NASA Astrophysics Data System (ADS)
Brünig, M.
The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the rate-independent finite strain analysis of solids undergoing large elastic-plastic deformations. The formulation relies on the introduction of a mixed-variant metric transformation tensor which will be multiplicatively decomposed into a plastic and an elastic part. This leads to the definition of an appropriate logarithmic strain measure whose rate is shown to be additively decomposed into elastic and plastic strain rate tensors. The mixed-variant logarithmic elastic strain tensor provides a basis for the definition of a local isotropic hyperelastic stress response in the elastic-plastic solid. Additionally, the plastic material behavior is assumed to be governed by a generalized J2 yield criterion and rate-independent isochoric plastic strain rates are computed using an associated flow rule. On the numerical side, the computation of the logarithmic strain tensors is based on 1st and higher order Padé approximations. Estimates of the stress and strain histories are obtained via a highly stable and accurate explicit scalar integration procedure which employs a plastic predictor followed by an elastic corrector step. The development of a consistent elastic-plastic tangent operator as well as its implementation into a nonlinear finite element program will also be discussed. Finally, the numerical solution of finite strain elastic-plastic problems is presented to demonstrate the efficiency of the algorithm.
NASA Technical Reports Server (NTRS)
Rodal, J. J. A.; Witmer, E. A.
1979-01-01
A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.
Generalization of strain-gradient theory to finite elastic deformation for isotropic materials
NASA Astrophysics Data System (ADS)
Beheshti, Alireza
2017-03-01
This paper concerns finite deformation in the strain-gradient continuum. In order to take account of the geometric nonlinearity, the original strain-gradient theory which is based on the infinitesimal strain tensor is rewritten given the Green-Lagrange strain tensor. Following introducing the generalized isotropic Saint Venant-Kirchhoff material model for the strain-gradient elasticity, the boundary value problem is investigated in not only the material configuration but also the spatial configuration building upon the principle of virtual work for a three-dimensional solid. By presenting one example, the convergence of the strain-gradient and classical theories is studied.
An approach for verification of finite-element analysis in nonlinear elasticity under large strains
NASA Astrophysics Data System (ADS)
Zingerman, K. M.; Vershinin, A. V.; Levin, V. A.
2016-11-01
An approach to verification of finite-element calculations of stress-strain state of nonlinear elastic bodies under large deformations is suggested. The problems that may be reduced to one-dimensional ones using a semi-inverse method are taken as test problems. An example of such a test problem is the Lame problem for a cylinder. Generally, this problem for compressible hyperelastic materials has no exact analytical solution, but it can be reduced to a boundary value problem for an ordinary second-order nonlinear differential equation, and in some cases - to the Cauchy problem. A numerical solution of this problem can be used as a test one for finite element calculations carried out in three-dimensional statement. Some results of such verification (finite element calculations were performed using the Fidesys CAE-system) are presented.
Reference map technique for finite-strain elasticity and fluid-solid interaction
NASA Astrophysics Data System (ADS)
Kamrin, Ken; Rycroft, Chris H.; Nave, Jean-Christophe
2012-11-01
The reference map, defined as the inverse motion function, is utilized in an Eulerian-frame representation of continuum solid mechanics, leading to a simple, explicit finite-difference method for solids undergoing finite deformations. We investigate the accuracy and applicability of the technique for a range of finite-strain elasticity laws under various geometries and loadings. Capacity to model dynamic, static, and quasi-static conditions is shown. Specifications of the approach are demonstrated for handling irregularly shaped and/or moving boundaries, as well as shock solutions. The technique is also integrated within a fluid-solid framework using a level-set to discern phases and using a standard explicit fluid solver for the fluid phases. We employ a sharp-interface method to institute the interfacial conditions, and the resulting scheme is shown to efficiently capture fluid-solid interaction solutions in several examples.
Homogenized mechanical properties of auxetic composite materials in finite-strain elasticity
NASA Astrophysics Data System (ADS)
Kochmann, Dennis M.; Venturini, Gabriela N.
2013-08-01
Careful microstructural design can result in materials with counterintuitive effective (macroscale) mechanical properties such as a negative Poisson’s ratio, commonly referred to as auxetic behavior. One specific approach to achieving auxetic behavior is to elastically connect structural elements with rotational degrees of freedom to result in elastic structures that unfold under uniaxial loading in specific directions, thereby giving rise to bi- or triaxial expansion, i.e. auxetic behavior (transverse expansion under uniaxial extension). This concept has been applied successfully to elastically coupled two-dimensional rigid rotational elements (such as rotating rectangles and triangles) which exhibit a negative effective in-plane Poisson’s ratio under uniaxial (ex)tension. Here, we adopt this fundamental design principle but take it to the next level by achieving auxetic behavior in finitely strained composites made of stiff inclusions in a hyperelastic matrix, and we study the resulting elastic properties under in-plane strain by numerical homogenization. Our results highlight the emergence of auxetic behavior based on geometric arrangement and properties of the base material and demonstrate a path towards simple inclusion-matrix composites with auxetic behavior.
A staggered approach for the coupling of Cahn-Hilliard type diffusion and finite strain elasticity
NASA Astrophysics Data System (ADS)
Areias, P.; Samaniego, E.; Rabczuk, T.
2016-02-01
We develop an algorithm and computational implementation for simulation of problems that combine Cahn-Hilliard type diffusion with finite strain elasticity. We have in mind applications such as the electro-chemo-mechanics of lithium ion (Li-ion) batteries. We concentrate on basic computational aspects. A staggered algorithm is proposed for the coupled multi-field model. For the diffusion problem, the fourth order differential equation is replaced by a system of second order equations to deal with the issue of the regularity required for the approximation spaces. Low order finite elements are used for discretization in space of the involved fields (displacement, concentration, nonlocal concentration). Three (both 2D and 3D) extensively worked numerical examples show the capabilities of our approach for the representation of (i) phase separation, (ii) the effect of concentration in deformation and stress, (iii) the effect of strain in concentration, and (iv) lithiation. We analyze convergence with respect to spatial and time discretization and found that very good results are achievable using both a staggered scheme and approximated strain interpolation.
NASA Technical Reports Server (NTRS)
Atluri, S. N.
1984-01-01
Nagtegaal and de Jong (1982) have studied stresses generated by simple finite shear in the case of elastic-plastic and rigid-plastic materials which exhibit anisotropic hardening. They reported that the shear stress is oscillatory in time. It was found that the occurrence of such an 'anomaly' is not restricted to anisotropic plasticity. Similar behavior in finite shear may result even in the case of hypoelasticity and classical isotropic hardening plasticity theory. The present investigation is concerned with the central problem of 'generalizing' with respect to the finite strain case, taking into account the constitutive relations of infinitesimal strain theories of classical plasticity with isotropic or kinematic hardening. The problem of hypoelasticity is also considered. It is shown that current controversies surrounding the choice of stress rate in the finite-strain generalizations of the constitutive relations and the anomalies surrounding kinematic hardening plasticity theory are easily resolvable.
Euler-Lagrange Elasticity: elasticity without stress or strain
NASA Astrophysics Data System (ADS)
Hardy, Humphrey
2014-03-01
A Euler-Lagrange (E-L) approach to elasticity is proposed that produces differential equations of elasticity without the need to define stress or strain tensors. The positions of the points within the body are the independent parameters instead of strain. Force replaces stress. The advantage of this approach is that the E-L differential equations are the same for both infinitesimal and finite deformations. Material properties are expressed in terms of the energy of deformation. The energy is expressed as a function of the principal invariants of the deformation gradient tensor. This scalar invariant representation of the energy of deformation enters directly into the E-L differential equations so that there is no need to define fourth order tensor material properties. By experimentally measuring the force and displacement of materials the functional form of the energy of deformation can be determined. The E-L differential equations can be input directly into finite element, finite difference, or other numerical models. If desired, stress and stain can be calculated as dependent parameters.
Cyclic creep analysis from elastic finite-element solutions
NASA Technical Reports Server (NTRS)
Kaufman, A.; Hwang, S. Y.
1986-01-01
A uniaxial approach was developed for calculating cyclic creep and stress relaxation at the critical location of a structure subjected to cyclic thermomechanical loading. This approach was incorporated into a simplified analytical procedure for predicting the stress-strain history at a crack initiation site for life prediction purposes. An elastic finite-element solution for the problem was used as input for the simplified procedure. The creep analysis includes a self-adaptive time incrementing scheme. Cumulative creep is the sum of the initial creep, the recovery from the stress relaxation and the incremental creep. The simplified analysis was exercised for four cases involving a benchmark notched plate problem. Comparisons were made with elastic-plastic-creep solutions for these cases using the MARC nonlinear finite-element computer code.
Solano-Altamirano, J M; Goldman, Saul
2015-12-01
We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another.
Finite-element formulations for problems of large elastic-plastic deformation
NASA Technical Reports Server (NTRS)
Mcmeeking, R. M.; Rice, J. R.
1975-01-01
An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is ideally suited to isotropically hardening Prandtl-Reuss materials. Further, the formulation is given in a manner which allows any conventional finite element program, for 'small strain' elastic-plastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. The paper closes with a unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures. Further, a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain, and the inadequacies of some of these are commented upon.
Elastic-plastic finite-element analyses of thermally cycled single-edge wedge specimens
NASA Technical Reports Server (NTRS)
Kaufman, A.
1982-01-01
Elastic-plastic stress-strain analyses were performed for single-edge wedge alloys subjected to thermal cycling in fluidized beds. Three cases (NASA TAZ-8A alloy under one cycling condition and 316 stainless steel alloy under two cycling conditions) were analyzed by using the MARC nonlinear, finite-element computer program. Elastic solutions from MARC showed good agreement with previously reported solutions that used the NASTRAN and ISO3DQ computer programs. The NASA TAZ-8A case exhibited no plastic strains, and the elastic and elastic-plastic analyses gave identical results. Elastic-plastic analyses of the 316 stainless steel alloy showed plastic strain reversal with a shift of the mean stresses in the compressive direction. The maximum equivalent total strain ranges for these cases were 13 to 22 percent greater than that calculated from elastic analyses.
Efficient parallel algorithms for elastic plastic finite element analysis
NASA Astrophysics Data System (ADS)
Ding, K. Z.; Qin, Q.-H.; Cardew-Hall, M.; Kalyanasundaram, S.
2008-03-01
This paper presents our new development of parallel finite element algorithms for elastic plastic problems. The proposed method is based on dividing the original structure under consideration into a number of substructures which are treated as isolated finite element models via the interface conditions. Throughout the analysis, each processor stores only the information relevant to its substructure and generates the local stiffness matrix. A parallel substructure oriented preconditioned conjugate gradient method, which is combined with MR smoothing and diagonal storage scheme are employed to solve linear systems of equations. After having obtained the displacements of the problem under consideration, a substepping scheme is used to integrate elastic plastic stress strain relations. The procedure outlined controls the error of the computed stress by choosing each substep size automatically according to a prescribed tolerance. The combination of these algorithms shows a good speedup when increasing the number of processors and the effective solution of 3D elastic plastic problems whose size is much too large for a single workstation becomes possible.
