials show a strong saturated absorption and nonlinear refraction. Red wine and glycerol proved to be the most interesting materials. For these samples, we have observed a change in the sign of the nonlinear absorption with increasing laser intensity, which was attributed to the competition between two-photon absorption and saturated absorption.

Estimation of non-linear effective permeability of magnetic materials with fine structure

International Nuclear Information System (INIS)

Waki, H.; Igarashi, H.; Honma, T.

2006-01-01

This paper describes a homogenization method for magnetic materials with fine structure. In this method, the structures of the magnetic materials are assumed to be periodic, and the unit cell is defined. The effective permeability is determined on the basis of magnetic energy balance in the unit cell. This method can be applied not only for linear problems but also for non-linear ones. In this paper, estimation of the effective permeability of non-linear magnetic materials by using the homogenization method is described in detail, and then the validity for the non-liner problems is tested for two-dimensional problems. It is shown that this homogenization method gives accurate non-linear effective permeability

Sound transmission through stiffened double-panel structures lined with elastic porous materials

Science.gov (United States)

Mathur, Gopal P.; Tran, Boi N.; Bolton, J. S.; Shiau, Nae-Ming

This paper presents transmission loss prediction models for a periodically stiffened panel and stiffened double-panel structures using the periodic structure theory. The inter-panel cavity in the double-panels structures can be modeled as being separated by an airspace or filled with an elastic porous layer in various configurations. The acoustic behavior of elastic porous layer is described by a theory capable of accounting fully for multi-dimensional wave propagation in such materials. The predicted transmission loss of a single stiffened panel is compared with the measured data.

Waves in nonlinear pre-stressed materials

CERN Document Server

Schneider, Wilhelm; Saccomandi, G

2007-01-01

The papers in this book provide a unique state-of-the-art multidisciplinary overview on the subject of waves in pre-stressed materials through the interaction of several topics, ranging from the mathematical modelling of incremental material response (elastic and inelastic), to the analysis of the governing differential equations and boundary-value problems, and to computational methods for the solution to these problems, with particular reference to industrial, geophysical, and biomechanical applications. A complete view on the title subject is proposed, including: The basic and fundamental theoretical issues (mechanical modelling, exact solutions, asymptotic methods, numerical treatment); A unified introduction to wave propagation (small on large and large on large); A look toward classical (such as geophysics and the mechanics of rubber-like solids) and emergent (such as biomechanics) applications.

Remarks on some reference materials for applications in elastic peak electron spectroscopy

International Nuclear Information System (INIS)

Jablonski, A.; Zemek, J.

2010-01-01

The quantification of results of electron spectroscopies, AES and XPS, requires knowledge of the inelastic mean free path (IMFP) of signal electrons in solids. This parameter determines the surface sensitivity of both techniques. There are two methods of determining the IMFPs that provide these parameters in agreement with the definition: (1) calculations based on the experimental optical data, and (2) calculations based on measurements of the electron elastic backscattering intensity. The latter method requires the use of some reference material for which the IMFP is known. In 1999, an extensive analysis of the published IMFPs has been performed; the results indicated that there is a very good agreement between the calculated and measured IMFPs for four elemental solids: Ni, Cu, Ag and Au. The averaged IMFPs for these elements are known under the name of the recommended IMFPs. However, no preference among these four elements has been established. In the present work, an attempt is made to select an element for which the recommended IMFPs result in the best agreement between the calculated and measured intensities of elastic electron backscattering. For this purpose, the elastic backscattering intensity has been measured at eight electron energies varying from 200 to 1500 eV. At each energy, the intensity was measured over a wide range of emission angles from 35deg to 74deg. The experiments were accompanied with Monte Carlo calculations of the elastic backscattering probability for the same energies and experimental configurations. It has been found, from comparison, that the best agreement is observed for Au, and this element is thus recommended as the reference material. It has been shown that the shape of the emission angle dependence of the elastic backscattering intensity is noticeably influenced by the surface energy losses. (author)

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

Evaluation of Ultrasonic Nonlinear Characteristics in Heat-Treated Aluminum Alloy (Al-Mg-Si-Cu

Directory of Open Access Journals (Sweden)

JongBeom Kim

2013-01-01

Full Text Available The nonlinear ultrasonic technique has been known to be more sensitive to minute variation of elastic properties in material than the conventional linear ultrasonic method. In this study, the ultrasonic nonlinear characteristics in the heat-treated aluminum alloy (Al-Mg-Si-Cu have been evaluated. For this, the specimens were heat treated for various heating period up to 50 hours at three different heating temperatures: 250°C, 300°C, and 350°C. The ultrasonic nonlinear characteristics of each specimen were evaluated by measuring the ultrasonic nonlinear parameter β from the amplitudes of fundamental and second harmonic frequency components in the transmitted ultrasonic wave. After the ultrasonic test, tensile strengths and elongations were obtained by the tensile test to compare with the parameter β. The heating time showing a peak in the parameter β was identical to that showing critical change in the tensile strength and elongation, and such peak appeared at the earlier heating time in the higher heating temperature. These results suggest that the ultrasonic nonlinear parameter β can be used for monitoring the variations in elastic properties of aluminum alloys according to the heat treatment.

Bulk solitary waves in elastic solids

Science.gov (United States)

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

Experimental determination of third-order elastic constants of diamond.

Science.gov (United States)

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.

The chemistry and physics of nonlinear optical materials

International Nuclear Information System (INIS)

Velsko, S.P.; Eimerl, D.

1989-01-01

Recent efforts to engineer new nonlinear optical materials with specific desired characteristics has engendered a need for a theoretical description of optical properties which is readily accessible to chemists, yet correctly treats the essential physics of dielectric response. This paper describes a simple empirical molecular orbital model which gives useful insights into the relationship between chemical composition, crystalline structure, and optical susceptibilities. The authors compare the probabilities of finding new harmonic generators in various chemical classes. Rigorous bounds on the magnitudes of linear and nonlinear optical coefficients and their anisotropies are also discussed

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.)

Elastic-Plastic Calculation of a Dilatation Compensation Component

Science.gov (United States)

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.

Nonlinear static analysis of single layer annular/circular graphene sheets embedded in Winkler–Pasternak elastic matrix based on non-local theory of Eringen

Directory of Open Access Journals (Sweden)

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.

Some fundamental definitions of the elastic parameters for homogeneous isotropic linear elastic materials in pavement design and analysis

CSIR Research Space (South Africa)

De Beer, Morris

2008-07-01

Full Text Available - wave and ρ the material density. The elastic moduli P-wave modulus, M, is defined so that M = K + 4µ / 3 and M can then be determined by Equation 11, with a known speed Vp P MV 2 ρ = (11) It should however also... gas (such as air within compacted road materials), the adiabatic bulk modulus KS is approximately given by pKS κ= (4) Where: κ is the adiabatic index, (sometimes calledγ ); p is the pressure. In a fluid (such as moisture...

Tunable elastic parity-time symmetric structure based on the shunted piezoelectric materials

Science.gov (United States)

Hou, Zhilin; Assouar, Badreddine

2018-02-01

We theoretically and numerically report on the tunable elastic Parity-Time (PT) symmetric structure based on shunted piezoelectric units. We show that the elastic loss and gain can be archived in piezoelectric materials when they are shunted by external circuits containing positive and negative resistances. We present and discuss, as an example, the strongly dependent relationship between the exceptional points of a three-layered system and the impedance of their external shunted circuit. The achieved results evidence that the PT symmetric structures based on this proposed concept can actively be tuned without any change of their geometric configurations.

Nonlinear elastic inclusions in isotropic solids

KAUST Repository

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

Nonlinear response and avalanche behavior in metallic glasses

Science.gov (United States)

Riechers, B.; Samwer, K.

2017-08-01

The response to different stress amplitudes at temperatures below the glass transition temperature is analyzed by mechanical oscillatory excitation of Pd40Ni40P20 metallic glass samples in single cantilever bending geometry. While low amplitude oscillatory excitations are commonly used in mechanical spectroscopy to probe the relaxation spectrum, in this work the response to comparably high amplitudes is investigated. The strain response of the material is well below the critical yield stress even for highest stress amplitudes, implying the expectation of a linear relation between stress and strain according to Hooke's Law. However, a deviation from the linear behavior is evident, which is analyzed in terms of temperature dependence and influence of the applied stress amplitude by two different approaches of evaluation. The nonlinear approach is based on a nonlinear expansion of the stress-strain-relation, assuming an intrinsic nonlinear character of the shear or elastic modulus. The degree of nonlinearity is extracted by a period-by-period Fourier-analysis and connected to nonlinear coefficients, describing the intensity of nonlinearity at the fundamental and higher harmonic frequencies. The characteristic timescale to adapt to a significant change in stress amplitude in terms of a recovery timescale to a steady state value is connected to the structural relaxation time of the material, suggesting a connection between the observed nonlinearity and primary relaxation processes. The second approach of evaluation is termed the incremental analysis and relates the observed response behavior to avalanches, which occur due to the activation and correlation of local microstructural rearrangements. These rearrangements are connected with shear transformation zones and correspond to localized plastic events, which are superimposed on the linear response behavior of the material.

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

Nonlinear dynamics and control of a vibrating rectangular plate

Science.gov (United States)

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.

Nonlinear Buckling Analysis of Functionally Graded Graphene Reinforced Composite Shallow Arches with Elastic Rotational Constraints under Uniform Radial Load.

Science.gov (United States)

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.

Effective X-ray elastic constant measurement for in situ stress measurement of biaxially strained AA5754-O

International Nuclear Information System (INIS)

Iadicola, Mark A.; Gnäupel-Herold, Thomas H.

2012-01-01

Accurate measurement of stresses by X-ray diffraction requires accurate X-ray elastic constants. Calibration experiments are one method to determine these for a specific material in a specific condition. In this paper, uniaxial tension experiments are used to investigate the variation of these constants after uniaxial and equal-biaxial plastic deformation for an aluminum alloy (AA5754-O) of interest to the automotive industry. These data are critical for accurate measurement of the biaxial mechanical properties of the material using a recent experimental method combining specialized sheet metal forming equipment with portable X-ray diffraction equipment. The measured effective X-ray elastic constants show some minor variation with increased plastic deformation, and this behavior was found to be consistent for both uniaxially and equal-biaxially strained samples. The use of two average values for effective X-ray elastic constants, one in the rolling direction and one transverse to the rolling direction of the sheet material, is shown to be of sufficient accuracy for the combined tests of interest. Comparison of uniaxial data measured using X-ray diffraction and standard methods show good agreement, and biaxial stress–strain results show good repeatability. Additionally, the calibration data show some non-linear behavior, which is analyzed in regards to crystallographic texture and intergranular stress effects. The non-linear behavior is found to be the result of intergranular stresses based on comparison with additional measurements using other X-ray diffraction equipment and neutron diffraction.

Simultaneous spatial and temporal focusing: a route towards confined nonlinear materials processing

Science.gov (United States)

Kammel, Robert; Bergner, Klaus; Thomas, Jens; Ackermann, Roland; Skupin, Stefan; Nolte, Stefan

2016-03-01

Ultrashort pulse lasers enable reliable and versatile high precision ablation and surface processing of various materials such as metals, polymers and semiconductors. However, when modifications deep inside the bulk of transparent media are required, nonlinear pulse material interactions can decrease the precision, since weak focusing and the long propagation of the intense pulses within the nonlinear media may induce Kerr self-focusing, filamentation and white light generation. In order to improve the precision of those modifications, simultaneous spatial and temporal focusing (SSTF) allows to reduce detrimental nonlinear interactions, because the ultrashort pulse duration is only obtained at the focus, while outside of the focal region the continuously increasing pulse duration strongly reduces the pulse intensity. In this paper, we review the fundamental concepts of this technology and provide an overview of its applications for purposes of multiphoton microscopy and laser materials processing. Moreover, numerical simulations on the nonlinear pulse propagation within transparent media illustrate the linear and nonlinear pulse propagation, highlighting the differences between conventional focusing and SSTF. Finally, fs-laser induced modifications in gelatine are presented to compare nonlinear side-effects caused by conventional focusing and SSTF. With conventional focusing the complex interplay of self-focusing and filamentation induces strongly inhomogeneous, elongated disruptions. In contrast, disruptions induced by SSTF are homogeneously located at the focal plane and reduced in length by a factor >2, which is in excellent agreement with the numerical simulations of the nonlinear pulse propagation and might favor SSTF for demanding applications such as intraocular fs-laser surgery.