Elastic-plastic finite-element analyses of thermally cycled double-edge wedge specimens
NASA Technical Reports Server (NTRS)
Kaufman, A.; Hunt, L. E.
1982-01-01
Elastic-plastic stress-strain analyses were performed for double-edge wedge specimens subjected to thermal cycling in fluidized beds at 316 and 1088 C. Four cases involving different nickel-base alloys (IN 100, Mar M-200, NASA TAZ-8A, and Rene 80) were analyzed by using the MARC nonlinear, finite element computer program. Elastic solutions from MARC showed good agreement with previously reported solutions obtained by using the NASTRAN and ISO3DQ computer programs. Equivalent total strain ranges at the critical locations calculated by elastic analyses agreed within 3 percent with those calculated from elastic-plastic analyses. The elastic analyses always resulted in compressive mean stresses at the critical locations. However, elastic-plastic analyses showed tensile mean stresses for two of the four alloys and an increase in the compressive mean stress for the highest plastic strain case.
Finite element formulations for problems of large elastic-plastic deformation
NASA Technical Reports Server (NTRS)
Mcmeeking, R. M.; Rice, J. R.
1974-01-01
An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is suited to isotropically hardening Prandtl-Reuss materials. The formulation is given in a manner which allows any conventional finite element program, for "small strain" elasticplastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. A unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures, and a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain.
On Dynamic Nonlinear Elasticity and Small Strain
NASA Astrophysics Data System (ADS)
Johnson, P. A.; Sutin, A.; Guyer, R. A.; Tencate, J. A.
2002-12-01
We are addressing the question of whether or not there is a threshold strain behavior where anomalous nonlinear fast dynamics (ANFD) commences in rock and other similar solids, or if the elastic nonlinearity persists to the smallest measurable values. In qualitative measures of many rock types and other materials that behave in the same manner, we have not observed a threshold; however the only careful, small strain level study conducted under controlled conditions that we are aware of is that of TenCate et al. in Berea sandstone (Phys. Rev. Lett. 85, 1020-1024 (2000)). This work indicates that in Berea sandstone, the elastic nonlinearity persists to the minimum measured strains of at least 10-8. Recently, we have begun controlled experiments in other materials that exhibit ANFD in order to see whether or not they behave as Berea sandstone does. We are employing Young's mode resonance to study resonance peak shift and amplitude variations as a function of drive level and detected strain level. In this type of experiment, the time average amplitude is recorded as the sample is driven by a continuous wave source from below to above the fundamental mode resonance. The drive level is increased, and the measurement is repeated progressively over larger and larger drive levels. Experiments are conducted at ambient pressure. Pure alumina ceramic is a material that is highly, elastically-nonlinear and nonporous, and therefore the significant influence of relative humidity on elastic nonlinear response that rock suffers is avoided. Temperature is carefully monitored. Measurements on pure alumina ceramic show that, like Berea sandstone, there is no threshold of elastic nonlinearity within our measurement capability. We are now studying other solids that exhibit ANFD including rock and mixed phase metal. These results indicate that elastic nonlinearity influences all elastic measurments on these solids including modulus and Q at ambient conditions. There appears to be no
Simple bounds on limit loads by elastic finite element analysis
Mackenzie, D.; Nadarajah, C.; Shi, J.; Boyle, J.T. . Dept. of Mechanical Engineering)
1993-02-01
A method for bounding limit loads by an iterative elastic continuum finite element analysis procedure, referred to as the elastic compensation method, is proposed. A number of sample problems are considered, based on both exact solutions and finite element analysis, and it is concluded that the method may be used to obtain limit-load bounds for pressure vessel design by analysis applications with useful accuracy.
1994-02-01
LOO estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials, RAIRO Anal...Superconvergence of the gradient of finite element solutions, RAIRO Anal. Numir., 13 (1979), pp. 139-166. 11. R.Z. DAUTOV, A.V. LAPIN AND A.D...PDEs, 3 (1987), pp. 65-82. 15. M.T. NAKAo, Superconvergence of the gradient of Galerkin approzimations for elliptic problems, RAIRO Math. Model
Finite elastic-plastic deformation of polycrystalline metals
NASA Technical Reports Server (NTRS)
Iwakuma, T.; Nemat-Nasser, S.
1984-01-01
Applying Hill's self-consistent method to finite elastic-plastic deformations, the overall moduli of polycrystalline solids are estimated. The model predicts a Bauschinger effect, hardening, and formation of vertex or corner on the yield surface for both microscopically non-hardening and hardening crystals. The changes in the instantaneous moduli with deformation are examined, and their asymptotic behavior, especially in relation to possible localization of deformations, is discussed. An interesting conclusion is that small second-order quantities, such as shape changes of grains and residual stresses (measured relative to the crystal elastic moduli), have a first-order effect on the overall response, as they lead to a loss of the overall stability by localized deformation. The predicted incipience of localization for a uniaxial deformation in two dimensions depends on the initial yield strain, but the orientation of localization is slightly less than 45 deg with respect to the tensile direction, although the numerical instability makes it very difficult to estimate this direction accurately.
ZIP3D: An elastic and elastic-plastic finite-element analysis program for cracked bodies
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Newman, J. C., Jr.
1990-01-01
ZIP3D is an elastic and an elastic-plastic finite element program to analyze cracks in three dimensional solids. The program may also be used to analyze uncracked bodies or multi-body problems involving contacting surfaces. For crack problems, the program has several unique features including the calculation of mixed-mode strain energy release rates using the three dimensional virtual crack closure technique, the calculation of the J integral using the equivalent domain integral method, the capability to extend the crack front under monotonic or cyclic loading, and the capability to close or open the crack surfaces during cyclic loading. The theories behind the various aspects of the program are explained briefly. Line-by-line data preparation is presented. Input data and results for an elastic analysis of a surface crack in a plate and for an elastic-plastic analysis of a single-edge-crack-tension specimen are also presented.
NASA Astrophysics Data System (ADS)
Haddag, Badis; Abed-Meraim, Farid; Balan, Tudor
2007-05-01
In this work, an advanced anisotropic elastic-plasticity model is combined with a damage model and a strain localization criterion in the aim to describe accurately the mechanical behavior of sheet metals. Large strain, fully three-dimensional, implicit time integration algorithms are developed for this model and implemented in the finite element code Abaqus. The resulting code is used to predict the strain localization limits as well as the springback after forming of sheet steels. The impact of strain-path dependent hardening models on the limit strains and on the amount of springback is addressed.
NASA Astrophysics Data System (ADS)
Jiang, Limei; Xu, Xiaofei; Zhou, Yichun
2016-12-01
With the development of the integrated circuit technology and decreasing of the device size, ferroelectric films used in nano ferroelectric devices become thinner and thinner. Along with the downscaling of the ferroelectric film, there is an increasing influence of two strain gradient related terms. One is the strain gradient elasticity and the other one is flexoelectricity. To investigate the interrelationship between flexoelectricity and strain gradient elasticity and their combined effect on the domain structure in ferroelectric nanofilms, a phase field model of flexoelectricity and strain gradient elasticity on the ferroelectric domain evolution is developed based on Mindlin's theory of strain-gradient elasticity. Weak form is derived and implemented in finite element formulations for numerically solving the model equations. The simulation results show that upper bounds for flexoelectric coefficients can be enhanced by increasing strain gradient elasticity coefficients. While a large flexoelectricity that exceeds the upper bound can induce a transition from a ferroelectric state to a modulated/incommensurate state, a large enough strain gradient elasticity may lead to a conversion from an incommensurate state to a ferroelectric state. Strain gradient elasticity and the flexoelectricity have entirely opposite effects on polarization. The observed interrelationship between the strain gradient elasticity and flexoelectricity is rationalized by an analytical solution of the proposed theoretical model. The model proposed in this paper could help us understand the mechanism of phenomena observed in ferroelectric nanofilms under complex electromechanical loads and provide some guides on the practical application of ferroelectric nanofilms.
Numerical solution of acoustic scattering by finite perforated elastic plates
NASA Astrophysics Data System (ADS)
Cavalieri, A. V. G.; Wolf, W. R.; Jaworski, J. W.
2016-04-01
We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k0 based on the plate length. However, at low k0, finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k0. The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k0 for perforated elastic plates.
Finite element methods for nonlinear elastostatic problems in rubber elasticity
NASA Technical Reports Server (NTRS)
Oden, J. T.; Becker, E. B.; Miller, T. H.; Endo, T.; Pires, E. B.
1983-01-01
A number of finite element methods for the analysis of nonlinear problems in rubber elasticity are outlined. Several different finite element schemes are discussed. These include the augmented Lagrangian method, continuation or incremental loading methods, and associated Riks-type methods which have the capability of incorporating limit point behavior and bifurcations. Algorithms for the analysis of limit point behavior and bifurcations are described and the results of several numerical experiments are presented. In addition, a brief survey of some recent work on modelling contact and friction in elasticity problems is given. These results pertain to the use of new nonlocal and nonlinear friction laws.
Models for elastic shells with incompatible strains
Lewicka, Marta; Mahadevan, L.; Pakzad, Mohammad Reza
2014-01-01
The three-dimensional shapes of thin lamina, such as leaves, flowers, feathers, wings, etc., are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric given on the thin sheet as a function of location in the central plane and also across its thickness. The shape is then a consequence of elastic energy minimization on the frustrated geometrical object. Here, we provide a rigorous derivation of the asymptotic theories for shapes of residually strained thin lamina with non-trivial curvatures, i.e. growing elastic shells in both the weakly and strongly curved regimes, generalizing earlier results for the growth of nominally flat plates. The different theories are distinguished by the scaling of the mid-surface curvature relative to the inverse thickness and growth strain, and also allow us to generalize the classical Föppl–von Kármán energy to theories of prestrained shallow shells. PMID:24808750
Tunable thermoelectric transport in nanomeshes via elastic strain engineering
Piccione, Brian; Gianola, Daniel S.
2015-03-16
Recent experimental explorations of silicon nanomeshes have shown that the unique metastructures exhibit reduced thermal conductivity while preserving bulk electrical conductivity via feature sizes between relevant phonon and electron mean free paths, aiding in the continued promise that nanometer-scale engineering may further enhance thermoelectric behavior. Here, we introduce a strategy for tuning thermoelectric transport phenomena in semiconductor nanomeshes via heterogeneous elastic strain engineering, using silicon as a model material for demonstration of the concept. By combining analytical models for electron mobility in uniformly stressed silicon with finite element analysis of strained silicon nanomeshes in a lumped physical model, we show that the nonuniform and multiaxial strain fields defined by the nanomesh geometry give rise to spatially varying band shifts and warping, which in aggregate accelerate electron transport along directions of applied stress. This allows for global electrical conductivity and Seebeck enhancements beyond those of homogenous samples under equivalent far-field stresses, ultimately increasing thermoelectric power factor nearly 50% over unstrained samples. The proposed concept and structures—generic to a wide class of materials with large dynamic ranges of elastic strain in nanoscale volumes—may enable a new pathway for active and tunable control of transport properties relevant to waste heat scavenging and thermal management.