Effect of Nonlinear Hardening of Lead Rubber Bearing on Long Term Behavior of Base Isolated Containment Building

International Nuclear Information System (INIS)

Park, Junhee; Choun, Young-Sun; Kim, Min-Kyu

2015-01-01

The rubber material used in laminated rubber bearings is the hyper elastic material whose stress-strain relationship can be defined as nonlinearly elastic. From the previous research, it was presented that the rubber hardness and stiffness was increased by the aging of LRB. The mechanical properties of LRB changed by aging can directly affect a nonlinear hardening behavior. Therefore it is needed to consider the nonlinear hardening effect for exactly evaluating the seismic safety of base isolated structure during the life time. In this study, the seismic response analysis of base isolated containment building was performed by using the bilinear model and the hardening model to identify the effect of structural response on the nonlinear hardening behavior of isolator. Moreover the floor response spectrum of base isolated structure considering the aging was analyzed by according to the analysis model of LRB.. The hardening behavior of lead rubber bearing occurs at high strain. Therefore it is reasonable to assume that the hysteretic model of LRB is the nonlinear hardening model for exactly evaluating the seismic response of base isolated structure. The nonlinear analysis of base isolated containment was performed by using the nonlinear hardening variables which was resulted from the test results and finite element analysis. From the analysis results, it was represented that the FRS was higher about 40% with nonlinear hardening model than with the bilinear model. Therefore the seismic response of base isolated structure with bilinear model can be underestimated than the real response. It is desired that the nonlinear hardening model of LRB is applied for the seismic risk evaluation requiring the ultimate state of LRB

Geometrically non linear analysis of functionally graded material ...

African Journals Online (AJOL)

user

when compared to the other engineering materials (Akhavan and Hamed, 2010). However, FGM plates under mechanical loading may undergo elastic instability. Hence, the non-linear behavior of functionally graded plates has to be understood for their optimum design. Reddy (2000) proposed the theoretical formulation ...

Wave propagation in ordered, disordered, and nonlinear photonic band gap materials

Energy Technology Data Exchange (ETDEWEB)

Lidorikis, Elefterios [Iowa State Univ., Ames, IA (United States)

1999-12-10

Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. In this dissertation the author studied two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material, while, the second area is focused on the mechanisms responsible for the gap formation as well as other properties of two-dimensional PBG materials. He first studied, in Chapter 2, the general adequacy of an approximate structure model in which the nonlinearity is assumed to be concentrated in equally-spaced very thin layers, or 6-functions, while the rest of the space is linear. This model had been used before, but its range of validity and the physical reasons for its limitations were not quite clear yet. He performed an extensive examination of many aspects of the model's nonlinear response and comparison against more realistic models with finite-width nonlinear layers, and found that the d-function model is quite adequate, capturing the essential features in the transmission characteristics. The author found one exception, coming from the deficiency of processing a rigid bottom band edge, i.e. the upper edge of the gaps is always independent of the refraction index contrast. This causes the model to miss-predict that there are no soliton solutions for a positive Kerr-coefficient, something known to be untrue.

Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load

Science.gov (United States)

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.

Nonlinear isochrones in murine left ventricular pressure-volume loops: how well does the time-varying elastance concept hold?

Science.gov (United States)

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.

A Membrane Model from Implicit Elasticity Theory

Science.gov (United States)

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

Rotation, inversion and perversion in anisotropic elastic cylindrical tubes and membranes

KAUST Repository

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

Nonlinear dynamics between linear and impact limits

CERN Document Server

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.

JAC3D -- A three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method; Yucca Mountain Site Characterization Project

Energy Technology Data Exchange (ETDEWEB)

Biffle, J.H.

1993-02-01

JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.

JAC2D: A two-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method; Yucca Mountain Site Characterization Project

Energy Technology Data Exchange (ETDEWEB)

Biffle, J.H.; Blanford, M.L.

1994-05-01

JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.

Characterization and modeling of performance of Polymer Composites Reinforced with Highly Non-Linear Cellulosic Fibers

International Nuclear Information System (INIS)

Rozite, L; Joffe, R; Varna, J; Nyström, B

2012-01-01

The behaviour of highly non-linear cellulosic fibers and their composite is characterized. Micro-mechanisms occurring in these materials are identified. Mechanical properties of regenerated cellulose fibers and composites are obtained using simple tensile test. Material visco-plastic and visco-elastic properties are analyzed using creep tests. Two bio-based resins are used in this study – Tribest and EpoBioX. The glass and flax fiber composites are used as reference materials to compare with Cordenka fiber laminates.

Characterization and modeling of performance of Polymer Composites Reinforced with Highly Non-Linear Cellulosic Fibers

Science.gov (United States)

Rozite, L.; Joffe, R.; Varna, J.; Nyström, B.

2012-02-01

The behaviour of highly non-linear cellulosic fibers and their composite is characterized. Micro-mechanisms occurring in these materials are identified. Mechanical properties of regenerated cellulose fibers and composites are obtained using simple tensile test. Material visco-plastic and visco-elastic properties are analyzed using creep tests. Two bio-based resins are used in this study - Tribest and EpoBioX. The glass and flax fiber composites are used as reference materials to compare with Cordenka fiber laminates.

Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling

Science.gov (United States)

Chen, Wei-Qiu

2015-10-01

Significant progress has been made in mixed boundary-value problems associated with three-dimensional (3D) crack and contact analyses of advanced materials featuring more complexities compared to the conventional isotropic elastic materials. These include material anisotropy and multifield coupling, two typical characteristics of most current multifunctional materials. In this paper we try to present a state-of-the-art description of 3D exact/analytical solutions derived for crack and contact problems of elastic solids with both transverse isotropy and multifield coupling in the latest decade by the potential theory method in the spirit of V. I. Fabrikant, whose ingenious breakthrough brings new vigor and vitality to the old research subject of classical potential theory. We are particularly interested in crack and contact problems with certain nonlinear features. Emphasis is also placed on the coupling between the temperature field (or the like) and other physical fields (e.g., elastic, electric, and magnetic fields). We further highlight the practical significance of 3D contact solutions, in particular in applications related to modern scanning probe microscopes.

Multi-crack imaging using nonclassical nonlinear acoustic method

Science.gov (United States)

Zhang, Lue; Zhang, Ying; Liu, Xiao-Zhou; Gong, Xiu-Fen

2014-10-01

Solid materials with cracks exhibit the nonclassical nonlinear acoustical behavior. The micro-defects in solid materials can be detected by nonlinear elastic wave spectroscopy (NEWS) method with a time-reversal (TR) mirror. While defects lie in viscoelastic solid material with different distances from one another, the nonlinear and hysteretic stress—strain relation is established with Preisach—Mayergoyz (PM) model in crack zone. Pulse inversion (PI) and TR methods are used in numerical simulation and defect locations can be determined from images obtained by the maximum value. Since false-positive defects might appear and degrade the imaging when the defects are located quite closely, the maximum value imaging with a time window is introduced to analyze how defects affect each other and how the fake one occurs. Furthermore, NEWS-TR-NEWS method is put forward to improve NEWS-TR scheme, with another forward propagation (NEWS) added to the existing phases (NEWS and TR). In the added phase, scanner locations are determined by locations of all defects imaged in previous phases, so that whether an imaged defect is real can be deduced. NEWS-TR-NEWS method is proved to be effective to distinguish real defects from the false-positive ones. Moreover, it is also helpful to detect the crack that is weaker than others during imaging procedure.

Estimating the price elasticity of expenditure for prescription drugs in the presence of non-linear price schedules: an illustration from Quebec, Canada.

Science.gov (United States)

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.

Enhancing Thermoelectric Performance Using Nonlinear Transport Effects

Science.gov (United States)

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.

On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

Science.gov (United States)

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.

Studies of nonlinear femtosecond pulse propagation in bulk materials

Science.gov (United States)

Eaton, Hilary Kaye

2000-10-01

Femtosecond pulse lasers are finding widespread application in a variety of fields including medical research, optical switching and communications, plasma formation, high harmonic generation, and wavepacket formation and control. As the number of applications for femtosecond pulses increases, so does the need to fully understand the linear and nonlinear processes involved in propagating these pulses through materials under various conditions. Recent advances in pulse measurement techniques, such as frequency-resolved optical gating (FROG), allow measurement of the full electric field of the pulse and have made detailed investigations of short- pulse propagation effects feasible. In this thesis, I present detailed experimental studies of my work involving nonlinear propagation of femtosecond pulses in bulk media. Studies of plane-wave propagation in fused silica extend the SHG form of FROG from a simple pulse diagnostic to a useful method of interrogating the nonlinear response of a material. Studies of nonlinear propagation are also performed in a regime where temporal pulse splitting occurs. Experimental results are compared with a three- dimensional nonlinear Schrödinger equation. This comparison fuels the development of a more complete model for pulse splitting. Experiments are also performed at peak input powers above those at which pulse splitting is observed. At these higher intensities, a broadband continuum is generated. This work presents a detailed study of continuum behavior and power loss as well as the first near-field spatial- spectral measurements of the generated continuum light. Nonlinear plane-wave propagation of short pulses in liquids is also investigated, and a non-instantaneous nonlinearity with a surprisingly short response time of 10 fs is observed in methanol. Experiments in water confirm that this effect in methanol is indeed real. Possible explanations for the observed effect are discussed and several are experimentally rejected. This

Hysteresis, Discrete Memory, and Nonlinear Wave Propagation in Rock: A New Paradigm

International Nuclear Information System (INIS)

Guyer, R.A.; McCall, K.R.; Boitnott, G.N.

1995-01-01

The structural elements in a rock are characterized by their density in Preisach-Mayergoyz space (PM space). This density is found for a Berea sandstone from stress-strain data and used to study the response of the sandstone to elaborate pressure protocols. Hysteresis with discrete memory, in agreement with experiment, is found. The relationship between strain, quasistatic modulus, and dynamic modulus is established. Nonlinear wave propagation, the production of copious harmonics, and nonlinear attenuation are demonstrated. PM space is shown to be the central construct in a new paradigm for the description of the elastic behavior of consolidated materials

Modeling elastic anisotropy in strained heteroepitaxy.

Science.gov (United States)

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

Science.gov (United States)

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.

Elastic-Plastic J-Integral Solutions or Surface Cracks in Tension Using an Interpolation Methodology. Appendix C -- Finite Element Models Solution Database File, Appendix D -- Benchmark Finite Element Models Solution Database File

Science.gov (United States)

Allen, Phillip A.; Wells, Douglas 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.

Nonlinear phononics and structural control of strongly correlated materials

Energy Technology Data Exchange (ETDEWEB)

Mankowsky, Roman

2016-01-20

Mid-infrared light pulses can be used to resonantly excite infrared-active vibrational modes for the phase control of strongly correlated materials on subpicosecond timescales. As the energy is transferred directly into atomic motions, dissipation into the electronic system is reduced, allowing for the emergence of unusual low energy collective properties. Light-induced superconductivity, insulator-metal transitions and melting of magnetic order demonstrate the potential of this method. An understanding of the mechanism, by which these transitions are driven, is however missing. The aim of this work is to uncover this process by investigating the nonlinear lattice dynamics induced by the excitation and to elucidate their contribution to the modulation of collective properties of strongly correlated materials. The first signature of nonlinear lattice dynamics was reported in the observation of coherent phonon oscillations, resonant with the excitation of an infrared-active phonon mode in a manganite. This nonlinear phononic coupling can be described within a model, which predicts not only oscillatory coherent phonons dynamics but also directional atomic displacements along the coupled modes on average, which could cause the previously observed transitions. We verified this directional response and quantified the anharmonic coupling constant by tracing the atomic motions in a time-resolved hard X-ray diffraction experiment with sub-picometer spatial and femtosecond temporal resolution. In a subsequent study, we investigated the role of nonlinear lattice dynamics in the emergence of superconductivity far above the equilibrium transition temperature, an intriguing effect found to follow lattice excitation of YBa{sub 2}Cu{sub 3}O{sub 6+x}. By combining density functional theory (DFT) calculations of the anharmonic coupling constants with time-resolved X-ray diffraction experiments, we identified a structural rearrangement, which appears and decays with the same temporal

Quantifying the Mechanical Properties of Materials and the Process of Elastic-Plastic Deformation under External Stress on Material

Directory of Open Access Journals (Sweden)

Jan Valíček

2015-11-01

Full Text Available The paper solves the problem of the nonexistence of a new method for calculation of dynamics of stress-deformation states of deformation tool-material systems including the construction of stress-strain diagrams. The presented solution focuses on explaining the mechanical behavior of materials after cutting by abrasive waterjet technology (AWJ, especially from the point of view of generated surface topography. AWJ is a flexible tool accurately responding to the mechanical resistance of the material according to the accurately determined shape and roughness of machined surfaces. From the surface topography, it is possible to resolve the transition from ideally elastic to quasi-elastic and plastic stress-strain states. For detecting the surface structure, an optical profilometer was used. Based on the analysis of experimental measurements and the results of analytical studies, a mathematical-physical model was created and an exact method of acquiring the equivalents of mechanical parameters from the topography of surfaces generated by abrasive waterjet cutting and external stress in general was determined. The results of the new approach to the construction of stress-strain diagrams are presented. The calculated values agreed very well with those obtained by a certified laboratory VÚHŽ.

Quantifying the Mechanical Properties of Materials and the Process of Elastic-Plastic Deformation under External Stress on Material

Science.gov (United States)

Valíček, Jan; Harničárová, Marta; Öchsner, Andreas; Hutyrová, Zuzana; Kušnerová, Milena; Tozan, Hakan; Michenka, Vít; Šepelák, Vladimír; Mitaľ, Dušan; Zajac, Jozef

2015-01-01

The paper solves the problem of the nonexistence of a new method for calculation of dynamics of stress-deformation states of deformation tool-material systems including the construction of stress-strain diagrams. The presented solution focuses on explaining the mechanical behavior of materials after cutting by abrasive waterjet technology (AWJ), especially from the point of view of generated surface topography. AWJ is a flexible tool accurately responding to the mechanical resistance of the material according to the accurately determined shape and roughness of machined surfaces. From the surface topography, it is possible to resolve the transition from ideally elastic to quasi-elastic and plastic stress-strain states. For detecting the surface structure, an optical profilometer was used. Based on the analysis of experimental measurements and the results of analytical studies, a mathematical-physical model was created and an exact method of acquiring the equivalents of mechanical parameters from the topography of surfaces generated by abrasive waterjet cutting and external stress in general was determined. The results of the new approach to the construction of stress-strain diagrams are presented. The calculated values agreed very well with those obtained by a certified laboratory VÚHŽ. PMID:28793645

On Optimal Shapes in Materials and Structures

DEFF Research Database (Denmark)

Pedersen, Pauli

2000-01-01

In the micromechanics design of materials, as well as in the design of structural connections, the boundary shape plays an important role. The objective may be the stiffest design, the strongest design or just a design of uniform energy density along the shape. In an energy formulation it is proven...... that these three objectives have the same solution, at least within the limits of geometrical constraints, including the parametrization. Without involving stress/strain fields, the proof holds for 3D-problems, for power-law nonlinear elasticity and for anisotropic elasticity. To clarify the importance...

Linearity and Non-linearity of Photorefractive effect in Materials ...

African Journals Online (AJOL)

Linearity and Non-linearity of Photorefractive effect in Materials using the Band transport ... For low light beam intensities the change in the refractive index is ... field is spatially phase shifted by /2 relative to the interference fringe pattern, which ...

Elastic and Viscoelastic Stresses of Nonlinear Rotating Functionally Graded Solid and Annular Disks with Gradually Varying Thickness

Directory of Open Access Journals (Sweden)

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.

Nonlinear Optics: Materials, Fundamentals, and Applications. Postdeadline papers

Science.gov (United States)

1992-08-01

The Nonlinear Optics: Materials, Fundamentals, and Applications conference was held on 17-21 Aug. 1992. The following topics were addressed: subpicosecond time resolved four-wave mixing spectroscopy in heteroepitaxial ZnSe thin layers; anisotropic two-photon transition in GaAs/AlGaAs multiple quantum well waveguides; two picosecond, narrow-band, tunable, optical parametric systems using BBO and LBO; second generation in an optically active liquid: experimental observation of a fourth-order optical nonlinearity due to molecular chirality; optical image recognition system implemented with a 3-D memory disk; phase-matched second-harmonic generation in waveguides of polymeric Langmuir-Blodgett films; fluence dependent dynamics observed in the resonant third-order optical response of C60 and C70 films; temporal modulation of spatial optical solitons: a variational approach; measurements of light-scattering noise during two-wave mixing in a Kerr medium; excess noise introduced by beam propagation through an atomic vapor; an approach to all-optical switching based on second-order nonlinearities; multilayer, nonlinear ARROW waveguides for surface emitted sum-frequency mixing; energy scaling of SBS phase conjugate mirrors to 4J; vector versus scalar theory for the double phase conjugate mirror; cross-talk and error probability in counter-beam lambda-multiplexed digital holograms; and modal growth of SHG in doped silica thin film waveguides.

Elastic Characterization of Transversely Isotropic Soft Materials by Dynamic Shear and Asymmetric Indentation

OpenAIRE

Namani, R.; Feng, Y.; Okamoto, R. J.; Jesuraj, N.; Sakiyama-Elbert, S. E.; Genin, G. M.; Bayly, P. V.

2012-01-01

The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isot...

Estimation of parameters of constant elasticity of substitution production functional model

Science.gov (United States)

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.

From non-linear magnetoacoustics and spin reorientation transition to magnetoelectric micro/nano-systems

Science.gov (United States)

Tiercelin, Nicolas; Preobrazhensky, Vladimir; BouMatar, Olivier; Talbi, Abdelkrim; Giordano, Stefano; Dusch, Yannick; Klimov, Alexey; Mathurin, Théo.; Elmazria, Omar; Hehn, Michel; Pernod, Philippe

2017-09-01

The interaction of a strongly nonlinear spin system with a crystalline lattice through magnetoelastic coupling results in significant modifications of the acoustic properties of magnetic materials, especially in the vicinity of magnetic instabilities associated with the spin-reorientation transition (SRT). The magnetoelastic coupling transfers the critical properties of the magnetic subsystem to the elastic one, which leads to a strong decrease of the sound velocity in the vicinity of the SRT, and allows a large control over acoustic nonlinearities. The general principles of the non-linear magneto-acoustics (NMA) will be introduced and illustrated in `bulk' applications such as acoustic wave phase conjugation, multi-phonon coupling, explosive instability of magneto-elastic vibrations, etc. The concept of the SRT coupled to magnetoelastic interaction has been transferred into nanostructured magnetoelastic multilayers with uni-axial anisotropy. The high sensitivity and the non-linear properties have been demonstrated in cantilever type actuators, and phenomena such as magneto-mechanical RF demodulation have been observed. The combination of the magnetic layers with piezoelectric materials also led to stress-mediated magnetoelectric (ME) composites with high ME coefficients, thanks to the SRT. The magnetoacoustic effects of the SRT have also been studied for surface acoustic waves propagating in the magnetoelastic layers and found to be promising for highly sensitive magnetic field sensors working at room temperature. On the other hand, mechanical stress is a very efficient way to control the magnetic subsystem. The principle of a very energy efficient stress-mediated magnetoelectric writing and reading in a magnetic memory is described.

Cumulative Second Harmonic Generation in Lamb Waves for the Detection of Material Nonlinearities

International Nuclear Information System (INIS)

Bermes, Christian; Jacobs, Laurence J.; Kim, Jin-Yeon; Qu, Jianmin

2007-01-01

An understanding of the generation of higher harmonics in Lamb waves is of critical importance for applications such as remaining life prediction of plate-like structural components. The objective of this work is to use nonlinear Lamb waves to experimentally investigate inherent material nonlinearities in aluminum plates. These nonlinearities, e.g. lattice anharmonicities, precipitates or vacancies, cause higher harmonics to form in propagating Lamb waves. The amplitudes of the higher harmonics increase with increasing propagation distance due to the accumulation of nonlinearity while the Lamb wave travels along its path. Special focus is laid on the second harmonic, and a relative nonlinearity parameter is defined as a function of the fundamental and second harmonic amplitude. The experimental setup uses an ultrasonic transducer and a wedge for the Lamb wave generation, and laser interferometry for detection. The experimentally measured Lamb wave signals are processed with a short-time Fourier transformation (STFT), which yields the amplitudes at different frequencies as functions of time, allowing the observation of the nonlinear behavior of the material. The increase of the relative nonlinearity parameter with propagation distance as an indicator of cumulative second harmonic generation is shown in the results for the alloy aluminum 1100-H14

Nonlinear Microstructured Material to Reduce Noise and Vibrations at Low Frequencies

International Nuclear Information System (INIS)

Lavazec, Deborah; Cumunel, Gwendal; Duhamel, Denis; Soize, Christian; Batou, Anas

2016-01-01

At low frequencies, for which the wavelengths are wide, the acoustic waves and the mechanical vibrations cannot easily be reduced in the structures at macroscale by using dissipative materials, contrarily to the middle- and high-frequency ranges. The final objective of this work is to reduce the vibrations and the induced noise on a broad low-frequency band by using a microstructured material by inclusions that are randomly arranged in the material matrix. The dynamical regimes of the inclusions will be imposed in the nonlinear domain in order that the energy be effectively pumped over a broad frequency band around the resonance frequency, due to the nonlinearity. The first step of this work is to design and to analyze the efficiency of an inclusion, which is made up of a hollow frame including a point mass centered on a beam. This inclusion is designed in order to exhibit nonlinear geometric effects in the low-frequency band that is observed. For this first step, the objective is to develop the simplest mechanical model that has the capability to roughly predict the experimental results that are measured. The second step, which is not presented in the paper, will consist in developing a more sophisticated nonlinear dynamical model of the inclusion. In this paper, devoted to the first step, it is proved that the nonlinearity induces an attenuation on a broad frequency band around the resonance, contrarily to its linear behavior for which the attenuation is only active in a narrow frequency band around the resonance. We will present the design in terms of geometry, dimension and materials for the inclusion, the experimental manufacturing of this system realized with a 3D printing system, and the experimental measures that have been performed. We compare the prevision given by the stochastic computational model with the measurements. The results obtained exhibit the physical attenuation over a broad low-frequency band, which were expected. (paper)

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

Analytical Modeling of Hard-Coating Cantilever Composite Plate considering the Material Nonlinearity of Hard Coating

Directory of Open Access Journals (Sweden)

Wei Sun

2015-01-01

Full Text Available Due to the material nonlinearity of hard coating, the coated structure produces the nonlinear dynamical behaviors of variable stiffness and damping, which make the modeling of hard-coating composite structure become a challenging task. In this study, the polynomial was adopted to characterize this material nonlinearity and an analytical modeling method was developed for the hard-coating composite plate. Firstly, to relate the hard-coating material parameters obtained by test and the analytical model, the expression of equivalent strain of composite plate was derived. Then, the analytical model of hard-coating composite plate was created by energy method considering the material nonlinearity of hard coating. Next, using the Newton-Raphson method to solve the vibration response and resonant frequencies of composite plate and a specific calculation procedure was also proposed. Finally, a cantilever plate coated with MgO + Al2O3 hard coating was chosen as study case; the vibration response and resonant frequencies of composite plate were calculated using the proposed method. The calculation results were compared with the experiment and general linear calculation, and the correctness of the created model was verified. The study shows the proposed method can still maintain an acceptable precision when the material nonlinearity of hard coating is stronger.

A direct vulnerable atherosclerotic plaque elasticity reconstruction method based on an original material-finite element formulation: theoretical framework

Science.gov (United States)

Bouvier, Adeline; Deleaval, Flavien; Doyley, Marvin M.; Yazdani, Saami K.; Finet, Gérard; Le Floc'h, Simon; Cloutier, Guy; Pettigrew, Roderic I.; Ohayon, Jacques

2013-12-01

The peak cap stress (PCS) amplitude is recognized as a biomechanical predictor of vulnerable plaque (VP) rupture. However, quantifying PCS in vivo remains a challenge since the stress depends on the plaque mechanical properties. In response, an iterative material finite element (FE) elasticity reconstruction method using strain measurements has been implemented for the solution of these inverse problems. Although this approach could resolve the mechanical characterization of VPs, it suffers from major limitations since (i) it is not adapted to characterize VPs exhibiting high material discontinuities between inclusions, and (ii) does not permit real time elasticity reconstruction for clinical use. The present theoretical study was therefore designed to develop a direct material-FE algorithm for elasticity reconstruction problems which accounts for material heterogeneities. We originally modified and adapted the extended FE method (Xfem), used mainly in crack analysis, to model material heterogeneities. This new algorithm was successfully applied to six coronary lesions of patients imaged in vivo with intravascular ultrasound. The results demonstrated that the mean relative absolute errors of the reconstructed Young's moduli obtained for the arterial wall, fibrosis, necrotic core, and calcified regions of the VPs decreased from 95.3±15.56%, 98.85±72.42%, 103.29±111.86% and 95.3±10.49%, respectively, to values smaller than 2.6 × 10-8±5.7 × 10-8% (i.e. close to the exact solutions) when including modified-Xfem method into our direct elasticity reconstruction method.

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...

Nonlinear kinematics for piezoelectricity in ALEGRA-EMMA.

Energy Technology Data Exchange (ETDEWEB)

Mitchell, John Anthony; Fuller, Timothy Jesse

2013-09-01

This report develops and documents nonlinear kinematic relations needed to implement piezoelectric constitutive models in ALEGRA-EMMA [5], where calculations involving large displacements and rotations are routine. Kinematic relationships are established using Gausss law and Faradays law; this presentation on kinematics goes beyond piezoelectric materials and is applicable to all dielectric materials. The report then turns to practical details of implementing piezoelectric models in an application code where material principal axes are rarely aligned with user defined problem coordinate axes. This portion of the report is somewhat pedagogical but is necessary in order to establish documentation for the piezoelectric implementation in ALEGRA-EMMA. This involves transforming elastic, piezoelectric, and permittivity moduli from material principal axes to problem coordinate axes. The report concludes with an overview of the piezoelectric implementation in ALEGRA-EMMA and small verification examples.