Second strain gradient elasticity of nano-objects
NASA Astrophysics Data System (ADS)
Cordero, Nicolas M.; Forest, Samuel; Busso, Esteban P.
2016-12-01
Mindlin's second strain gradient continuum theory for isotropic linear elastic materials is used to model two different kinds of size-dependent surface effects observed in the mechanical behaviour of nano-objects. First, the existence of an initial higher order stress represented by Mindlin's cohesion parameter, b0, makes it possible to account for the relaxation behaviour of traction-free surfaces. Second, the higher order elastic moduli, ci, coupling the strain tensor and its second gradient are shown to significantly affect the apparent elastic properties of nano-beams and nano-films under uni-axial loading. These two effects are independent from each other and allow for separated identification of the corresponding material parameters. Analytical results are provided for the size-dependent apparent shear modulus of a nano-thin strip under shear. Finite element simulations are then performed to derive the dependence of the apparent Young modulus and Poisson ratio of nano-films with respect to their thickness, and to illustrate hole free surface relaxation in a periodic nano-porous material.
Influence of thermal residual stresses on the elastic phase-strain
Shi, N.; Bourke, M.A.M.; Goldstone, J.A.
1996-04-01
The development of elastic lattice phase strains in a 15 vol. pct TiC particulate reinforced 2219-T6 Al composite was modeled as a function of tensile uniaxial loading by finite element method (FEM). In the relationship of applied stress vs. elastic lattice phase strain, the slopes vary with the applied load even before the macroscopic yielding. The slopes for the phase-strain perpendicular to loading follow nonmonotonic changes with loading, while, in the direction parallel to loading, the slopes change monotonically with the applied load. In this investigation, we have demonstrated via FEM that thermal residual stresses from thermal expansion mismatch between phases affect initiation of matrix plasticity. And the differences in the matrix plasticity initiation influence the internal stress distribution. The changes in the slope are dictated by the internal stress transfer between phases. FEM models with and without thermal history show significant differences in the response of elastic strain component, a mechanics equivalent of the lattice elastic strain. Agreement with experiment can only be obtained by including the thermal history. From a simple elasto-plastic spring model we are able to demonstrate that, with matrix plasticity propagating as predicted by FEM, the elastic strain component responds similarly to the more rigorous numerical predictions, suggesting that the morphology of elastic strain evolution is dictated by the development of matrix plasticity.
Automated Finite Element Analysis of Elastically-Tailored Plates
NASA Technical Reports Server (NTRS)
Jegley, Dawn C. (Technical Monitor); Tatting, Brian F.; Guerdal, Zafer
2003-01-01
A procedure for analyzing and designing elastically tailored composite laminates using the STAGS finite element solver has been presented. The methodology used to produce the elastic tailoring, namely computer-controlled steering of unidirectionally reinforced composite material tows, has been reduced to a handful of design parameters along with a selection of construction methods. The generality of the tow-steered ply definition provides the user a wide variety of options for laminate design, which can be automatically incorporated with any finite element model that is composed of STAGS shell elements. Furthermore, the variable stiffness parameterization is formulated so that manufacturability can be assessed during the design process, plus new ideas using tow steering concepts can be easily integrated within the general framework of the elastic tailoring definitions. Details for the necessary implementation of the tow-steering definitions within the STAGS hierarchy is provided, and the format of the ply definitions is discussed in detail to provide easy access to the elastic tailoring choices. Integration of the automated STAGS solver with laminate design software has been demonstrated, so that the large design space generated by the tow-steering options can be traversed effectively. Several design problems are presented which confirm the usefulness of the design tool as well as further establish the potential of tow-steered plies for laminate design.
Constitutive modeling and computational implementation for finite strain plasticity
NASA Technical Reports Server (NTRS)
Reed, K. W.; Atluri, S. N.
1985-01-01
This paper describes a simple alternate approach to the difficult problem of modeling material behavior. Starting from a general representation for a rate-tpe constitutive equation, it is shown by example how sets of test data may be used to derive restrictions on the scalar functions appearing in the representation. It is not possible to determine these functions from experimental data, but the aforementioned restrictions serve as a guide in their eventual definition. The implications are examined for hypo-elastic, isotropically hardening plastic, and kinematically hardening plastic materials. A simple model for the evolution of the 'back-stress,' in a kinematic-hardening plasticity theory, that is entirely analogous to a hypoelastic stress-strain relation is postulated and examined in detail in modeling finitely plastic tension-torsion test. The implementation of rate-type material models in finite element algorithms is also discussed.
Solution of elastic-plastic stress analysis problems by the p-version of the finite element method
NASA Astrophysics Data System (ADS)
Szabo, Barna A.; Actis, Ricardo L.; Holzer, Stefan M.
1993-11-01
The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.
Solution of elastic-plastic stress analysis problems by the p-version of the finite element method
NASA Technical Reports Server (NTRS)
Szabo, Barna A.; Actis, Ricardo L.; Holzer, Stefan M.
1993-01-01
The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.
Thermo-Elastic Finite Element Analyses of Annular Nuclear Fuels
NASA Astrophysics Data System (ADS)
Kwon, Y. D.; Kwon, S. B.; Rho, K. T.; Kim, M. S.; Song, H. J.
In this study, we tried to examine the pros and cons of the annular type of fuel concerning mainly with the temperatures and stresses of pellet and cladding. The inner and outer gaps between pellet and cladding may play an important role on the temperature distribution and stress distribution of fuel system. Thus, we tested several inner and outer gap cases, and we evaluated the effect of gaps on fuel systems. We conducted thermo-elastic-plastic-creep analyses using an in-house thermo-elastic-plastic-creep finite element program that adopted the 'effective-stress-function' algorithm. Most analyses were conducted until the gaps disappeared; however, certain analyses lasted for 1582 days, after which the fuels were replaced. Further study on the optimal gaps sizes for annular nuclear fuel systems is still required.
PLASTICITY AND NON-LINEAR ELASTIC STRAINS
conditions existing in plane waves in an extended medium to give the time rate of change of stress as a function of the time rate of change of strain, the stress invariants, the total strain and the plastic strain. (Author)
NASA Technical Reports Server (NTRS)
Gayda, J.; Srolovitz, D. J.
1989-01-01
This paper presents a specialized microstructural lattice model, MCFET (Monte Carlo finite element technique), which simulates microstructural evolution in materials in which strain energy has an important role in determining morphology. The model is capable of accounting for externally applied stress, surface tension, misfit, elastic inhomogeneity, elastic anisotropy, and arbitrary temperatures. The MCFET analysis was found to compare well with the results of analytical calculations of the equilibrium morphologies of isolated particles in an infinite matrix.
Elastic finite-difference method for irregular grids
Oprsal, I.; Zahradnik, J.
1999-01-01
Finite-difference (FD) modeling of complicated structures requires simple algorithms. This paper presents a new elastic FD method for spatially irregular grids that is simple and, at the same time, saves considerable memory and computing time. Features like faults, low-velocity layers, cavities, and/or nonplanar surfaces are treated on a fine grid, while the remaining parts of the model are, with equal accuracy, represented on a coarse grid. No interpolation is needed between the fine and coarse parts due to the rectangular grid cells. Relatively abrupt transitions between the small and large grid steps produce no numerical artifacts in the present method. Planar or nonplanar free surfaces, including underground cavities, are treated in a way similar to internal grid points but with consideration of the zero-valued elastic parameters and density outside the free surface (vacuum formalism). A theoretical proof that vacuum formalism fulfills the free-surface conditions is given. Numerical validation is performed through comparison with independent methods, comparing FD with explicitly prescribed boundary conditions and finite elements. Memory and computing time needed in the studied models was only about 10 to 40% of that employing regular square grids of equal accuracy. A practical example of a synthetic seismic section, showing clear signatures of a coal seam and cavity, is presented. The method can be extended to three dimensions.
Finite element investigation of thermo-elastic and thermo-plastic consolidation
Aboustit, B.L.
1984-01-01
The transient response of saturated continua due to thermal as well as mechanical loads is investigated in both elastic and plastic ranges. When the two phase saturated media are subjected to thermomechanical loading, the energy equation is coupled with the mass flow and solid deformation equations resulting in the initial boundary value problem of thermal consolidation. The solid behavior may be assumed to be either elastic or elastoplastic leading to the associated theories of thermoelastic and thermoelastoplastic consolidation. The governing equations for the quasi-static infinitesimal theory of thermoelastic consolidation are developed by using the theory of mixtures. An equivalent variational principle is developed along with associated finite element formulations. Two isoparametric elements of the composite type are employed for the spatial discretization. The formulation is extended to the plastic ranges by modeling the solid phase as an elastic work hardening material with an associated flow rule. An incremental iterative scheme is developed to solve this nonlinear transient problem. Several special purpose computer codes are developed for evaluating the isothermal, thermal, elastic and elastoplastic plane strain consolidation responses. These codes have been evaluated against limiting cases available in the literature. The effects of temporal and spatial interpolation schemes are investigated for one-dimensional thermoelastic consolidation problems. An application dealing with a plane strain underground coal gasification problem is also presented.
Hao, Shijie; Cui, Lishan; Wang, Hua; Jiang, Daqiang; Liu, Yinong; Yan, Jiaqiang; Ren, Yang; Han, Xiaodong; Brown, Dennis E.; Li, Ju
2016-02-10
Crystals held at ultrahigh elastic strains and stresses may exhibit exceptional physical and chemical properties. Individual metallic nanowires can sustain ultra-large elastic strains of 4-7%. However, retaining elastic strains of such magnitude in kilogram-scale nanowires is challenging. Here, we find that under active load, ~5.6% elastic strain can be achieved in Nb nanowires in a composite material. Moreover, large tensile (2.8%) and compressive (-2.4%) elastic strains can be retained in kilogram-scale Nb nanowires when the composite is unloaded to a free-standing condition. It is then demonstrated that the retained tensile elastic strains of Nb nanowires significantly increase their superconducting transition temperature and critical magnetic fields, corroborating ab initio calculations based on BCS theory. This free-standing nanocomposite design paradigm opens new avenues for retaining ultra-large elastic strains in great quantities of nanowires and elastic-strain-engineering at industrial scale.
Three-dimensional elastic-plastic finite-element analysis of fatigue crack propagation
NASA Technical Reports Server (NTRS)
Goglia, G. L.; Chermahini, R. G.