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

Parametric dependence of a morphing wind turbine blade on material elasticity

International Nuclear Information System (INIS)

Puterbaugh, Martin; Beyene, Asfaw

2011-01-01

A few recent works have suggested a morphing blade for wind turbine energy conversion. The concept is derived from fin and wing motions that better adapt to varying load conditions. Previous research has provided the fluid mechanic justification of this new concept. This paper establishes a parametric relationship between an asymmetric wind turbine blade and constituent material modulus to predict the geometric response of the morphing blade for a given material characteristic. The airfoil's trailing edge deflection is associated to a prescribed fluid exit angle via the Moment Area (MA) method. Subsequently, a mathematical model is derived to predict material deformation with respect to imparted aerodynamic forces. Results show that an airfoil, much like a tapered beam, can be modeled as a non-prismatic cantilevered beam using this well established method. -- Research highlights: →A mathematical model relating morphing airfoil thickness and elastic modulus was established. →For non-prismatic beam under a uniform distributive load, the slope and deflection of the airfoil's trailing edge were related to the fluid exit angle. →The main driver of blade deformation was the angular drag force. The Moment Area method was used, verified by Finite Element method. →Displacement to the exit angle is predicated upon the elastic modulus value given that other parameters are constant. →Optimum power output is obtained in part load conditions when the blade deforms to the applicable exit angle.

Nonlinear ultrasonic stimulated thermography for damage assessment in isotropic fatigued structures

Science.gov (United States)

Fierro, Gian Piero Malfense; Calla', Danielle; Ginzburg, Dmitri; Ciampa, Francesco; Meo, Michele

2017-09-01

Traditional non-destructive evaluation (NDE) and structural health monitoring (SHM) systems are used to analyse that a structure is free of any harmful damage. However, these techniques still lack sensitivity to detect the presence of material micro-flaws in the form of fatigue damage and often require time-consuming procedures and expensive equipment. This research work presents a novel "nonlinear ultrasonic stimulated thermography" (NUST) method able to overcome some of the limitations of traditional linear ultrasonic/thermography NDE-SHM systems and to provide a reliable, rapid and cost effective estimation of fatigue damage in isotropic materials. Such a hybrid imaging approach combines the high sensitivity of nonlinear acoustic/ultrasonic techniques to detect micro-damage, with local defect frequency selection and infrared imaging. When exciting structures with an optimised frequency, nonlinear elastic waves are observed and higher frictional work at the fatigue damaged area is generated due to clapping and rubbing of the crack faces. This results in heat at cracked location that can be measured using an infrared camera. A Laser Vibrometer (LV) was used to evaluate the extent that individual frequency components contribute to the heating of the damage region by quantifying the out-of-plane velocity associated with the fundamental and second order harmonic responses. It was experimentally demonstrated the relationship between a nonlinear ultrasound parameter (βratio) of the material nonlinear response to the actual temperature rises near the crack. These results demonstrated that heat generation at damaged regions could be amplified by exciting at frequencies that provide nonlinear responses, thus improving the imaging of material damage and the reliability of NUST in a quick and reproducible manner.

The porosity effect on properties of sintered materials as their conductivity and Youngs modulus of elasticity

International Nuclear Information System (INIS)

Ondracek, G.; Thuemmler, F.

1979-01-01

A set of equations derived demonstrates quantitatively the influence of closed pores on the conductivity as well as on Youngsmodulus of elasticity of sintered materials. There are three microstructural parameters following from the theoretical derivation controlling the porosity effect on the properties, which are the total porosity, the form factor and the orientation factor of the pores. By quantitative microstructure analysis these factors become available providing together with the equations the tool - to calculate the conductivity and Youngs modulus of elasticity from microstructural quantities of sintered materials thus substituting direct property measurements by quantitative microstructure analysis if desired - to endeaver technologically optimum microstructures to obtain theoretically predicted special property values and to precalculate property alterations by microstructure variations ('taylor-made-materials') - to supplement the conventional microstructural quality control by calculated property data. (orig.) [de

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.)

Determination of the buckling safety of reinforced concrete shells considering the nonlinear material-behavior

International Nuclear Information System (INIS)

Zerna, W.; Mungan, I.; Steffen, W.

1980-01-01

The equations of the bending and stability theories for the orthotropic shell are solved using the FEM. A biaxial material law for concrete and a nearly bilinear stress-strain diagram for reinforcing steel were considered. Taking a layered ring element the influence of bending moments together with the membrane forces can be followed under increasing load up to failure of concrete or steel. At each level the bucking factor can be calculated considering the stress dependent buckling stiffness. The method of calculation is applied to a cooling tower shell under dead load acting simultaneously with an axi-symmetric loading to compensate for the wind effect. Due to orthotropy and descending tangent modulus at the ultimate load the buckling load factor drops to the half of the value obtained assuming a linear elastic behaviour. Additional parametric studies demonstrate the effect of some hypothetic cracks of different position and depth of the bifurcation results. The variation of the safety factors against buckling and ultimate load is obtained by changing the shell thickness. For the shell investigated it turns out that the buckling safety is influenced much more than the safety against material failure if the wall thickness is varied. It is recommended to split the buckling analysis of reinforced concrete shells in two parts. For shells of parts of a shell under only slightly disturbed membrane stress state the buckling analysis governs, otherwise the ultimate state considering the geometric and material nonlinearities is decisive to obtain not only the wall thickness but also the amount of reinforced necessary. (orig./HP) [de

A constructive nonlinear array (CNA) method for barely visible impact detection in composite materials

Science.gov (United States)

Malfense Fierro, Gian Piero; Meo, Michele

2017-04-01

Currently there are numerous phased array techniques such as Full Matrix Capture (FMC) and Total Focusing Method (TFM) that provide good damage assessment for composite materials. Although, linear methods struggle to evaluate and assess low levels of damage, while nonlinear methods have shown great promise in early damage detection. A sweep and subtraction evaluation method coupled with a constructive nonlinear array method (CNA) is proposed in order to assess damage specific nonlinearities, address issues with frequency selection when using nonlinear ultrasound imaging techniques and reduce equipment generated nonlinearities. These methods were evaluated using multiple excitation locations on an impacted composite panel with a complex damage (barely visible impact damage). According to various recent works, damage excitation can be accentuated by exciting at local defect resonance (LDR) frequencies; although these frequencies are not always easily determinable. The sweep methodology uses broadband excitation to determine both local defect and material resonances, by assessing local defect generated nonlinearities using a laser vibrometer it is possible to assess which frequencies excite the complex geometry of the crack. The dual effect of accurately determining local defect resonances, the use of an image subtraction method and the reduction of equipment based nonlinearities using CNA result in greater repeatability and clearer nonlinear imaging (NIM).

Sensitivity of acoustic nonlinearity parameter to the microstructural changes in cement-based materials

Science.gov (United States)

Kim, Gun; Kim, Jin-Yeon; Kurtis, Kimberly E.; Jacobs, Laurence J.

2015-03-01

This research experimentally investigates the sensitivity of the acoustic nonlinearity parameter to microcracks in cement-based materials. Based on the second harmonic generation (SHG) technique, an experimental setup using non-contact, air-coupled detection is used to receive the consistent Rayleigh surface waves. To induce variations in the extent of microscale cracking in two types of specimens (concrete and mortar), shrinkage reducing admixture (SRA), is used in one set, while a companion specimen is prepared without SRA. A 50 kHz wedge transducer and a 100 kHz air-coupled transducer are implemented for the generation and detection of nonlinear Rayleigh waves. It is shown that the air-coupled detection method provides more repeatable fundamental and second harmonic amplitudes of the propagating Rayleigh waves. The obtained amplitudes are then used to calculate the relative nonlinearity parameter βre, the ratio of the second harmonic amplitude to the square of the fundamental amplitude. The experimental results clearly demonstrate that the nonlinearity parameter (βre) is highly sensitive to the microstructural changes in cement-based materials than the Rayleigh phase velocity and attenuation and that SRA has great potential to avoid shrinkage cracking in cement-based materials.

Elastic properties of various ceramic materials

International Nuclear Information System (INIS)

Zimmermann, H.

1992-09-01

The Young's modulus and the Poisson's ratio of various ceramics have been investigated at room temperature and compared with data from the literature. The ceramic materials investigated are Al 2 O 3 , Al 2 O 3 -ZrO 2 , MgAl 2 O 4 , LiAlO 2 , Li 2 SiO 3 , Li 4 SiO 4 , UO 2 , AlN, SiC, B 4 C, TiC, and TiB 2 . The dependence of the elastic moduli on porosity and temperature have been reviewed. Measurements were also performed on samples of Al 2 O 3 , AlN, and SiC, which had been irradiated to maximum neutron fluences of 1.6.10 26 n/m 2 (E>0.1 MeV) at different temperatures. The Young's modulus is nearly unaffected at fluences up to about 4.10 24 n/m 2 . However, it decreases with increasing neutron fluence and seems to reach a saturation value depending upon the irradiation temperature. The reduction of the Young's modulus is lowest in SiC. (orig.) [de

Multi-crack imaging using nonclassical nonlinear acoustic method

International Nuclear Information System (INIS)

Zhang Lue; Zhang Ying; Liu Xiao-Zhou; Gong Xiu-Fen

2014-01-01

Solid materials with cracks exhibit the nonclassical nonlinear acoustical behavior. The micro-defects in solid materials can be detected by nonlinear elastic wave spectroscopy (NEWS) method with a time-reversal (TR) mirror. While defects lie in viscoelastic solid material with different distances from one another, the nonlinear and hysteretic stress—strain relation is established with Preisach—Mayergoyz (PM) model in crack zone. Pulse inversion (PI) and TR methods are used in numerical simulation and defect locations can be determined from images obtained by the maximum value. Since false-positive defects might appear and degrade the imaging when the defects are located quite closely, the maximum value imaging with a time window is introduced to analyze how defects affect each other and how the fake one occurs. Furthermore, NEWS-TR-NEWS method is put forward to improve NEWS-TR scheme, with another forward propagation (NEWS) added to the existing phases (NEWS and TR). In the added phase, scanner locations are determined by locations of all defects imaged in previous phases, so that whether an imaged defect is real can be deduced. NEWS-TR-NEWS method is proved to be effective to distinguish real defects from the false-positive ones. Moreover, it is also helpful to detect the crack that is weaker than others during imaging procedure. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics.

Science.gov (United States)

Liu, Xiaofeng; Guo, Qiangbing; Qiu, Jianrong

2017-04-01

Low-dimensional (LD) materials demonstrate intriguing optical properties, which lead to applications in diverse fields, such as photonics, biomedicine and energy. Due to modulation of electronic structure by the reduced structural dimensionality, LD versions of metal, semiconductor and topological insulators (TIs) at the same time bear distinct nonlinear optical (NLO) properties as compared with their bulk counterparts. Their interaction with short pulse laser excitation exhibits a strong nonlinear character manifested by NLO absorption, giving rise to optical limiting or saturated absorption associated with excited state absorption and Pauli blocking in different materials. In particular, the saturable absorption of these emerging LD materials including two-dimensional semiconductors as well as colloidal TI nanoparticles has recently been utilized for Q-switching and mode-locking ultra-short pulse generation across the visible, near infrared and middle infrared wavelength regions. Beside the large operation bandwidth, these ultrafast photonics applications are especially benefit from the high recovery rate as well as the facile processibility of these LD materials. The prominent NLO response of these LD materials have also provided new avenues for the development of novel NLO and photonics devices for all-optical control as well as optical circuits beyond ultrafast lasers. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A discrete element model for the investigation of the geometrically nonlinear behaviour of solids

Science.gov (United States)

Ockelmann, Felix; Dinkler, Dieter

2018-07-01

A three-dimensional discrete element model for elastic solids with large deformations is presented. Therefore, an discontinuum approach is made for solids. The properties of elastic material are transferred analytically into the parameters of a discrete element model. A new and improved octahedron gap-filled face-centred cubic close packing of spheres is split into unit cells, to determine the parameters of the discrete element model. The symmetrical unit cells allow a model with equal shear components in each contact plane and fully isotropic behaviour for Poisson's ratio above 0. To validate and show the broad field of applications of the new model, the pin-pin Euler elastica is presented and investigated. The thin and sensitive structure tends to undergo large deformations and rotations with a highly geometrically nonlinear behaviour. This behaviour of the elastica can be modelled and is compared to reference solutions. Afterwards, an improved more realistic simulation of the elastica is presented which softens secondary buckling phenomena. The model is capable of simulating solids with small strains but large deformations and a strongly geometrically nonlinear behaviour, taking the shear stiffness of the material into account correctly.

A 3D Orthotropic Strain-Rate Dependent Elastic Damage Material Model.

Energy Technology Data Exchange (ETDEWEB)

English, Shawn Allen

2014-09-01

A three dimensional orthotropic elastic constitutive model with continuum damage and cohesive based fracture is implemented for a general polymer matrix composite lamina. The formulation assumes the possibility of distributed (continuum) damage followed b y localized damage. The current damage activation functions are simply partially interactive quadratic strain criteria . However, the code structure allows for changes in the functions without extraordinary effort. The material model formulation, implementation, characterization and use cases are presented.

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

Science.gov (United States)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

Nonlinear effects of high temperature on buckling of structural elements

International Nuclear Information System (INIS)

Iyengar, N.G.R.

1975-01-01

Structural elements used in nuclear reactors are subjected to high temperatures. Since with increase in temperature there is a gradual fall in the elastic modulus and the stress-strain relationship is nonlinear at these operating load levels, a realistic estimate of the buckling load should include this nonlinearity. In this paper the buckling loads for uniform columns with circular and rectangular cross-sections and different boundary conditions under high temperature environment are estimated. The stress-strain relationship for the material has been assumed to follow inverse Ramberg-Osgood law. In view of the fact that no closed form solutions are possible, approximate methods like perturbation and Galerkin techniques are used. Further, the solution for general value for 'm' is quite involved. Results have been obtained with values for 'm' as 3 and 5. Studies reveal that the influence of material nonlinearity on the buckling load is of the softening type, and it increases with increase in the value of 'm'. The nonlinear effects are more for clamped boundaries than for simply supported boundaries. For the first mode analysis both the methods are powerful. It is, however, felt that for higher modes the Galerkin method might be better in view of its simplicity. This investigation may be considered as a step towards a more general solution

Nonlinear Dynamic Phenomena in Mechanics

CERN Document Server

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

Microstructure, elastic deformation behavior and mechanical properties of biomedical β-type titanium alloy thin-tube used for stents.

Science.gov (United States)

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.

Elastoplastic Stability and Failure Analysis of FGM Plate with Temperature Dependent Material Properties under Thermomechanical Loading

Directory of Open Access Journals (Sweden)

Kanishk Sharma

Full Text Available Abstract The present paper explores the stability and failure response of elastoplastic Ni/Al2O3 functionally graded plate under thermomechanical load using non-linear finite element formulation based on first-order shear deformation theory and von-Karman’s nonlinear kinematics. The temperature dependent thermoelastic material properties of FGM plate are varied in the thickness direction by controlling the volume fraction of the constituent materials (i.e., ceramic and metal with a power law, and Mori-Tanaka homogenization scheme is applied to evaluate the properties at a particular thickness coordinate of FGM plate. The elastoplastic behavior of FGM plate is assumed to follow J2-plasticity with isotropic hardening, wherein the ceramic phase is considered to be elastic whereas the metal is assumed to be elastic-plastic in accordance with the Tamura-Tomota-Ozawa model. Numerical studies are conducted to examine the effects of material and geometrical parameters, viz. material in-homogeneity, slenderness and aspect ratios on the elastoplastic bucking and postbuckling behavior and the failure response of FGM plate. It is revealed that material gradation affects the stability and failure behavior of FGM plate considerably. Furthermore, it is also concluded that FGM plate with elastic material properties exhibits only stable equilibrium path, whereas the elastoplastic FGM plate shows destabilizing response after the ultimate failure point.

Nonlinear Thermo-mechanical Finite Element Analysis of Polymer Foam Cored Sandwich Structures including Geometrical and Material Nonlinearity

DEFF Research Database (Denmark)

Palleti, Hara Naga Krishna Teja; Thomsen, Ole Thybo; Taher, Siavash Talebi

In this paper, polymer foam cored sandwich structures with fibre reinforced composite face sheets subjected to combined mechanical and thermal loads will be analysed using the commercial FE code ABAQUS® incorporating both material and geometrical nonlinearity. Large displacements and rotations...

Determination of the reduced matrix of the piezoelectric, dielectric, and elastic material constants for a piezoelectric material with C∞ symmetry.

Science.gov (United States)

Sherrit, Stewart; Masys, Tony J; Wiederick, Harvey D; Mukherjee, Binu K

2011-09-01

We present a procedure for determining the reduced piezoelectric, dielectric, and elastic coefficients for a C(∞) material, including losses, from a single disk sample. Measurements have been made on a Navy III lead zirconate titanate (PZT) ceramic sample and the reduced matrix of coefficients for this material is presented. In addition, we present the transform equations, in reduced matrix form, to other consistent material constant sets. We discuss the propagation of errors in going from one material data set to another and look at the limitations inherent in direct calculations of other useful coefficients from the 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.

Estimation of Single-Crystal Elastic Constants of Polycrystalline Materials from Back-Scattered Grain Noise

International Nuclear Information System (INIS)

Haldipur, P.; Margetan, F. J.; Thompson, R. B.

2006-01-01

Single-crystal elastic stiffness constants are important input parameters for many calculations in material science. There are well established methods to measure these constants using single-crystal specimens, but such specimens are not always readily available. The ultrasonic properties of metal polycrystals, such as velocity, attenuation, and backscattered grain noise characteristics, depend in part on the single-crystal elastic constants. In this work we consider the estimation of elastic constants from UT measurements and grain-sizing data. We confine ourselves to a class of particularly simple polycrystalline microstructures, found in some jet-engine Nickel alloys, which are single-phase, cubic, equiaxed, and untextured. In past work we described a method to estimate the single-crystal elastic constants from measured ultrasonic velocity and attenuation data accompanied by metallographic analysis of grain size. However, that methodology assumes that all attenuation is due to grain scattering, and thus is not valid if appreciable absorption is present. In this work we describe an alternative approach which uses backscattered grain noise data in place of attenuation data. Efforts to validate the method using a pure copper specimen are discussed, and new results for two jet-engine Nickel alloys are presented

Single-nary philosophy for non-linear study of mechanics of materials

International Nuclear Information System (INIS)

Tran, C.

2005-01-01

Non-linear study of mechanics of materials is formulated in this paper as a problem of meta-intelligent system analysis. Non-linearity will be singled out as an important concept for understanding of high-order complex systems. Through single-nary thinking, which will be represented in this work, we introduce a modification of Aristotelian philosophy using modal logic and multi-valued logic (these logics we call 'high-order' logic). Next, non-linear cause - effect relations are expressed through non-additive measures and multiple-information aggregation principles based on fuzzy integration. The study of real time behaviors, required experiences and intuition, will be realized using truth measures (non-additive measures) and a procedure for information processing in intelligence levels. (author)

Magnetic hysteresis at the domain scale of a multi-scale material model for magneto-elastic behaviour

Energy Technology Data Exchange (ETDEWEB)

Vanoost, D., E-mail: dries.vanoost@kuleuven-kulak.be [KU Leuven Technology Campus Ostend, ReMI Research Group, Oostende B-8400 (Belgium); KU Leuven Kulak, Wave Propagation and Signal Processing Research Group, Kortrijk B-8500 (Belgium); Steentjes, S. [Institute of Electrical Machines, RWTH Aachen University, Aachen D-52062 (Germany); Peuteman, J. [KU Leuven Technology Campus Ostend, ReMI Research Group, Oostende B-8400 (Belgium); KU Leuven, Department of Electrical Engineering, Electrical Energy and Computer Architecture, Heverlee B-3001 (Belgium); Gielen, G. [KU Leuven, Department of Electrical Engineering, Microelectronics and Sensors, Heverlee B-3001 (Belgium); De Gersem, H. [KU Leuven Kulak, Wave Propagation and Signal Processing Research Group, Kortrijk B-8500 (Belgium); TU Darmstadt, Institut für Theorie Elektromagnetischer Felder, Darmstadt D-64289 (Germany); Pissoort, D. [KU Leuven Technology Campus Ostend, ReMI Research Group, Oostende B-8400 (Belgium); KU Leuven, Department of Electrical Engineering, Microelectronics and Sensors, Heverlee B-3001 (Belgium); Hameyer, K. [Institute of Electrical Machines, RWTH Aachen University, Aachen D-52062 (Germany)

2016-09-15

This paper proposes a multi-scale energy-based material model for poly-crystalline materials. Describing the behaviour of poly-crystalline materials at three spatial scales of dominating physical mechanisms allows accounting for the heterogeneity and multi-axiality of the material behaviour. The three spatial scales are the poly-crystalline, grain and domain scale. Together with appropriate scale transitions rules and models for local magnetic behaviour at each scale, the model is able to describe the magneto-elastic behaviour (magnetostriction and hysteresis) at the macroscale, although the data input is merely based on a set of physical constants. Introducing a new energy density function that describes the demagnetisation field, the anhysteretic multi-scale energy-based material model is extended to the hysteretic case. The hysteresis behaviour is included at the domain scale according to the micro-magnetic domain theory while preserving a valid description for the magneto-elastic coupling. The model is verified using existing measurement data for different mechanical stress levels. - Highlights: • A ferromagnetic hysteretic energy-based multi-scale material model is proposed. • The hysteresis is obtained by new proposed hysteresis energy density function. • Avoids tedious parameter identification.

Linearity and Non-linearity of Photorefractive effect in Materials ...

African Journals Online (AJOL)

In this paper we have studied the Linearity and Non-linearity of Photorefractive effect in materials using the band transport model. For low light beam intensities the change in the refractive index is proportional to the electric field for linear optics while for non- linear optics the change in refractive index is directly proportional ...

Nonlinear Dynamic Modeling of a Supersonic Commercial Transport Turbo-Machinery Propulsion System for Aero-Propulso-Servo-Elasticity Research

Science.gov (United States)

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.

Material model for non-linear finite element analyses of large concrete structures

NARCIS (Netherlands)

Engen, Morten; Hendriks, M.A.N.; Øverli, Jan Arve; Åldstedt, Erik; Beushausen, H.

2016-01-01

A fully triaxial material model for concrete was implemented in a commercial finite element code. The only required input parameter was the cylinder compressive strength. The material model was suitable for non-linear finite element analyses of large concrete structures. The importance of including

Nonlinear analysis of end slabs in prestressed concrete reactor vessels

International Nuclear Information System (INIS)

Abdulrahman, H.O.

1978-01-01

A procedure for the nonlinear analysis of end slabs is prestressed concrete reactor vessels (PCRVs), based on the finite element method, is presented. The applicability of the procedure to the ultimate load analysis of small-scale models of the primary containment of nuclear reactors is shown. Material nonlinearity only is considered. The procedure utilizes the four-node linear quadrilateral isoparametric element with the choice of incorporating the nonconforming modes. This element is used for modeling the vessel as an axisymmetric solid. Concrete is assumed to be an isotropic material in the elastic range. The compressive stresses are judged according to a special form of the Mohr-Coulomb criterion. The nonlinear problem was solved using a generalized Newton-Raphson procedure. A detailed example problem of a pressure vessel with penetrations is presented. This is followed by a summary of the other cases studied. The solutions obtained match very closely the measured response of the test vessels under increasing internal pressure up to failure. The procedure is thus adequate for the assessment of the ultimate load behavior and failure of actual pressure vessels with a moderate demand on human and computational resources

A 3D domain decomposition approach for the identification of spatially varying elastic material parameters

KAUST Repository

Moussawi, Ali; Lubineau, Gilles; Xu, Jiangping; Pan, Bing

2015-01-01

Summary: The post-treatment of (3D) displacement fields for the identification of spatially varying elastic material parameters is a large inverse problem that remains out of reach for massive 3D structures. We explore here the potential

Anisotropic failure and size effects in periodic honeycomb materials: A gradient-elasticity approach

Science.gov (United States)

Réthoré, Julien; Dang, Thi Bach Tuyet; Kaltenbrunner, Christine

2017-02-01

This paper proposes a fracture mechanics model for the analysis of crack propagation in periodic honeycomb materials. The model is based on gradient-elasticity which enables us to account for the effect of the material structure at the macroscopic scale. For simulating the propagation of cracks along an arbitrary path, the numerical implementation is elaborated based on an extended finite element method with the required level of continuity. The two main features captured by the model are directionality and size effect. The numerical predictions are consistent with experimental results on honeycomb materials but also with results reported in the literature for microstructurally short cracks in metals.

Universality of Nonclassical Nonlinearity Applications to Non-Destructive Evaluations and Ultrasonic

CERN Document Server

Delsanto, Pier Paolo

2006-01-01

This book comes as a result of the research work developed in the framework of two international projects: the European Science Foundation supported program NATEMIS (Nonlinear Acoustic Techniques for Micro-Scale Damage Diagnostics) and a Los Alamos-based international network. The main topics of both the programs and the book cover the phenomenology, theory and applications of Nonclassical Nonlinearity (NCNL). NCNL techniques have been found in recent years to be extremely powerful (up to 1000 times more than the corresponding linear techniques) in a wide range of applications, including Material Characterization, Ultrasonics, Geophysics and Maintenance and Restoration of artifacts. These techniques are being adopted as the main inspection and research tool in another European program: AERONEWS (Health monitoring of aircraft by nonlinear elastic wave propagation). In the future, the proposed Universality of NCNL is expected to extend the range of applications to numerous other fields and scientific discipline...

Effects of non-linearity of material properties on the coupled mechanical-hydraulic-thermal behavior in rock mass

International Nuclear Information System (INIS)

Kobayashi, Akira; Ohnishi, Yuzo

1986-01-01

The nonlinearity of material properties used in the coupled mechanical-hydraulic-thermal analysis is investigated from the past literatures. Some nonlinearity that is respectively effective for the system is introduced into our computer code for analysis such a coupling problem by using finite element method. And the effects of nonlinearity of each material property on the coupled behavior in rock mass are examined for simple model and Stripa project model with the computer code. (author)

Elastic band prediction equations for combined free-weight and elastic band bench presses and squats.