1985-01-01
Fatigue cracks are a major problem in designing structures subjected to cyclic loading. Cracks frequently occur in structures such as aircraft and spacecraft. The inspection intervals of many aircraft structures are based on crack-propagation lives. Therefore, improved prediction of propagation lives under flight-load conditions (variable-amplitude loading) are needed to provide more realistic design criteria for these structures. The main thrust was to develop a three-dimensional, nonlinear, elastic-plastic, finite element program capable of extending a crack and changing boundary conditions for the model under consideration. The finite-element model is composed of 8-noded (linear-strain) isoparametric elements. In the analysis, the material is assumed to be elastic-perfectly plastic. The cycle stress-strain curve for the material is shown Zienkiewicz's initial-stress method, von Mises's yield criterion, and Drucker's normality condition under small-strain assumptions are used to account for plasticity. The three-dimensional analysis is capable of extending the crack and changing boundary conditions under cyclic loading.
Development of the average lattice phase-strain and global elastic macro-strain in Al/TiC composites
Shi, N.; Bourke, M.A.M.; Goldstone, J.A.; Allison, J.E.
1994-02-01
The development of elastic lattice phase strains and global elastic macro-strain in a 15 vol% TiC particle reinforced 2219-T6 Al composite was modeled by finite element method (FEM) as a function of tensile uniaxial loading. The numerical predictions are in excellent agreement with strain measurements at a spallation neutron source. Results from the measurements and modeling indicate that the lattice phase-strains go through a ``zigzag`` increase with the applied load in the direction perpendicular to the load, while the changes of slope in the parallel direction are monotonic. FEM results further showed that it is essential to consider the effect of thermal residual stresses (TRS) in understanding this anomalous behavior. It was demonstrated that, due to TRS, the site of matrix plastic flow initiation changed. On the other hand, the changes of slope of the elastic global macrostrain is solely determined by the phase-stress partition in the composite. An analytical calculation showed that both experimental and numerical slope changes during elastic global strain response under loading could be accurately reproduced by accounting for the changes of phase-stress ratio between the matrix and the matrix.
Finite gradient elasticity and plasticity: a constitutive thermodynamical framework
NASA Astrophysics Data System (ADS)
Bertram, Albrecht
2016-05-01
In Bertram (Continuum Mech Thermodyn. doi:
Visualization of elastic wavefields computed with a finite difference code
Larsen, S.; Harris, D.
1994-11-15
The authors have developed a finite difference elastic propagation model to simulate seismic wave propagation through geophysically complex regions. To facilitate debugging and to assist seismologists in interpreting the seismograms generated by the code, they have developed an X Windows interface that permits viewing of successive temporal snapshots of the (2D) wavefield as they are calculated. The authors present a brief video displaying the generation of seismic waves by an explosive source on a continent, which propagate to the edge of the continent then convert to two types of acoustic waves. This sample calculation was part of an effort to study the potential of offshore hydroacoustic systems to monitor seismic events occurring onshore.
Elastic Wave Radiation from a Line Source of Finite Length
Aldridge, D.F.
1998-11-04
Straightforward algebraic expressions describing the elastic wavefield produced by a line source of finite length are derived in circular cylindrical coordinates. The surrounding elastic medium is assumed to be both homogeneous and isotropic, anc[ the source stress distribution is considered axisymmetic. The time- and space-domain formulae are accurate at all distances and directions from the source; no fa-field or long-wavelength assumptions are adopted for the derivation. The mathematics yield a unified treatment of three different types of sources: an axial torque, an axial force, and a radial pressure. The torque source radiates only azirnuthally polarized shear waves, whereas force and pressure sources generate simultaneous compressional and shear radiation polarized in planes containing the line source. The formulae reduce to more familiar expressions in the two limiting cases where the length of the line source approaches zero and infinity. Far-field approximations to the exact equations indicate that waves radiated parallel to the line source axI.s are attenuated relative to those radiated normal to the axis. The attenuation is more severe for higher I?equencies and for lower wavespeeds. Hence, shear waves are affected more than compressional waves. This fi-equency- and directiondependent attenuation is characterized by an extremely simple mathematical formula, and is readily apparent in example synthetic seismograms.
Elastic wave propagation in finitely deformed layered materials
NASA Astrophysics Data System (ADS)
Galich, Pavel I.; Fang, Nicholas X.; Boyce, Mary C.; Rudykh, Stephan
2017-01-01
We analyze elastic wave propagation in highly deformable layered media with isotropic hyperelastic phases. Band gap structures are calculated for the periodic laminates undergoing large deformations. Compact explicit expressions for the phase and group velocities are derived for the long waves propagating in the finitely deformed composites. Elastic wave characteristics and band gaps are shown to be highly tunable by deformation. The influence of deformation on shear and pressure wave band gaps for materials with various composition and constituent properties are studied, finding advantageous compositions for producing highly tunable complete band gaps in low-frequency ranges. The shear wave band gaps are influenced through the deformation induced changes in effective material properties, whereas pressure wave band gaps are mostly influenced by deformation induced geometry changes. The wide shear wave band gaps are found in the laminates with small volume fractions of a soft phase embedded in a stiffer material; pressure wave band gaps of the low-frequency range appear in the laminates with thin highly compressible layers embedded in a nearly incompressible phase. Thus, by constructing composites with a small amount of a highly compressible phase, wide complete band gaps at the low-frequency range can be achieved; furthermore, these band gaps are shown to be highly tunable by deformation.
Evidence for residual elastic strain in deformed natural quartz
Kunz, Martin; Chen, Kai; Tamura,Nobumichi; Wenk, Hans-Rudolf
2009-01-30
Residual elastic strain in naturally deformed, quartz-containing rocks can be measured quantitatively in a petrographic thin section with high spatial resolution using Laue microdiffraction with white synchrotron x-rays. The measurements with a resolution of one micrometer allow the quantitative determination of the deviatoric strain tensor as a function of position within the crystal investigated. The observed equivalent strain values of 800-1200 microstrains represent a lower bound of the actual preserved residual strain in the rock, since the stress component perpendicular to the cut sample surface plane is released. The measured equivalent strain translates into an equivalent stress in the order of {approx} 50 MPa.
Finite Difference Elastic Wave Field Simulation On GPU
NASA Astrophysics Data System (ADS)
Hu, Y.; Zhang, W.
2011-12-01
Numerical modeling of seismic wave propagation is considered as a basic and important aspect in investigation of the Earth's structure, and earthquake phenomenon. Among various numerical methods, the finite-difference method is considered one of the most efficient tools for the wave field simulation. However, with the increment of computing scale, the power of computing has becoming a bottleneck. With the development of hardware, in recent years, GPU shows powerful computational ability and bright application prospects in scientific computing. Many works using GPU demonstrate that GPU is powerful . Recently, GPU has not be used widely in the simulation of wave field. In this work, we present forward finite difference simulation of acoustic and elastic seismic wave propagation in heterogeneous media on NVIDIA graphics cards with the CUDA programming language. We also implement perfectly matched layers on the graphics cards to efficiently absorb outgoing waves on the fictitious edges of the grid Simulations compared with the results on CPU platform shows reliable accuracy and remarkable efficiency. This work proves that GPU can be an effective platform for wave field simulation, and it can also be used as a practical tool for real-time strong ground motion simulation.
NASA Astrophysics Data System (ADS)
Latorre, Marcos; Montáns, Francisco Javier
2015-09-01
In this paper a purely phenomenological formulation and finite element numerical implementation for quasi-incompressible transversely isotropic and orthotropic materials is presented. The stored energy is composed of distinct anisotropic equilibrated and non-equilibrated parts. The nonequilibrated strains are obtained from the multiplicative decomposition of the deformation gradient. The procedure can be considered as an extension of the Reese and Govindjee framework to anisotropic materials and reduces to such formulation for isotropic materials. The stress-point algorithmic implementation is based on an elastic-predictor viscous-corrector algorithm similar to that employed in plasticity. The consistent tangent moduli for the general anisotropic case are also derived. Numerical examples explain the procedure to obtain the material parameters, show the quadratic convergence of the algorithm and usefulness in multiaxial loading. One example also highlights the importance of prescribing a complete set of stress-strain curves in orthotropic materials.
The atomistic representation of first strain-gradient elastic tensors
NASA Astrophysics Data System (ADS)
Admal, Nikhil Chandra; Marian, Jaime; Po, Giacomo
2017-02-01
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical second-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products of relative atomic positions. Moreover, all expressions are local, in the sense that they depend only on the atomic neighborhood of a lattice site. Our results emanate from the condition of energetic equivalence between continuum and atomistic representations of a crystal, when the kinematics of the latter is governed by the Cauchy-Born rule. Using the derived expressions, we prove that the odd-order tensors vanish if the lattice basis admits central-symmetry. The analytical expressions are implemented as a KIM compliant algorithm to compute the strain gradient elastic tensors for various materials. Numerical results are presented to compare representative interatomic potentials used in the literature for cubic crystals, including simple lattices (fcc Al and Cu and bcc Fe and W) and multi-lattices (diamond-cubic Si). We observe that central potentials exhibit generalized Cauchy relations for the rank-six tensor of strain-gradient elastic moduli. In addition, this tensor is found to be indefinite for many potentials. We discuss the relationship between indefiniteness and material stability. Finally, the atomistic representations are specialized to central potentials in simple lattices. These expressions are used with analytical potentials to study the sensitivity of the elastic tensors to the choice of the cutoff radius.
Near tip stress and strain fields for short elastic cracks
NASA Technical Reports Server (NTRS)
Soediono, A. H.; Kardomateas, G. A.; Carlson, R. L.
1994-01-01
Recent experimental fatigue crack growth studies have concluded an apparent anomalous behavior of short cracks. To investigate the reasons for this unexpected behavior, the present paper focuses on identifying the crack length circumstances under which the requirements for a single parameter (K(sub I) or delta K(sub I) if cyclic loading is considered) characterization are violated. Furthermore, an additional quantity, the T stress, as introduced by Rice, and the related biaxiality ratio, B, are calculated for several crack lengths and two configurations, the single-edge-cracked and the centrally-cracked specimen. It is postulated that a two-parameter characterization by K and T (or B) is needed for the adequate description of the stress and strain field around a short crack. To further verify the validity of this postulate, the influence of the third term of the Williams series on the stress, strain and displacement fields around the crack tip and in particular on the B parameter is also examined. It is found that the biaxiality ratio would be more negative if the third term effects are included in both geometries. The study is conducted using the finite element method with linearly elastic material and isoparametric elements and axial (mode I) loading. Moreover, it is clearly shown that it is not proper to postulate the crack size limits for 'short crack' behavior as a normalized ratio with the specimen width, a/w; it should instead be stated as an absolute, or normalized with respect to a small characteristic dimension such as the grain size. Finally, implications regarding the prediction of cyclic (fatigue) growth of short cracks are discussed.
Two Propositions on the Application of Point Elasticities to Finite Price Changes.
ERIC Educational Resources Information Center
Daskin, Alan J.
1992-01-01
Considers counterintuitive propositions about using point elasticities to estimate quantity changes in response to price changes. Suggests that elasticity increases with price along a linear demand curve, but falling quantity demand offsets it. Argues that point elasticity with finite percentage change in price only approximates percentage change…
Energy trapping in power transmission through an elastic plate by finite piezoelectric transducers.