Science.gov (United States)

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.

Stochastic isotropic hyperelastic materials: constitutive calibration and model selection

Science.gov (United States)

Mihai, L. Angela; Woolley, Thomas E.; Goriely, Alain

2018-03-01

Biological and synthetic materials often exhibit intrinsic variability in their elastic responses under large strains, owing to microstructural inhomogeneity or when elastic data are extracted from viscoelastic mechanical tests. For these materials, although hyperelastic models calibrated to mean data are useful, stochastic representations accounting also for data dispersion carry extra information about the variability of material properties found in practical applications. We combine finite elasticity and information theories to construct homogeneous isotropic hyperelastic models with random field parameters calibrated to discrete mean values and standard deviations of either the stress-strain function or the nonlinear shear modulus, which is a function of the deformation, estimated from experimental tests. These quantities can take on different values, corresponding to possible outcomes of the experiments. As multiple models can be derived that adequately represent the observed phenomena, we apply Occam's razor by providing an explicit criterion for model selection based on Bayesian statistics. We then employ this criterion to select a model among competing models calibrated to experimental data for rubber and brain tissue under single or multiaxial loads.

Eddy current modeling in linear and nonlinear multifilamentary composite materials

Science.gov (United States)

Menana, Hocine; Farhat, Mohamad; Hinaje, Melika; Berger, Kevin; Douine, Bruno; Lévêque, Jean

2018-04-01

In this work, a numerical model is developed for a rapid computation of eddy currents in composite materials, adaptable for both carbon fiber reinforced polymers (CFRPs) for NDT applications and multifilamentary high temperature superconductive (HTS) tapes for AC loss evaluation. The proposed model is based on an integro-differential formulation in terms of the electric vector potential in the frequency domain. The high anisotropy and the nonlinearity of the considered materials are easily handled in the frequency domain.

Development of a formalism of movable cellular automaton method for numerical modeling of fracture of heterogeneous elastic-plastic materials

Directory of Open Access Journals (Sweden)

S. Psakhie

2013-04-01

Full Text Available A general approach to realization of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of particle-based numerical methods is proposed in the paper. It is based on building many-body forces of particle interaction, which provide response of particle ensemble correctly conforming to the response (including elastic-plastic behavior and fracture of simulated solids. Implementation of proposed approach within particle-based methods is demonstrated by the example of the movable cellular automaton (MCA method, which integrates the possibilities of particle-based discrete element method (DEM and cellular automaton methods. Emergent advantages of the developed approach to formulation of many-body interaction are discussed. Main of them are its applicability to various realizations of the concept of discrete elements and a possibility to realize various rheological models (including elastic-plastic or visco-elastic-plastic and models of fracture to study deformation and fracture of solid-phase materials and media. Capabilities of particle-based modeling of heterogeneous solids are demonstrated by the problem of simulation of deformation and fracture of particle-reinforced metal-ceramic composites.

Strongly nonlinear optical glass fibers from noncentrosymmetric phase-change chalcogenide materials.

Science.gov (United States)

Chung, In; Jang, Joon I; Malliakas, Christos D; Ketterson, John B; Kanatzidis, Mercouri G

2010-01-13

We report that the one-dimensional polar selenophosphate compounds APSe(6) (A = K, Rb), which show crystal-glass phase-change behavior, exhibit strong second harmonic generation (SHG) response in both crystal and glassy forms. The crystalline materials are type-I phase-matchable with SHG coefficients chi((2)) of 151.3 and 149.4 pm V(-1) for K(+) and Rb(+) salts, respectively, which is the highest among phase-matchable nonlinear optical (NLO) materials with band gaps over 1.0 eV. The glass of APSe(6) exhibits comparable SHG intensities to the top infrared NLO material AgGaSe(2) without any poling treatments. APSe(6) exhibit excellent mid-IR transparency. We demonstrate that starting from noncentrosymmetric phase-change materials such as APSe(6) (A = K, Rb), we can obtain optical glass fibers with strong, intrinsic, and temporally stable second-order nonlinear optical (NLO) response. The as-prepared glass fibers exhibit SHG and difference frequency generation (DFG) responses over a wide range of wavelengths. Raman spectroscopy and pair distribution function (PDF) analyses provide further understanding of the local structure in amorphous state of KPSe(6) bulk glass and glass fiber. We propose that this approach can be widely applied to prepare permanent NLO glass from materials that undergo a phase-change process.

Stressed-deformed state of mountain rocks in elastic stage and between elasticity

Directory of Open Access Journals (Sweden)

Samedov A.M.

2017-12-01

Full Text Available The problems of the stress-strain state of rocks in the elastic stage and beyond the elastic limits, and the ways of schematizing the tension and compression diagrams were reviewed in the article. To simplify calculations outside the elastic range, the tension (compression diagrams are usually schematized, i.e. are replaced by curved smooth lines having a fairly simple mathematical expression and at the same time well coinciding with the experimentally obtained diagrams. When diagram is to be schematized, it is necessary to take a constant temperature of superheated water steam if a rock test is planned in a relaxed form. Note that when the diagram is schematizing, the difference between the limits of proportionality and fluidity is erased. This allows the limit of proportionality to be considered the limit of fluidity. Schematicization can be carried out in the area where the tensile strength (compression is planned to be destroyed with the established weakening of rocks by exposure to water steam or chemical reagents. Samples of rocks in natural form were tested and weakened by means of superheated water steam (220 °C and more and chemical reagents for tension and compression. The data are obtained, the diagrams of deformation are constructed and schematized in the elastic stage and beyond the elastic limit. Based on the schematic diagrams of deformation, the components of stress and strain were composed in the elastic stage and beyond the elastic limit. It is established in the publication that rocks under compression and stretching deform, both within the elastic stage, and beyond the limits of elasticity. This could be seen when the samples, both in natural and in weakened state, with superheated water steam (more than 220 °C or chemical reagents were tested. In their natural form, they are mainly deformed within the elastic stage and are destroyed as a brittle material, and in a weakened form they can deform beyond the elastic stage and

Reduced-order computational model in nonlinear structural dynamics for structures having numerous local elastic modes in the low-frequency range. Application to fuel assemblies

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

Reduced-order computational model in nonlinear structural dynamics for structures having numerous local elastic modes in the low-frequency range. Application to fuel assemblies

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.

A frictional contact problem with wear involving elastic-viscoplastic materials with damage and thermal effects

Directory of Open Access Journals (Sweden)

Abdelmoumene Djabi

2015-05-01

Full Text Available We consider a mathematical problem for quasistatic contact between a thermo-elastic-viscoplastic body with damage and an obstacle. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. We employ the thermo-elasticviscoplastic with damage constitutive law for the material. The damage of the material caused by elastic deformations. The evolution of the damage is described by an inclusion of parabolic type. The problem is formulated as a coupled system of an elliptic variational inequality for the displacement, a parabolic variational inequality for the damage and the heat equation for the temperature. We establish a variational formulation for the model and we prove the existence of a unique weak solution to the problem. The proof is based on a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed point arguments.

Stress evaluation of metallic material under steady state based on nonlinear critically refracted longitudinal wave

Science.gov (United States)

Mao, Hanling; Zhang, Yuhua; Mao, Hanying; Li, Xinxin; Huang, Zhenfeng

2018-06-01

This paper presents the study of applying the nonlinear ultrasonic wave to evaluate the stress state of metallic materials under steady state. The pre-stress loading method is applied to guarantee components with steady stress. Three kinds of nonlinear ultrasonic experiments based on critically refracted longitudinal wave are conducted on components which the critically refracted longitudinal wave propagates along x, x1 and x2 direction. Experimental results indicate the second and third order relative nonlinear coefficients monotonically increase with stress, and the normalized relationship is consistent with simplified dislocation models, which indicates the experimental result is logical. The combined ultrasonic nonlinear parameter is proposed, and three stress evaluation models at x direction are established based on three ultrasonic nonlinear parameters, which the estimation error is below 5%. Then two stress detection models at x1 and x2 direction are built based on combined ultrasonic nonlinear parameter, the stress synthesis method is applied to calculate the magnitude and direction of principal stress. The results show the prediction error is within 5% and the angle deviation is within 1.5°. Therefore the nonlinear ultrasonic technique based on LCR wave could be applied to nondestructively evaluate the stress of metallic materials under steady state which the magnitude and direction are included.

Elastic Characterization of Transversely Isotropic Soft Materials by Dynamic Shear and Asymmetric Indentation

Science.gov (United States)

Namani, R.; Feng, Y.; Okamoto, R. J.; Jesuraj, N.; Sakiyama-Elbert, S. E.; Genin, G. M.; Bayly, P. V.

2012-01-01

The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isotropic soft material. A soft gel with controlled anisotropy was obtained by polymerizing a mixture of fibrinogen and thrombin solutions in a high field magnet (B = 11.7 T); fibrils in the resulting gel were predominantly aligned parallel to the magnetic field. Aligned fibrin gels were subject to dynamic (20–40 Hz) shear deformation in two orthogonal directions. The shear storage modulus was 1.08 ± 0. 42 kPa (mean ± std. dev.) for shear in a plane parallel to the dominant fiber direction, and 0.58 ± 0.21 kPa for shear in the plane of isotropy. Gels were indented by a rectangular tip of a large aspect ratio, aligned either parallel or perpendicular to the normal to the plane of transverse isotropy. Aligned fibrin gels appeared stiffer when indented with the long axis of a rectangular tip perpendicular to the dominant fiber direction. Three-dimensional numerical simulations of asymmetric indentation were used to determine the relationship between direction-dependent differences in indentation stiffness and material parameters. This approach enables the estimation of a complete set of parameters for an incompressible, transversely isotropic, linear elastic material. PMID:22757501

Weakly nonlinear dispersion and stop-band effects for periodic structures

DEFF Research Database (Denmark)

Sorokin, Vladislav; Thomsen, Jon Juel

of frequency band-gaps, i.e. frequency ranges in which elastic waves cannot propagate. Most existing analytical methods in the field are based on Floquet theory [1]; e.g. this holds for the classical Hill’s method of infinite determinants [1,2], and themethod of space-harmonics [3]. However, application...... of these methods for studying nonlinear problems isimpossible or cumbersome, since Floquet theory is applicable only for linear systems. Thus the nonlinear effects for periodic structures are not yet fully uncovered, while at the same time applications may demand effects of nonlinearity on structural response...... to be accounted for.The paper deals with analytically predicting dynamic response for nonlinear elastic structures with a continuous periodic variation in structural properties. Specifically, for a Bernoulli-Euler beam with aspatially continuous modulation of structural properties in the axial direction...

Thermo-elastic Green's functions for an infinite bi-material of one-dimensional hexagonal quasi-crystals

International Nuclear Information System (INIS)

Li, P.D.; Li, X.Y.; Zheng, R.F.

2013-01-01

This Letter is concerned with thermo-elastic fundamental solutions of an infinite space, which is composed of two half-infinite bodies of different one-dimensional hexagonal quasi-crystals. A point thermal source is embedded in a half-space. The interface can be either perfectly bonded or smoothly contacted. On the basis of the newly developed general solution, the temperature-induced elastic field in full space is explicitly presented in terms of elementary functions. The interactions among the temperature, phonon and phason fields are revealed. The present work can play an important role in constructing farther analytical solutions for crack, inclusion and dislocation problems. -- Highlights: ► Green's functions are constructed in terms of 10 quasi-harmonic functions. ► Thermo-elastic field of a 1D hexagonal QC bi-material body is expressed explicitly. ► Both perfectly bonded and smoothly contacted interfaces are considered

Self-Assembly of Nanocomposite Nonlinear Optical Materials for Photonic Devices, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — This program targets the development of new highly anisotropic nonlinear optical nanocomposite materials for NASA and non-NASA applications in advanced photonic and...

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.

Damage of the Interface Between an Orthodontic Bracket and Enamel - the Effect of Some Elastic Properties of the Adhesive Material

Science.gov (United States)

Durgesh, B. H.; Alkheraif, A. A.; Al Sharawy, M.; Varrela, J.; Vallittu, P. K.

2016-01-01

The aim of this study was to investigate the magnitude of debonding stress of an orthodontic bracket bonded to the enamel with resin systems having different elastic properties. For the same purpose, sixty human premolars were randomly divided into four groups according to the adhesive system used for bonding brackets: G Fix flowable resin (GFI) with Everstick NET (ESN), GFI, G Aenial Universal Flow (GAU) with ESN, and GAU. The brackets were stressed in the occlusogingival direction on a universal testing machine. The values of debonding load and displacement were determined at the point of debonding. The elastic modulus of the tested materials was determined using nanoindentation. An analysis of variance showed a significant difference in the loads required to debond the bracket among the groups tested. The GAU group had the highest elastic modulus, followed by the GFI and ESN groups. ARI (Adhesive Remnant Index) scores demonstrated more remnants of the adhesive material on the bracket surface with adhesives having a higher elastic modulus. Taking into consideration results of the present in-vitro study, it can be concluded that the incorporation of a glass-fiber-reinforced composite resin (FRC) with a low elastic modulus between the orthodontic bracket and enamel increases the debonding force and strain more than with adhesive systems having a higher elastic modulus.

Coupled modeling and simulation of electro-elastic materials at large strains

Science.gov (United States)

Possart, Gunnar; Steinmann, Paul; Vu, Duc-Khoi

2006-03-01

In the recent years various novel materials have been developed that respond to the application of electrical loading by large strains. An example is the class of so-called electro-active polymers (EAP). Certainly these materials are technologically very interesting, e.g. for the design of actuators in mechatronics or in the area of artificial tissues. This work focuses on the phenomenological modeling of such materials within the setting of continuum-electro-dynamics specialized to the case of electro-hyperelastostatics and the corresponding computational setting. Thereby a highly nonlinear coupled problem for the deformation and the electric potential has to be considered. The finite element method is applied to solve the underlying equations numerically and some exemplary applications are presented.

Synthesis of polymeric micro- and nanostructural materials for application in non-linear optics

International Nuclear Information System (INIS)

Kravets, Lyubov; Palistrant, Natalia; Bivol, Valerii; Robu, Stepan; Barba, Nikolai; Orelovitch, Oleg

2007-01-01

The present paper describes a new approach developed for the preparation of micro- and nanostructural materials on the basis of polymeric compositions used as a matrix in non-linear optics. This approach consists in filling the pores of poly(ethylene terephthalate) track membranes (PET TM) from polymeric compositions using an impregnation method. It is shown that depending on the concentration of polymeric compositions in the solution it is possible to form a variety of micro- and nanostructural materials (tubules and wires as well as composite membranes) with a wide spectrum of characteristics. The developed method of producing micro- and nanostructural materials provides a possible way for creating polymeric objects with non-linear optic properties which can be used to design electronic micro- and nanodevices and to obtain chemical and optical sensors

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

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.

Nonlinear dynamical triggering of slow slip

Energy Technology Data Exchange (ETDEWEB)

Johnson, Paul A [Los Alamos National Laboratory; Knuth, Matthew W [WISCONSIN; Kaproth, Bryan M [PENN STATE; Carpenter, Brett [PENN STATE; Guyer, Robert A [Los Alamos National Laboratory; Le Bas, Pierre - Yves [Los Alamos National Laboratory; Daub, Eric G [Los Alamos National Laboratory; Marone, Chris [PENN STATE

2010-12-10

Among the most fascinating, recent discoveries in seismology have been the phenomena of triggered slip, including triggered earthquakes and triggered-tremor, as well as triggered slow, silent-slip during which no seismic energy is radiated. Because fault nucleation depths cannot be probed directly, the physical regimes in which these phenomena occur are poorly understood. Thus determining physical properties that control diverse types of triggered fault sliding and what frictional constitutive laws govern triggered faulting variability is challenging. We are characterizing the physical controls of triggered faulting with the goal of developing constitutive relations by conducting laboratory and numerical modeling experiments in sheared granular media at varying load conditions. In order to simulate granular fault zone gouge in the laboratory, glass beads are sheared in a double-direct configuration under constant normal stress, while subject to transient perturbation by acoustic waves. We find that triggered, slow, silent-slip occurs at very small confining loads ({approx}1-3 MPa) that are smaller than those where dynamic earthquake triggering takes place (4-7 MPa), and that triggered slow-slip is associated with bursts of LFE-like acoustic emission. Experimental evidence suggests that the nonlinear dynamical response of the gouge material induced by dynamic waves may be responsible for the triggered slip behavior: the slip-duration, stress-drop and along-strike slip displacement are proportional to the triggering wave amplitude. Further, we observe a shear-modulus decrease corresponding to dynamic-wave triggering relative to the shear modulus of stick-slips. Modulus decrease in response to dynamical wave amplitudes of roughly a microstrain and above is a hallmark of elastic nonlinear behavior. We believe that the dynamical waves increase the material non-affine elastic deformation during shearing, simultaneously leading to instability and slow-slip. The inferred

Non-linear optical measurement of the twist elastic constant in thermotropic and DNA lyotropic chiral nematics

OpenAIRE

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...

Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model

Energy Technology Data Exchange (ETDEWEB)

Ghorbanpour Arani, A., E-mail: aghorban@kashanu.ac.ir [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of); Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan (Iran, Islamic Republic of); Zarei, M.Sh.; Amir, S.; Khoddami Maraghi, Z. [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of)

2013-02-01

In this work nonlinear vibration of double-walled carbon nanotube (DWCNT) embedded in an elastic medium and subjected to an axial fluid flow (incompressible and non-viscose) is investigated. The elastic medium is simulated using Pasternak foundation in which adjacent layer interactions are assumed to have been coupled by van der Waals (VdW) force. The higher-order equation of motion is derived using Hamilton's principle and nonlocal-nonlinear shell theory. Galerkin and averaging methods are adopted to solve the higher-order governing equations. Elastic medium, small scale parameter, velocity and fluid density are taken into account to calculate the effects of axial and circumferential wave numbers in this study. Results reveal that increasing circumferential wave number, leads to enhanced nonlinearity. Critical flow velocities of DWCNT are inversely related to the non-local parameter (e{sub 0}a), so that increase in the later lead to reduced critical flow velocities.

Delayed hydride cracking and elastic properties of Excel, a candidate CANDU-SCWR pressure tube material

International Nuclear Information System (INIS)

Pan, Z.L.

2010-01-01

Excel, a Zr alloy which contains 3.5%Sn, 0.8%Nb and 0.8%Mo, shows high strength, good corrosion resistance, excellent creep-resistance and dimension stability and thus is selected as a candidate pressure tube material for CANDU-SCWR. In the present work, the delayed hydride cracking properties (K IH and the DHC growth rates), the hydrogen solubility and elastic modulus were measured in the irradiated and unirradiated Excel pressure tube material. (author)

Modal representation of geometrically nonlinear behavior by the finite element method

International Nuclear Information System (INIS)

Nagy, D.A.

1977-01-01

A method is presented for representing mild geometrically nonlinear static behavior of thin-type structures, within the finite element method, in terms of linear elastic and linear (bifurcation) buckling analysis results for structural loading or geometry situations which violate the idealized restrictive (perfect) interpretation of linear behavior up to bifurcation. Formulation of the finite element displacement method for material linearity but retaining the full, nonlinear strain-displacement relations (geometric nonlinearity) leads to highly nonlinear equations relating the unknown nodal generalized displacements r to the applied loading R. Restriction to small strains alone does not linearize these equations for thin-type structural configurations; only explicitly requiring that all products of displacement gadients be much smaller than the gadients themselves reduces the equations to the familiar linear form Ksub(e)r=R, where Ksub(e) is the elastic stiffness. Assuming then that the solutions r of the linear equations also satisfies the full nonlinear equations (i.e., that the above explicit requirement is satisfied), a second solution to the full equations can be sought for a one-parameter loading path lambdaR, leading to the well-known linear (bifurcation) buckling eigenvalue problem Ksub(e)X=-Ksub(g)XΛ where Ksub(g) is the geometric stiffness, X the matrix whose columns are the eigenvectors (so-called buckling mode shapes) and Λ is a diagonal matrix of eigenvalues lambda(i) (so-called load scale factors). From the viewpoint of the practising structural analyst using finite element software, the method presented here gives broader and deeper significance to an existing linear (bifurcation) buckling analysis capability, in that the additional computations are minimal beyond those already required for a linear static and buckling analysis, and should be easily performable within any well-designed general purpose finite element system

Approximate solutions of a nonlinear oscillator typified as a mass attached to a stretched elastic wire by the homotopy perturbation method

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.

Three-Dimensional Elasticity Solutions for Sound Radiation of Functionally Graded Materials Plates considering State Space Method

Directory of Open Access Journals (Sweden)

Tieliang Yang

2016-01-01

Full Text Available This paper presents an analytical study for sound radiation of functionally graded materials (FGM plate based on the three-dimensional theory of elasticity. The FGM plate is a mixture of metal and ceramic, and its material properties are assumed to have smooth and continuous variation in the thickness direction according to a power-law distribution in terms of volume fractions of the constituents. Based on the three-dimensional theory of elasticity and state space method, the governing equations with variable coefficients of the FGM plate are derived. The sound radiation of the vibration plate is calculated with Rayleigh integral. Comparisons of the present results with those of solutions in the available literature are made and good agreements are achieved. Finally, some parametric studies are carried out to investigate the sound radiation properties of FGM plates.

Elastic-plastic collapse of super-elastic shock waves in face-centered-cubic solids

International Nuclear Information System (INIS)

Zhakhovsky, Vasily V; Demaske, Brian J; Oleynik, Ivan I; Inogamov, Nail A; White, Carter T

2014-01-01

Shock waves in the [110] and [111] directions of single-crystal Al samples were studied using molecular dynamics (MD) simulations. Piston-driven simulations were performed to investigate the split shock-wave regime. At low piston velocities, the material is compressed initially to a metastable over-compressed elastic state leading to a super-elastic single shock wave. This metastable elastic state later collapses to a plastic state resulting in the formation of a two-wave structure consisting of an elastic precursor followed by a slower plastic wave. The single two-zone elastic-plastic shock-wave regime appearing at higher piston velocities was studied using moving window MD. The plastic wave attains the same average speed as the elastic precursor to form a single two-zone shock wave. In this case, repeated collapse of the highly over-compressed elastic state near the plastic shock front produces ultrashort triangle pulses that provide the pressure support for the leading elastic precursor.

Elastic-Plastic Nonlinear Response of a Space Shuttle External Tank Stringer. Part 1; Stringer-Feet Imperfections and Assembly

Science.gov (United States)

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.

Determination of dynamic fracture initiation toughness of elastic-plastic materials at intermediate strain rates

International Nuclear Information System (INIS)

Fernandez-Saez, J.; Luna de, S.; Rubio, L.; Perez-Castellanos, J. L.; Navarro, C.

2001-01-01

An earlier paper dealt with the experimental techniques used to determine the dynamic fracture properties of linear elastic materials. Here we describe those most commonly used as elastoplastic materials, limiting the study to the initiation fracture toughness at the intermediate strain rate (of around 10''2 s''-1). In this case the inertial forces are negligible and it is possible to apply the static solutions. With this stipulation, the analysis can be based on the methods of testing in static conditions. The dynamic case differs basically, from the static one, in the influence of the strain rate on the properties of the material. (Author) 57 refs

Nonlinear and turbulent processes in physics. Volume 2. Nonlinear effects in various areas of science

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.

Some aspects of floor spectra of 1DOF nonlinear primary structures

International Nuclear Information System (INIS)

Politopoulos, I.; Feau, C.

2007-01-01

In this paper the influence of the nonlinear behaviour of the primary structure on floor spectra is investigated by means of simple models. The general trends of floor spectra for different types of nonlinear behaviour of one degree of freedom (1DOF) primary structure are shown and we point out their common futures and their differences. A special attention is given to the cases of elastoplastic and nonlinear elastic behaviours and methods to determine an equivalent linear oscillator are proposed. The properties (frequency and damping) of this equivalent linear oscillator are quite different from the properties of equivalent linear oscillators commonly considered in practice. In particular, in the case of elastoplastic behaviour, there is no frequency shift and damping is smaller than assumed by other methods commonly used. In the case of nonlinear elastic behaviour, the concept of an equivalent frequency which is a random variable is used. Finally, a design floor spectrum of primary structures, exhibiting energy dissipating nonlinear behaviour is proposed. (authors)

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...

Structure/property relationships in non-linear optical materials

Energy Technology Data Exchange (ETDEWEB)

Cole, J M [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France); [Durham Univ. (United Kingdom); Howard, J A.K. [Durham Univ. (United Kingdom); McIntyre, G J [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)

1997-04-01

The application of neutrons to the study of structure/property relationships in organic non-linear optical materials (NLOs) is described. In particular, charge-transfer effects and intermolecular interactions are investigated. Charge-transfer effects are studied by charge-density analysis and an example of one such investigation is given. The study of intermolecular interactions concentrates on the effects of hydrogen-bonding and an example is given of two structurally similar molecules with very disparate NLO properties, as a result of different types of hydrogen-bonding. (author). 3 refs.

CONCERNING THE ELASTIC ORTHOTROPIC MODEL APPLIED TO WOOD ELASTIC PROPERTIES

OpenAIRE

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...