Yang, Zengtao; Yang, Jiashi; Hu, Yuantai
2008-11-01
We study transmission of electric energy through an elastic plate by acoustic wave propagation and piezoelectric transducers. Our mechanics model consists of an elastic plate with finite piezoelectric patches on both sides of the plate. A theoretical analysis using the equations of elasticity and piezoelectricity is performed. Energy trapping that describes the confinement and localization of the vibration energy is examined.
Approaching the ideal elastic strain limit in silicon nanowires
Zhang, Hongti; Tersoff, Jerry; Xu, Shang; Chen, Huixin; Zhang, Qiaobao; Zhang, Kaili; Yang, Yong; Lee, Chun-Sing; Tu, King-Ning; Li, Ju; Lu, Yang
2016-01-01
Achieving high elasticity for silicon (Si) nanowires, one of the most important and versatile building blocks in nanoelectronics, would enable their application in flexible electronics and bio-nano interfaces. We show that vapor-liquid-solid–grown single-crystalline Si nanowires with diameters of ~100 nm can be repeatedly stretched above 10% elastic strain at room temperature, approaching the theoretical elastic limit of silicon (17 to 20%). A few samples even reached ~16% tensile strain, with estimated fracture stress up to ~20 GPa. The deformations were fully reversible and hysteresis-free under loading-unloading tests with varied strain rates, and the failures still occurred in brittle fracture, with no visible sign of plasticity. The ability to achieve this “deep ultra-strength” for Si nanowires can be attributed mainly to their pristine, defect-scarce, nanosized single-crystalline structure and atomically smooth surfaces. This result indicates that semiconductor nanowires could have ultra-large elasticity with tunable band structures for promising “elastic strain engineering” applications. PMID:27540586
NASA Technical Reports Server (NTRS)
Wu, R. W.; Witmer, E. A.
1972-01-01
Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.
NASA Astrophysics Data System (ADS)
Norouzzadeh, A.; Ansari, R.
2017-04-01
Stress-strain relation in Eringen's nonlocal elasticity theory was originally formulated within the framework of an integral model. Due to difficulty of working with that integral model, the differential model of nonlocal constitutive equation is widely used for nanostructures. However, paradoxical results may be obtained by the differential model for some boundary and loading conditions. Presented in this article is a finite element analysis of Timoshenko nano-beams based on the integral model of nonlocal continuum theory without employing any simplification in the model. The entire procedure of deriving equations of motion is carried out in the matrix form of representation, and hence, they can be easily used in the finite element analysis. For comparison purpose, the differential counterparts of equations are also derived. To study the outcome of analysis based on the integral and differential models, some case studies are presented in which the influences of boundary conditions, nonlocal length scale parameter and loading factor are analyzed. It is concluded that, in contrast to the differential model, there is no paradox in the numerical results of developed integral model of nonlocal continuum theory for different situations of problem characteristics. So, resolving the mentioned paradoxes by means of a purely numerical approach based on the original integral form of nonlocal elasticity theory is the major contribution of present study.
Three-dimensional elastic-plastic finite-element analyses of constraint variations in cracked bodies
NASA Technical Reports Server (NTRS)
Newman, J. C., Jr.; Bigelow, C. A.; Shivakumar, K. N.
1993-01-01
Three-dimensional elastic-plastic (small-strain) finite-element analyses were used to study the stresses, deformations, and constraint variations around a straight-through crack in finite-thickness plates for an elastic-perfectly plastic material under monotonic and cyclic loading. Middle-crack tension specimens were analyzed for thicknesses ranging from 1.25 to 20 mm with various crack lengths. Three local constraint parameters, related to the normal, tangential, and hydrostatic stresses, showed similar variations along the crack front for a given thickness and applied stress level. Numerical analyses indicated that cyclic stress history and crack growth reduced the local constraint parameters in the interior of a plate, especially at high applied stress levels. A global constraint factor alpha(sub g) was defined to simulate three-dimensional effects in two-dimensional crack analyses. The global constraint factor was calculated as an average through-the-thickness value over the crack-front plastic region. Values of alpha(sub g) were found to be nearly independent of crack length and were related to the stress-intensity factor for a given thickness.
Elastic-plastic mixed-iterative finite element analysis: Implementation and performance assessment
NASA Technical Reports Server (NTRS)
Sutjahjo, Edhi; Chamis, Christos C.
1993-01-01
An elastic-plastic algorithm based on Von Mises and associative flow criteria is implemented in MHOST-a mixed iterative finite element analysis computer program developed by NASA Lewis Research Center. The performance of the resulting elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors of 4-node quadrilateral shell finite elements are tested for elastic-plastic performance. Generally, the membrane results are excellent, indicating the implementation of elastic-plastic mixed-iterative analysis is appropriate.
Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity
NASA Astrophysics Data System (ADS)
Gourgiotis, P. A.; Georgiadis, H. G.
2009-11-01
The present study aims at determining the elastic stress and displacement fields around the tips of a finite-length crack in a microstructured solid under remotely applied plane-strain loading (mode I and II cases). The material microstructure is modeled through the Toupin-Mindlin generalized continuum theory of dipolar gradient elasticity. According to this theory, the strain-energy density assumes the form of a positive-definite function of the strain tensor (as in classical elasticity) and the gradient of the strain tensor (additional term). A simple but yet rigorous version of the theory is employed here by considering an isotropic linear expression of the elastic strain-energy density that involves only three material constants (the two Lamé constants and the so-called gradient coefficient). First, a near-tip asymptotic solution is obtained by the Knein-Williams technique. Then, we attack the complete boundary value problem in an effort to obtain a full-field solution. Hypersingular integral equations with a cubic singularity are formulated with the aid of the Fourier transform. These equations are solved by analytical considerations on Hadamard finite-part integrals and a numerical treatment. The results show significant departure from the predictions of standard fracture mechanics. In view of these results, it seems that the classical theory of elasticity is inadequate to analyze crack problems in microstructured materials. Indeed, the present results indicate that the stress distribution ahead of the crack tip exhibits a local maximum that is bounded. Therefore, this maximum value may serve as a measure of the critical stress level at which further advancement of the crack may occur. Also, in the vicinity of the crack tip, the crack-face displacement closes more smoothly as compared to the standard result and the strain field is bounded. Finally, the J-integral (energy release rate) in gradient elasticity was evaluated. A decrease of its value is noticed
Medical ultrasound: imaging of soft tissue strain and elasticity
Wells, Peter N. T.; Liang, Hai-Dong
2011-01-01
After X-radiography, ultrasound is now the most common of all the medical imaging technologies. For millennia, manual palpation has been used to assist in diagnosis, but it is subjective and restricted to larger and more superficial structures. Following an introduction to the subject of elasticity, the elasticity of biological soft tissues is discussed and published data are presented. The basic physical principles of pulse-echo and Doppler ultrasonic techniques are explained. The history of ultrasonic imaging of soft tissue strain and elasticity is summarized, together with a brief critique of previously published reviews. The relevant techniques—low-frequency vibration, step, freehand and physiological displacement, and radiation force (displacement, impulse, shear wave and acoustic emission)—are described. Tissue-mimicking materials are indispensible for the assessment of these techniques and their characteristics are reported. Emerging clinical applications in breast disease, cardiology, dermatology, gastroenterology, gynaecology, minimally invasive surgery, musculoskeletal studies, radiotherapy, tissue engineering, urology and vascular disease are critically discussed. It is concluded that ultrasonic imaging of soft tissue strain and elasticity is now sufficiently well developed to have clinical utility. The potential for further research is examined and it is anticipated that the technology will become a powerful mainstream investigative tool. PMID:21680780
Medical ultrasound: imaging of soft tissue strain and elasticity.
Wells, Peter N T; Liang, Hai-Dong
2011-11-07
After X-radiography, ultrasound is now the most common of all the medical imaging technologies. For millennia, manual palpation has been used to assist in diagnosis, but it is subjective and restricted to larger and more superficial structures. Following an introduction to the subject of elasticity, the elasticity of biological soft tissues is discussed and published data are presented. The basic physical principles of pulse-echo and Doppler ultrasonic techniques are explained. The history of ultrasonic imaging of soft tissue strain and elasticity is summarized, together with a brief critique of previously published reviews. The relevant techniques-low-frequency vibration, step, freehand and physiological displacement, and radiation force (displacement, impulse, shear wave and acoustic emission)-are described. Tissue-mimicking materials are indispensible for the assessment of these techniques and their characteristics are reported. Emerging clinical applications in breast disease, cardiology, dermatology, gastroenterology, gynaecology, minimally invasive surgery, musculoskeletal studies, radiotherapy, tissue engineering, urology and vascular disease are critically discussed. It is concluded that ultrasonic imaging of soft tissue strain and elasticity is now sufficiently well developed to have clinical utility. The potential for further research is examined and it is anticipated that the technology will become a powerful mainstream investigative tool.
Dynamic Buckling of Elastic Bar under Axial Impact Based on Finite Difference Method
NASA Astrophysics Data System (ADS)
Ma, Hao; Yang, Qiang; Han, Zhi-Jun; Lu, Guo-Yun
2016-05-01
Considering first order shear deformation theory, the dynamic buckling governing equations of elastic bar with initial imperfections, transverse inertia and axial inertia are derived by Hamilton principle. The equations are converted into the form of non-dimension. Based on the finite difference method, the equations are solved approximately. The buckling mode of elastic bar under different axial impact velocities has been obtained. The influence of different axial impact velocity on the dynamic buckling of elastic bar is discussed.
Fully Consistent Finite-Strain Landau Theory for High-Pressure Phase Transitions
NASA Astrophysics Data System (ADS)
Tröster, A.; Schranz, W.; Karsai, F.; Blaha, P.
2014-07-01
Landau theory (LT) is an indispensable cornerstone in the thermodynamic description of phase transitions. As with structural transitions, most applications require one to consistently take into account the role of strain. If temperature drives the transition, the relevant strains are, as a rule, small enough to be treated as infinitesimal, and therefore one can get away with linearized elasticity theory. However, for transitions driven by high pressure, strains may become so large that it is absolutely mandatory to treat them as finite and deal with the nonlinear nature of the accompanying elastic energy. In this paper, we explain how to set up and apply what is, in fact, the only possible consistent Landau theory of high-pressure phase transitions that systematically allows us to take these geometrical and physical nonlinearities into account. We also show how to incorporate available information on the pressure dependence of elastic constants taken from experiment or simulation. We apply our new theory to the example of the high-pressure cubic-tetragonal phase transition in strontium titanate, a model perovskite that has played a central role in the development of the theory of structural phase transitions. Armed with pressure-dependent elastic constants calculated by density-functional theory, we give an accurate description of recent high-precision experimental data and predict a number of elastic transition anomalies accessible to experiments.
Hao, Shijie; Cui, Lishan; Wang, Hua; ...
2016-02-10
Crystals held at ultrahigh elastic strains and stresses may exhibit exceptional physical and chemical properties. Individual metallic nanowires can sustain ultra-large elastic strains of 4-7%. However, retaining elastic strains of such magnitude in kilogram-scale nanowires is challenging. Here, we find that under active load, ~5.6% elastic strain can be achieved in Nb nanowires in a composite material. Moreover, large tensile (2.8%) and compressive (-2.4%) elastic strains can be retained in kilogram-scale Nb nanowires when the composite is unloaded to a free-standing condition. It is then demonstrated that the retained tensile elastic strains of Nb nanowires significantly increase their superconducting transitionmore » temperature and critical magnetic fields, corroborating ab initio calculations based on BCS theory. This free-standing nanocomposite design paradigm opens new avenues for retaining ultra-large elastic strains in great quantities of nanowires and elastic-strain-engineering at industrial scale.« less
Prediction of the elastic strain limit of tendons.
Reyes, A M; Jahr, H; van Schie, H T M; Weinans, H; Zadpoor, A A
2014-02-01
The elastic strain limit (ESL) of tendons is the point where maximum elastic modulus is reached, after which micro-damage starts. Study of damage progression in tendons under repetitive (fatigue) loading requires a priori knowledge about ESL. In this study, we propose three different approaches for predicting ESL. First, one single value is assumed to represent the ESL of all tendon specimens. Second, different extrapolation curves are used for extrapolating the initial part of the stress-strain curve. Third, a method based on comparing the shape of the initial part of the stress-strain curve of specimens with a database of stress-strain curves is used. A large number of porcine tendon explants (97) were tested to examine the above-mentioned approaches. The variants of the third approach yielded significantly (p<0.05) smaller error values as compared to the other approaches. The mean absolute percentage error of the best-performing variant of the shape-based comparison was between 8.14±6.44% and 9.96±9.99% depending on the size of the initial part of the stress-strain curves. Interspecies generalizability of the best performing method was also studied by applying it for prediction of the ESL of horse tendons. The ESL of horse tendons was predicted with mean absolute percentage errors ranging between 10.53±7.6% and 19.16±14.31% depending on the size of the initial part of the stress-strain curves and the type of normalization. The results of this study suggest that both ESL and the shape of stress-strain curves may be highly different between different individuals and different anatomical locations.
Inverse problems of determining the shape of incompressible bodies under finite strains
NASA Astrophysics Data System (ADS)
Zhukov, B. A.
2014-05-01
Transformations preserving the volume under finite strains are given for some classes of two-dimensional problems. Several settings of nonlinear elasticity problems meant for determining the shape of mechanical rubber objects from a given configuration in a strained state are proposed on the basis of these transformations. Two axisymmetric problems are solved as an example. In the first problem, we determine the shape of a rubber bushing in a combined rubber-metal joint which has a prescribed configuration in the assembled state. In the second problem, we determine the shape of the rubber element of a cylindrical compression damper in working state.
Finite element elastic-plastic-creep and cyclic life analysis of a cowl lip
NASA Technical Reports Server (NTRS)
Arya, Vinod K.; Melis, Matthew E.; Halford, Gary R.
1990-01-01
Results are presented of elastic, elastic-plastic, and elastic-plastic-creep analyses of a test-rig component of an actively cooled cowl lip. A cowl lip is part of the leading edge of an engine inlet of proposed hypersonic aircraft and is subject to severe thermal loadings and gradients during flight. Values of stresses calculated by elastic analysis are well above the yield strength of the cowl lip material. Such values are highly unrealistic, and thus elastic stress analyses are inappropriate. The inelastic (elastic-plastic and elastic-plastic-creep) analyses produce more reasonable and acceptable stress and strain distributions in the component. Finally, using the results from these analyses, predictions are made for the cyclic crack initiation life of a cowl lip. A comparison of predicted cyclic lives shows the cyclic life prediction from the elastic-plastic-creep analysis to be the lowest and, hence, most realistic.
Controlling surface reactions with nanopatterned surface elastic strain.
Li, Zhisheng; Potapenko, Denis V; Osgood, Richard M
2015-01-27
The application of elastic lattice strain is a promising approach for tuning material properties, but the attainment of a systematic approach for introducing a high level of strain in materials so as to study its effects has been a major challenge. Here we create an array of intense locally varying strain fields on a TiO2 (110) surface by introducing highly pressurized argon nanoclusters at 6-20 monolayers under the surface. By combining scanning tunneling microscopy imaging and the continuum mechanics model, we show that strain causes the surface bridge-bonded oxygen vacancies (BBOv), which are typically present on this surface, to be absent from the strained area and generates defect-free regions. In addition, we find that the adsorption energy of hydrogen binding to oxygen (BBO) is significantly altered by local lattice strain. In particular, the adsorption energy of hydrogen on BBO rows is reduced by ∼ 35 meV when the local crystal lattice is compressed by ∼ 1.3%. Our results provide direct evidence of the influence of strain on atomic-scale surface chemical properties, and such effects may help guide future research in catalysis materials design.
Retaining Large and Adjustable Elastic Strains of Kilogram-Scale Nb Nanowires
Hao, Shijie; Cui, Lishan; Wang, Hua; Jiang, Daqiang; Liu, Yinong; Yan, Jiaqiang; Ren, Yang; Han, Xiaodong; Brown, Dennis E.; Li, Ju
2016-02-10
Individual metallic nanowires can sustain ultra-large elastic strains of 4-7%. However, achieving and retaining elastic strains of such magnitude in kilogram-scale nanowires are challenging. Here, we find that under active load, ~5.6% elastic strain can be achieved in Nb nanowires embedded in a metallic matrix deforming by detwinning. Moreover, large tensile (2.8%) and compressive (-2.4%) elastic strains can be retained in kilogram-scale Nb nanowires when the external load was fully removed, and adjustable in magnitude by processing control. It is then demonstrated that the retained tensile elastic strains of Nb nanowires can increase their superconducting transition temperature and critical magnetic field, in comparison with the unstrained original material. This study opens new avenues for retaining large and tunable elastic strains in great quantities of nanowires and elastic-strain-engineering at industrial scale.
NASA Astrophysics Data System (ADS)
González-Estrada, Octavio A.; Natarajan, Sundararajan; Ródenas, Juan José; Nguyen-Xuan, Hung; Bordas, Stéphane P. A.
2013-07-01
An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a "smooth + singular" decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.
NASA Astrophysics Data System (ADS)
Juan, Pierre-Alexandre; Dingreville, Rémi
2017-02-01
Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive "interferences" are directly affected by the interface structure and its elastic response. This general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.
Juan, Pierre -Alexandre; Dingreville, Remi
2016-10-31
Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive “interferences” are directly affected by the interface structure and its elastic response. Furthermore, this general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.
Juan, Pierre -Alexandre; Dingreville, Remi
2016-10-31
Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive “interferences” aremore » directly affected by the interface structure and its elastic response. Furthermore, this general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.« less
Two-way coupling of finitely extensible nonlinear elastic dumbbells with a turbulent shear flow
NASA Astrophysics Data System (ADS)
Peters, Thomas; Schumacher, Jörg
2007-06-01
We present numerical studies for finitely extensible nonlinear elastic dumbbells which are dispersed in a turbulent plane shear flow at moderate Reynolds number. The polymer ensemble is described on the mesoscopic level by a set of stochastic ordinary differential equations with Brownian noise. The dynamics of the Newtonian solvent is determined by the Navier-Stokes equations. Momentum transfer of the dumbbells with the solvent is implemented by an additional volume forcing term in the Navier-Stokes equations, such that both components of the resulting viscoelastic fluid are connected by a two-way coupling. The dynamics of the dumbbells is given then by Newton's second law of motion including small inertia effects. We investigate the dynamics of the flow for different degrees of dumbbell elasticity and inertia, as given by Weissenberg and Stokes numbers, respectively. For the parameters accessible in our study, the magnitude of the feedback of the polymers on the macroscopic properties of turbulence remains small as quantified by the global energy budget and the Reynolds stresses. A reduction of the turbulent drag by up to 20% is observed for the larger particle inertia. The angular statistics of the dumbbells shows an increasing alignment with the mean flow direction for both, increasing elasticity and inertia. This goes in line with a growing asymmetry of the probability density function of the transverse derivative of the streamwise turbulent velocity component. We find that dumbbells get stretched preferentially in regions where vortex stretching or biaxial strain dominate the local dynamics and topology of the velocity gradient tensor.
Elastoplastic notch root strains - Measurements versus finite-element predictions
NASA Technical Reports Server (NTRS)
Tregoning, R. L.
1992-01-01
A study intended to experimentally and computationally probe the nature of the elastoplastic strain fields created by notches with various levels of constraint is presented. An interferometric strain/displacement gage is used to measure both the axial and lateral strain at the center of a machined and polished notch. The monotonic response of various notches is determined using 3D finite-element calculations.
Breakdown of nonlinear elasticity in amorphous solids at finite temperatures
NASA Astrophysics Data System (ADS)
Procaccia, Itamar; Rainone, Corrado; Shor, Carmel A. B. Z.; Singh, Murari
2016-06-01
It is known [H. G. E. Hentschel et al., Phys. Rev. E 83, 061101 (2011), 10.1103/PhysRevE.83.061101] that amorphous solids at zero temperature do not possess a nonlinear elasticity theory: besides the shear modulus, which exists, none of the higher order coefficients exist in the thermodynamic limit. Here we show that the same phenomenon persists up to temperatures comparable to that of the glass transition. The zero-temperature mechanism due to the prevalence of dangerous plastic modes of the Hessian matrix is replaced by anomalous stress fluctuations that lead to the divergence of the variances of the higher order elastic coefficients. The conclusion is that in amorphous solids elasticity can never be decoupled from plasticity: the nonlinear response is very substantially plastic.
2010-01-01
Background The nonlinear mechanical properties of internal organs and tissues may be measured with unparalleled precision using ultrasound imaging with phase-sensitive speckle tracking. The many potential applications of this important noninvasive diagnostic approach include measurement of arterial stiffness, which is associated with numerous major disease processes. The accuracy of previous ultrasound measurements of arterial stiffness and vascular elasticity has been limited by the relatively low strain of nonlinear structures under normal physiologic pressure and the measurement assumption that the effect of the surrounding tissue modulus might be ignored in both physiologic and pressure equalized conditions. Methods This study performed high-resolution ultrasound imaging of the brachial artery in a healthy adult subject under normal physiologic pressure and the use of external pressure (pressure equalization) to increase strain. These ultrasound results were compared to measurements of arterial strain as determined by finite-element analysis models with and without a surrounding tissue, which was represented by homogenous material with fixed elastic modulus. Results Use of the pressure equalization technique during imaging resulted in average strain values of 26% and 18% at the top and sides, respectively, compared to 5% and 2%, at the top and sides, respectively, under physiologic pressure. In the artery model that included surrounding tissue, strain was 19% and 16% under pressure equalization versus 9% and 13% at the top and sides, respectively, under physiologic pressure. The model without surrounding tissue had slightly higher levels of strain under physiologic pressure compared to the other model, but the resulting strain values under pressure equalization were > 60% and did not correspond to experimental values. Conclusions Since pressure equalization may increase the dynamic range of strain imaging, the effect of the surrounding tissue on strain should
NASA Technical Reports Server (NTRS)
Oden, J. Tinsley; Fly, Gerald W.; Mahadevan, L.