Elastic silicone encapsulation of n-hexadecyl bromide by microfluidic approach as novel microencapsulated phase change materials

International Nuclear Information System (INIS)

Fu, Zhenjin; Su, Lin; Li, Jing; Yang, Ruizhuang; Zhang, Zhanwen; Liu, Meifang; Li, Jie; Li, Bo

2014-01-01

Highlights: • n-Hexadecyl bromide was encapsuled in elastic silicone shell. • The surfaces of microcapsules were smooth and the cross sections were compact. • Latent heat of microcapsules was 76.35 J g −1 . • The microencapsulation ratio was 49 wt.%. • The microcapsules had good thermal stability. - Abstract: The elastic silicone/n-hexadecyl bromide microcapsules were prepared as novel microencapsulated phase change materials by microfluidic approach with the co-flowing channels, where the double oil1-in-oil2-in-water (O1/O2/W) droplets with a core–shell geometry were fabricated. The thermal characterizations of the microcapsules were investigated using differential scanning calorimetry (DSC) and thermogravimetry analysis (TGA). The DSC results showed that the microcapsules had good energy storage capacity with melting and freezing enthalpies 76.35 J g −1 and 78.67 J g −1 , respectively. The TGA investigation showed that the microcapsules had good thermal stability. The surfaces of microcapsules were smooth and the cross sections were compact from the results of optical microscope and scanning electron microscopy (SEM). Optical microscope showed that the silicone shell can provide expansion place due to its elastic property. Therefore, the silicone/n-hexadecyl bromide microcapsules showed good potential as thermal regulating textile and thermal insulation materials

Analysis of HD Journal Bearings Considering Elastic Deformation and Non-Newtonian Rabinowitsch Fluid Model

Directory of Open Access Journals (Sweden)

J. Javorova

2016-06-01

Full Text Available The purpose of this paper is to study the performance of a finite length journal bearing, taking into account effects of non-Newtonian Rabinowitsch flow rheology and elastic deformations of the bearing liner. According to the Rabinowitsch fluid model, the cubic-stress constitutive equation is used to account for the non-Newtonian effects of pseudoplastic and dilatant lubricants. Integrating the continuity equation across the film, the nonlinear non-Newtonian Reynolds-type equation is derived. The elasticity part of the problem is solved on the base of Vlassov model of an elastic foundation. The numerical solution of the modified Reynolds equation is carried out by using FDM with over-relaxation technique. The results for steady state bearing performance characteristics have been calculated for various values of nonlinear factor and elasticity parameters. It was concluded that in comparison with the Newtonian lubricants, higher values of film pressure and load carrying capacity have been obtained for dilatant lubricants, while the case was reversed for pseudoplastic lubricants.

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

Effect of reorientation of anisotropic point defects on relaxation of crystal elastic coefficients of high order

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

The application of J integral to measure cohesive laws in materials undergoing large scale yielding

DEFF Research Database (Denmark)

Sørensen, Bent F.; Goutianos, Stergios

2015-01-01

We explore the possibility of determining cohesive laws by the J-integral approach for materials having non-linear stress-strain behaviour (e.g. polymers and composites) by the use of a DCB sandwich specimen, consisting of stiff elastic beams bonded to the non-linear test material, loaded with pure...... bending moments. For a wide range of parameters of the non-linear material, the plastic unloading during crack extension is small, resulting in J integral values (fracture resistance) that deviate maximum 15% from the work of the cohesive traction. Thus the method can be used to extract the cohesive laws...... directly from experiments without any presumption about their shape. Finally, the DCB sandwich specimen was also analysed using the I integral to quantify the overestimation of the steady-state fracture resistance obtained using the J integral based method....

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)

Femtosecond laser damage threshold and nonlinear characterization in bulk transparent SiC materials

International Nuclear Information System (INIS)

DesAutels, G. Logan; Finet, Marc; Ristich, Scott; Whitaker, Matt; Brewer, Chris; Juhl, Shane; Walker, Mark; Powers, Peter

2008-01-01

Semi-insulating and conducting SiC crystalline transparent substrates were studied after being processed by femtosecond (fs) laser radiation (780 nm at 160 fs). Z-scan and damage threshold experiments were performed on both SiC bulk materials to determine each sample's nonlinear and threshold parameters. 'Damage' in this text refers to an index of refraction modification as observed visually under an optical microscope. In addition, a study was performed to understand the damage threshold as a function of numerical aperture. Presented here for the first time, to the best of our knowledge, are the damage threshold, nonlinear index of refraction, and nonlinear absorption measured values

A two-dimensional linear elasticity problem for anisotropic materials, solved with a parallelization code

Directory of Open Access Journals (Sweden)

Mihai-Victor PRICOP

2010-09-01

Full Text Available The present paper introduces a numerical approach of static linear elasticity equations for anisotropic materials. The domain and boundary conditions are simple, to enhance an easy implementation of the finite difference scheme. SOR and gradient are used to solve the resulting linear system. The simplicity of the geometry is also useful for MPI parallelization of the code.

Elastic-plastic response of a piping system due to simulated double-ended guillotine break events

International Nuclear Information System (INIS)

Kussmaul, K.; Diem, H.; Hunger, H.; Katzenmeier, G.

1987-01-01

From the blowdown experiments performed on the HDR feedwater line with feedwater check valve the conclusion can be drawn that high transient loads of up to plastic strains of 3%, acting on an initially integer piping system, can be sustained without loss of integrity for a low number of load cycles due to the plasticizing capacity of the pipework materials nowadays used in the reactor technology. In the experiments carried out with ferritic piping of ND 400 pressure peaks up to about 31,5 mPA were achieved which resulted in excessive strains of up to 3%. By nonlinear finite element computations (ABAQUS) it was possible to describe the elastic-plastic behaviour of the piping in a good approximation. On account of the safety margins proved in the experiments, potential inaccuracies in theoretical structure analyses are recommended so as to be on the safe side. On the other hand, it appears that designing pipework with reference to elastic stress categories does not adequately take into account the actual reserves of the pipework material

FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE) NONLINEAR CALCULATIONS OF PLATES AND SHELLS

OpenAIRE

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.

Cell wall elasticity: I. A critique of the bulk elastic modulus approach and an analysis using polymer elastic principles

Science.gov (United States)

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.

The influence of time dependent flight and maneuver velocities and elastic or viscoelastic flexibilities on aerodynamic and stability derivatives

Energy Technology Data Exchange (ETDEWEB)

Cochrane, Alexander P. [Aerospace Engineering Department, University of Glasgow, University Avenue, Glasgow, Lanarkshire (United Kingdom); Merrett, Craig G. [Mechanical and Aerospace Engineering Department, Carleton Univ., 1125 Col. By Dr., Ottawa, ON (Canada); Hilton, Harry H. [Aerospace Engineering Department in the College of Engineering and Private Sector Program Division at the National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, 104 South Wright Street, Urbana, IL 61801 (United States)

2014-12-10

which control reversal takes place (V{sub REV}{sup E}). Since elastic formulations constitute viscoelastic initial conditions, viscoelastic reversal may occur at speeds V{sub REV<}{sup ≧}V{sub REV}{sup E}, but furthermore does so in time at 0 < t{sub REV} ≤ ∞. This paper reports on analytical analyses and simulations of the effects of flexibility and time dependent material properties (viscoelasticity) on aerodynamic derivatives and on lateral, longitudinal, directional and spin stability derivatives. Cases of both constant and variable flight and maneuver velocities are considered. Analytical results for maneuvers involving constant and time dependent rolling velocities are analyzed, discussed and evaluated. The relationships between rolling velocity p and aileron angular displacement β as well as control effectiveness are analyzed and discussed in detail for elastic and viscoelastic wings. Such analyses establish the roll effectiveness derivatives (∂[p(t)])/(V{sub ∞}∂β(t)) . Similar studies involving other stability and aerodynamic derivatives are also undertaken. The influence of the twin effects of viscoelastic and elastic materials and of variable flight, rolling, pitching and yawing velocities on longitudinal, lateral and directional are also investigated. Variable flight velocities, encountered during maneuvers, render the usually linear problem at constant velocities into a nonlinear one.

The influence of time dependent flight and maneuver velocities and elastic or viscoelastic flexibilities on aerodynamic and stability derivatives

International Nuclear Information System (INIS)

Cochrane, Alexander P.; Merrett, Craig G.; Hilton, Harry H.

2014-01-01

(V REV E ). Since elastic formulations constitute viscoelastic initial conditions, viscoelastic reversal may occur at speeds V REV< ≧ V REV E , but furthermore does so in time at 0 < t REV ≤ ∞. This paper reports on analytical analyses and simulations of the effects of flexibility and time dependent material properties (viscoelasticity) on aerodynamic derivatives and on lateral, longitudinal, directional and spin stability derivatives. Cases of both constant and variable flight and maneuver velocities are considered. Analytical results for maneuvers involving constant and time dependent rolling velocities are analyzed, discussed and evaluated. The relationships between rolling velocity p and aileron angular displacement β as well as control effectiveness are analyzed and discussed in detail for elastic and viscoelastic wings. Such analyses establish the roll effectiveness derivatives (∂[p(t)])/(V ∞ ∂β(t)) . Similar studies involving other stability and aerodynamic derivatives are also undertaken. The influence of the twin effects of viscoelastic and elastic materials and of variable flight, rolling, pitching and yawing velocities on longitudinal, lateral and directional are also investigated. Variable flight velocities, encountered during maneuvers, render the usually linear problem at constant velocities into a nonlinear one

Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers

Directory of Open Access Journals (Sweden)

Nicolás Peréz Alvarez

2015-11-01

Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.

[Physics of materials and female stress urinary continence: New concepts: I) Elasticity under bladder].

Science.gov (United States)

Guerquin, B

2015-09-01

Improving the understanding of the adaptation to stress of urinary continence. A transversal analysis between physics of materials and the female anatomy. Laws of physics of the materials and of their viscoelastic behavior are applied to the anatomy of the anterior vaginal wall. The anterior vaginal wall may be divided into two segments of different viscoelastic behavior, the vertical segment below the urethra and the horizontal segment below the bladder. If the urethra gets crushed on the first segment according to the hammock theory, the crushing of the bladder on the second segment is, on the other hand, damped by its important elasticity. The importance of this elasticity evokes an unknown function: damping under the bladder that moderates and delays the increase of intravesical pressure. This damping function below the bladder is increased in the cystocele, which is therefore a continence factor; on the other hand, it is impaired in obesity, which is therefore a factor of SUI. It is necessary to include in the theory of stress continence, the notion of a damping function below the bladder. Copyright © 2015 Elsevier Masson SAS. All rights reserved.

Elastic spheres can walk on water.

Science.gov (United States)

Belden, Jesse; Hurd, Randy C; Jandron, Michael A; Bower, Allan F; Truscott, Tadd T

2016-02-04

Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material compliance on water impact physics. Here we show that upon water impact, very compliant spheres naturally assume a disk-like geometry and dynamic orientation that are favourable for water-skipping. Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material. We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure. With these insights, we explain why softer spheres skip more easily than stiffer ones. Our results advance understanding of fluid-elastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys.

Code conforming determination of cumulative usage factors for general elastic-plastic finite element analyses

International Nuclear Information System (INIS)

Rudolph, Juergen; Goetz, Andreas; Hilpert, Roland

2012-01-01

The procedures of fatigue analyses of several relevant nuclear and conventional design codes (ASME, KTA, EN, AD) for power plant components differentiate between an elastic, simplified elastic-plastic and elastic-plastic fatigue check. As a rule, operational load levels will exclude the purely elastic fatigue check. The application of the code procedure of the simplified elastic-plastic fatigue check is common practice. Nevertheless, resulting cumulative usage factors may be overly conservative mainly due to high code based plastification penalty factors Ke. As a consequence, the more complex and still code conforming general elastic-plastic fatigue analysis methodology based on non-linear finite element analysis (FEA) is applied for fatigue design as an alternative. The requirements of the FEA and the material law to be applied have to be clarified in a first step. Current design codes only give rough guidelines on these relevant items. While the procedure for the simplified elastic-plastic fatigue analysis and the associated code passages are based on stress related cycle counting and the determination of pseudo elastic equivalent stress ranges, an adaptation to elastic-plastic strains and strain ranges is required for the elastic-plastic fatigue check. The associated requirements are explained in detail in the paper. If the established and implemented evaluation mechanism (cycle counting according to the peak and valley respectively the rainflow method, calculation of stress ranges from arbitrary load-time histories and determination of cumulative usage factors based on all load events) is to be retained, a conversion of elastic-plastic strains and strain ranges into pseudo elastic stress ranges is required. The algorithm to be applied is described in the paper. It has to be implemented in the sense of an extended post processing operation of FEA e.g. by APDL scripts in ANSYS registered . Variations of principal stress (strain) directions during the loading

Tailoring superelasticity of soft magnetic materials

Science.gov (United States)

Cremer, Peet; Löwen, Hartmut; Menzel, Andreas M.

2015-10-01

Embedding magnetic colloidal particles in an elastic polymer matrix leads to smart soft materials that can reversibly be addressed from outside by external magnetic fields. We discover a pronounced nonlinear superelastic stress-strain behavior of such materials using numerical simulations. This behavior results from a combination of two stress-induced mechanisms: a detachment mechanism of embedded particle aggregates and a reorientation mechanism of magnetic moments. The superelastic regime can be reversibly tuned or even be switched on and off by external magnetic fields and thus be tailored during operation. Similarities to the superelastic behavior of shape-memory alloys suggest analogous applications, with the additional benefit of reversible switchability and a higher biocompatibility of soft materials.

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...