1987-01-01
A hybrid stress finite element method is developed for accurate stress and vibration analysis of problems in linear anisotropic elasticity. A modified form of the Hellinger-Reissner principle is formulated for dynamic analysis and an algorithm for the determination of the anisotropic elastic and compliance constants from experimental data is developed. These schemes were implemented in a finite element program for static and dynamic analysis of linear anisotropic two dimensional elasticity problems. Specific numerical examples are considered to verify the accuracy of the hybrid stress approach and compare it with that of the standard displacement method, especially for highly anisotropic materials. It is that the hybrid stress approach gives much better results than the displacement method. Preliminary work on extensions of this method to three dimensional elasticity is discussed, and the stress shape functions necessary for this extension are included.
Finite Element Prediction of Acoustic Scattering and Radiation from Submerged Elastic Structures
NASA Technical Reports Server (NTRS)
Everstine, G. C.; Henderson, F. M.; Lipman, R. R.
1984-01-01
A finite element formulation is derived for the scattering and radiation of acoustic waves from submerged elastic structures. The formulation uses as fundamental unknowns the displacement in the structure and a velocity potential in the field. Symmetric coefficient matrices result. The outer boundary of the fluid region is terminated with an approximate local wave-absorbing boundary condition which assumes that outgoing waves are locally planar. The finite element model is capable of predicting only the near-field acoustic pressures. Far-field sound pressure levels may be determined by integrating the surface pressures and velocities over the wet boundary of the structure using the Helmholtz integral. Comparison of finite element results with analytic results show excellent agreement. The coupled fluid-structure problem may be solved with general purpose finite element codes by using an analogy between the equations of elasticity and the wave equation of linear acoustics.
NASA Technical Reports Server (NTRS)
Abdul-Aziz, Ali; Kalluri, Sreeramesh
1991-01-01
The temperature-dependent engineering elastic constants of a directionally solidified nickel-base superalloy were estimated from the single-crystal elastic constants of nickel and MAR-MOO2 superalloy by using Wells' method. In this method, the directionally solidified (columnar-grained) nickel-base superalloy was modeled as a transversely isotropic material, and the five independent elastic constants of the transversely isotropic material were determined from the three independent elastic constants of a cubic single crystal. Solidification for both the single crystals and the directionally solidified superalloy was assumed to be along the (001) direction. Temperature-dependent Young's moduli in longitudinal and transverse directions, shear moduli, and Poisson's ratios were tabulated for the directionally solidified nickel-base superalloy. These engineering elastic constants could be used as input for performing finite element structural analysis of directionally solidified turbine engine components.
Dependence of the elastic strain coefficient of copper on the pre-treatment
NASA Technical Reports Server (NTRS)
Kuntze, Wilhelm
1950-01-01
The effect of various pre-treatments on the elastic strain coefficient (alpha) (defined as the reciprocal of the modulus of elasticity E) (Epsilon) and on the mechanical hysteresis of copper has been investigated. Variables comprising the pre-treatments were pre-straining by stretching in a tensile testing machine and by drawing through a die, aging at room and elevated temperatures and annealing. The variation of the elastic strain coefficient with test stress was also investigated.
Saravana Kumar, Gurunathan; George, Subin Philip
2017-02-01
This work proposes a methodology involving stiffness optimization for subject-specific cementless hip implant design based on finite element analysis for reducing stress-shielding effect. To assess the change in the stress-strain state of the femur and the resulting stress-shielding effect due to insertion of the implant, a finite element analysis of the resected femur with implant assembly is carried out for a clinically relevant loading condition. Selecting the von Mises stress as the criterion for discriminating regions for elastic modulus difference, a stiffness minimization method was employed by varying the elastic modulus distribution in custom implant stem. The stiffness minimization problem is formulated as material distribution problem without explicitly penalizing partial volume elements. This formulation enables designs that could be fabricated using additive manufacturing to make porous implant with varying levels of porosity. Stress-shielding effect, measured as difference between the von Mises stress in the intact and implanted femur, decreased as the elastic modulus distribution is optimized.
Elastic/Plastic Drop Analysis Using Finite Element Techniques
R. E. Spears
1999-08-01
A Spent Nuclear Fuel (SNF) can, which is called the High Integrity Can (HIC), is being designed at the Idaho National Engineering and Environmental Laboratory (INEEL). Its intended use is to contain SNF sent to the Idaho Nuclear Technology and Engineering Center (INTEC). INTEC will then do the final work with the HIC to send it to the repository at Yucca Mountain, Nevada, for long-term storage. One portion of the analysis, which was required for the HIC, was accidental drop scenarios. This consisted of 19 simulated drops from a height of 30-feet with impact on a flat rigid surface. Elastic/plastic analyses were performed for the simulated drops. Additionally, two elastic/plastic analyses were performed for drops from a height of 17-feet with impact on a rigid surface having a narrow raised portion across its center. The purpose of the analyses was to determine if any breach occurred which opened a crack wider than 0.05-inches from these drop scenarios. Also some plastic deformations were needed from certain drop scenarios to support the Criticality Safety documentation. The analytical results for the simulated drop scenarios showed that, though the seal in the lid may be broken, no 0.05-inch breach occurred. Also, the deformations for Criticality Safety documentation were calculated and show on the applicable output plots.
2013-01-01
response (stress, internal state variables (ISVs)). The micromorphic continuum constitutive model will account for the inherent length scale of damaged ...2008, 56 (2), 297–335. 9. Regueiro, R. On finite strain micromorphic elastoplasticity . Int. J. Solids Struct. 2010, 47, 786–800. 10. Isbuga, V.; Regueiro
Impact of elasticity on lithospheric shortening and strain localization
NASA Astrophysics Data System (ADS)
Jaquet, Yoann; Schmalholz, Stefan M.; Duretz, Thibault
2015-04-01
The initiation of subduction is not well understood and also the mechanisms of localization in a compressive domain are incompletely understood. In order to better understand what controls strain localization during compression, we perform two dimensional numerical simulations with a finite element code using the MILAMIN solver with the Triangle mesh generator. Our model configuration consists of a lithosphere composed of an upper crust, a lower crust and a mantle with each layer having its own non-Newtonian rheology. We add a thermal perturbation (+100°C) to the right bottom side of the model. The model is then shortened with a fixed strain rate (5*10-15s-1) and we vary both the bottom temperature and the shear modulus. The latter allows variations between two extreme rheological models: visco-elasto-plastic and visco-plastic. The results show that (1) the lithosphere is subjected to buckling, (2) localization caused by shear heating can occur in one of the folds during ongoing buckling, and (3) a lower basal temperature favors higher stresses so that localization is facilitated. The visco-elasto-plastic model shows faster and more intense localization than the visco-plastic model. Moreover, as soon as strain localization initiates, strain rates suddenly increase by several orders of magnitude (>2) during a short period of time (
A computational framework for polyconvex large strain elasticity for geometrically exact beam theory
NASA Astrophysics Data System (ADS)
Ortigosa, Rogelio; Gil, Antonio J.; Bonet, Javier; Hesch, Christian
2016-02-01
In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, 2015) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55-70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney-Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator.
Harmonic three-phase circular inclusions in finite elasticity
NASA Astrophysics Data System (ADS)
Wang, Xu; Schiavone, Peter
2015-09-01
We study the exterior stress field in a three-phase circular inclusion which is bonded to the surrounding matrix through an intermediate interphase layer. All three phases belong to a particular class of compressible hyperelastic materials of harmonic type. We focus on the design of a harmonic elastic inclusion which by definition, does not disturb the sum of the normal stresses in the surrounding matrix. We show that in order to make the coated inclusion harmonic, certain inequalities concerning the material and geometric parameters of the three-phase composite must first be satisfied. The corresponding remote loading parameters can then be uniquely determined while keeping the associated phase angles arbitrary. Our results allow for both uniform and non-uniform remote loading. We show that the stress field inside the inclusion is uniform when the remote loading is uniform.
Feng, Xiaobing
1996-12-31
A non-overlapping domain decomposition iterative method is proposed and analyzed for mixed finite element methods for a sequence of noncoercive elliptic systems with radiation boundary conditions. These differential systems describe the motion of a nearly elastic solid in the frequency domain. The convergence of the iterative procedure is demonstrated and the rate of convergence is derived for the case when the domain is decomposed into subdomains in which each subdomain consists of an individual element associated with the mixed finite elements. The hybridization of mixed finite element methods plays a important role in the construction of the discrete procedure.
Biaxial load effects on the crack border elastic strain energy and strain energy rate
NASA Technical Reports Server (NTRS)
Eftis, J.; Subramonian, N.; Liebowitz, H.
1977-01-01
The validity of the singular solution (first term of a series representation) is investigated for the crack tip stress and displacement field in an infinite sheet with a flat line crack with biaxial loads applied to the outer boundaries. It is shown that if one retains the second contribution to the series approximations for stress and displacement in the calculation of the local elastic strain energy density and elastic strain energy rate in the crack border region, both these quantities have significant biaxial load dependency. The value of the J-integral does not depend on the presence of the second term of the series expansion for stress and displacement. Thus J(I) is insensitive to the presence of loads applied parallel to the plane of the crack.
A hybrid-stress finite element for linear anisotropic elasticity
NASA Technical Reports Server (NTRS)
Fly, Gerald W.; Oden, J. Tinsley; Pearson, Mark L.
1988-01-01
Standard assumed displacement finite elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased.
Multiscale finite-element method for linear elastic geomechanics
NASA Astrophysics Data System (ADS)
Castelletto, Nicola; Hajibeygi, Hadi; Tchelepi, Hamdi A.
2017-02-01
The demand for accurate and efficient simulation of geomechanical effects is widely increasing in the geoscience community. High resolution characterizations of the mechanical properties of subsurface formations are essential for improving modeling predictions. Such detailed descriptions impose severe computational challenges and motivate the development of multiscale solution strategies. We propose a multiscale solution framework for the geomechanical equilibrium problem of heterogeneous porous media based on the finite-element method. After imposing a coarse-scale grid on the given fine-scale problem, the coarse-scale basis functions are obtained by solving local equilibrium problems within coarse elements. These basis functions form the restriction and prolongation operators used to obtain the coarse-scale system for the displacement-vector. Then, a two-stage preconditioner that couples the multiscale system with a smoother is derived for the iterative solution of the fine-scale linear system. Various numerical experiments are presented to demonstrate accuracy and robustness of the method.
NASA Astrophysics Data System (ADS)
Yan, Hongyong; Yang, Lei; Dai, Hengchang; Li, Xiang-Yang
2016-10-01
Elastic reverse-time migration (RTM) can reflect the underground elastic information more comprehensively than single-component Pwave migration. One of the most important requirements of elastic RTM is to solve wave equations. The imaging accuracy and efficiency of RTM depends heavily on the algorithms used for solving wave equations. In this paper, we propose an efficient staggered-grid finite-difference (SFD) scheme based on a sampling approximation method with adaptive variable difference operator lengths to implement elastic prestack RTM. Numerical dispersion analysis and wavefield extrapolation results show that the sampling approximation SFD scheme has greater accuracy than the conventional Taylor-series expansion SFD scheme. We also test the elastic RTM algorithm on theoretical models and a field data set, respectively. Experiments presented demonstrate that elastic RTM using the proposed SFD scheme can generate better images than that using the Taylor-series expansion SFD scheme, particularly for PS images. FurH. thermore, the application of adaptive variable difference operator lengths can effectively improve the computational efficiency of elastic RTM.
A locking-free immersed finite element method for planar elasticity interface problems
NASA Astrophysics Data System (ADS)
Lin, Tao; Sheen, Dongwoo; Zhang, Xu
2013-08-01
This article proposes a nonconforming immersed finite element (IFE) method for solving planar elasticity interface problems with structured (or Cartesian) meshes even if the material interface has a nontrivial geometry. IFE functions developed in this article are applicable to arbitrary configurations of elasticity materials and interface locations. Optimal approximation capability is observed for this new IFE space. The displacement Galerkin method based on this IFE space is robust (locking-free). Numerical experiments are presented to demonstrate that the IFE solution converges optimally for both compressible and nearly incompressible materials.
Modeling of Uniaxial Compression of Fiber Reinforcements using Finite Strains
NASA Astrophysics Data System (ADS)
Comas-Cardona, S.; Le Grognec, P.; Binétruy, C.; Krawczak, P.
2007-04-01
Liquid Composite Molding (LCM) processes are increasingly used to produce composite parts. Most of those processes involve compression of the fiber reinforcement and resin flow. In order to accurately model LCM processes, a good knowledge of fiber reinforcement behavior in compression is required. Several models have already been published, but none of them include permanent deformations. Also because of the large deformation involved in the processes, a finite strain formulation is proposed. Results are given for a glass twill-weave fabric.
Numerical solution of an elastic and viscoelastic gravitational models by the finite element method
NASA Astrophysics Data System (ADS)
Arjona Almodóvar, A.; Chacón Rebollo, T.; Gómez Marmol, M.
2014-12-01
Volcanic areas present a lower effective viscosity than usually in the Earth's crust. Both the elastic-gravitational and the viscoelastic-gravitational models allow the computation of gravity, deformation, and gravitational potential changes in order to investigate crustal deformations of Earth (see for instance Battaglia & Segall, 2004; Fernández et al. 1999, 2001; Rundle 1980 and 1983). These models can be represented by a coupled system of linear parabolic (for the elastic deformations), hyperbolic (for the viscoelastic deformations) and elliptic partial differential equations (for gravitational potential changes) (see for instance Arjona et al. 2008 and 2010). The existence and uniqueness of weak solutions for both the elastic-gravitational and viscoelastic-gravitational problem was demonstrated in Arjona et al. (2008 and 2014). The stabilization to solutions of the associated stationary system was proved in Arjona and Díaz (2007). Here we consider the internal source as response to the effect of a pressurized magma reservoir into a multilayered, elastic-gravitational and viscoelastic-gravitational earth model. We introduce the numerical analysis of a simplified steady elastic-gravitational model, solved by means of the finite element method. We also present some numerical tests in realistic situations that confirm the predictions of theoretical order of convergence. Finally, we describe the methodology for both the elastic-gravitational and the viscoelastic-gravitational models using 2D and 3D test examples performed with FreeFEM++.
NASA Technical Reports Server (NTRS)
Kring, J.; Gyekenyesi, J.; Mendelson, A.
1977-01-01
The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement fields in finite geometry bars containing central, surface, and double-edge cracks under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Normal stresses and the stress intensity factor variation along the crack periphery are calculated using the obtained displacement field. The reported results demonstrate the usefulness of this method in calculating stress intensity factors for commonly encountered crack geometries in finite solids.
ML Renauld; H Lien
2004-12-13
The evolution of global and local stress/strain conditions in test fasteners under test conditions is investigated using elastic-plastic, time-dependent finite element analyses (FEA). For elastic-plastic response, tensile data from multiple specimens, material heats and test temperatures are integrated into a single, normalized flow curve from which temperature dependency is extracted. A primary creep model is calibrated with specimen- and fastener-based thermal relaxation data generated under a range of times, temperatures, stress levels and environments. These material inputs are used in analytical simulations of experimental test conditions for several types of fasteners. These fastener models are constructed with automated routines and contact conditions prescribed at all potentially mating surfaces. Thermal or mechanical room temperature pre-loading, as appropriate for a given fastener, is followed by a temperature ramp and a dwell time at constant temperature. While the amount of thermal stress relaxation is limited for the conditions modeled, local stress states are highly dependent upon geometry (thread root radius, for example), pre-loading history and thermal expansion differences between the test fastener and test fixture. Benefits of this FE approach over an elastic methodology for stress calculation will be illustrated with correlations of Stress Corrosion Cracking (SCC) initiation time and crack orientations in stress concentrations.
NASA Technical Reports Server (NTRS)
Rehfield, Lawrence W.; Pickings, Richard D.; Chang, Stephen; Holl, Michael
1991-01-01
Structural tailoring concepts were developed to create wings with elastically produced camber for the purpose of increasing lift during takeoff conditions. Simple models based upon enhancements to the thin walled composite beam theory of Rehfield were developed to investigate prospects for elastic tailoring of the chordwise deformation of wing structures. The purpose here is to provide a comparison of the theoretical results with a finite element model for the bending method of producing camber. Finite element correlation studies were completed for two cases: a bonded unstiffened structural box, and a bolted unstiffened structural box. Results from these studies show an error of less than one percent for the bonded case and less than six percent for the bolted case in predicting camber curvature for the structural box. Examination of the results shows that the theory is very accurate for the cases studied and will provide an excellent basis for conducting further tailoring studies.
Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling
NASA Astrophysics Data System (ADS)
Alastrué, V.; Martínez, M. A.; Doblaré, M.; Menzel, A.
2009-01-01
A fully three-dimensional anisotropic elastic model for vascular tissue modelling is presented here. The underlying strain energy density function is assumed to additively decouple into volumetric and deviatoric contributions. A straightforward isotropic neo-Hooke-type law is used to model the deviatoric response of the ground substance, whereas a micro-structurally or rather micro-sphere-based approach will be employed to model the contribution and distribution of fibres within the biological tissue of interest. Anisotropy was introduced by means of the use of von Mises orientation distribution functions. Two different micro-mechanical approaches—a, say phenomenological, exponential ansatz, and a worm-like-chain-based formulation—are applied to the micro-fibres and illustratively compared. The passage from micro-structural contributions to the macroscopic response is obtained by a computational homogenisation scheme, namely numerical integration over the surface of the individual micro-spheres. The algorithmic treatment of this integration is discussed in detail for the anisotropic problem at hand, so that several cubatures of the micro-sphere are tested in order to optimise the accuracy at reasonable computational cost. Moreover, the introduced material parameters are identified from simple tension tests on human coronary arterial tissue for the two micro-mechanical models investigated. Both approaches are able to recapture the experimental data. Based on the identified sets of parameters, we first discuss a homogeneous deformation in simple shear to evaluate the models' response at the micro-structural level. Later on, an artery-like two-layered tube subjected to internal pressure is simulated by making use of a non-linear finite element setting. This enables to obtain the micro- and macroscopic responses in an inhomogeneous deformation problem, namely a blood vessel representative boundary value problem. The effect of residual stresses is additionally
NASA Technical Reports Server (NTRS)
Gyekenyesi, J. P.; Mendelson, A.; Kring, J.
1973-01-01
A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.
NASA Astrophysics Data System (ADS)
Nestorović, M. D.; Triantafyllidis, N.
2004-04-01
A limiting factor in the design of fiber-reinforced composites is their failure under axial compression along the fiber direction. These critical axial stresses are significantly reduced in the presence of shear stresses. This investigation is motivated by the desire to study the onset of failure in fiber-reinforced composites under arbitrary multi-axial loading and in the absence of the experimentally inevitable imperfections and finite boundaries. By using a finite strain continuum mechanics formulation for the bifurcation (buckling) problem of a rate-independent, perfectly periodic (layered) solid of infinite extent, we are able to study the influence of load orientation, material properties and fiber volume fraction on the onset of instability in fiber-reinforced composites. Two applications of the general theory are presented in detail, one for a finitely strained elastic rubber composite and another for a graphite-epoxy composite, whose constitutive properties have been determined experimentally. For the latter case, extensive comparisons are made between the predictions of our general theory and the available experimental results as well as to the existing approximate structural theories. It is found that the load orientation, material properties and fiber volume fraction have substantial effects on the onset of failure stresses as well as on the type of the corresponding mode (local or global).
Three-dimensional finite strain from crinoid ossicles
NASA Astrophysics Data System (ADS)
Rowan, Mark G.
Randomly oriented crinoid ossicles are useful markers for the determination of three-dimensional finite strain. Two techniques are presented. Both make use of established methods to measure the two-dimensional strain ellipses on three surfaces, which are then combined to calculate the shape and orientation of the strain ellipsoid. First, ossicles positioned such that a thin section cuts across the cylinder appear as randomly oriented ellipses prior to deformation, and can be analyzed using standard Rfφ methods. Second, ossicles positioned such that the section cuts lengthwise through the cylinder appear as rectangular or sub-rectangular shapes with orthogonal geometries in the undeformed state. Measurements of angular shear strain on two or more such markers are analyzed using a non-linear least-squares solution to the Breddin graph, allowing determination of the best-fit strain ellipse. Both methods are applied to an echinoderm grainstone from the central Helvetic nappes of Switzerland. The results are internally consistent, and compatible with those from other strain analysis techniques.
Barkaoui, Abdelwahed; Tlili, Brahim; Vercher-Martínez, Ana; Hambli, Ridha
2016-10-01
Bone is a living material with a complex hierarchical structure which entails exceptional mechanical properties, including high fracture toughness, specific stiffness and strength. Bone tissue is essentially composed by two phases distributed in approximately 30-70%: an organic phase (mainly type I collagen and cells) and an inorganic phase (hydroxyapatite-HA-and water). The nanostructure of bone can be represented throughout three scale levels where different repetitive structural units or building blocks are found: at the first level, collagen molecules are arranged in a pentameric structure where mineral crystals grow in specific sites. This primary bone structure constitutes the mineralized collagen microfibril. A structural organization of inter-digitating microfibrils forms the mineralized collagen fibril which represents the second scale level. The third scale level corresponds to the mineralized collagen fibre which is composed by the binding of fibrils. The hierarchical nature of the bone tissue is largely responsible of their significant mechanical properties; consequently, this is a current outstanding research topic. Scarce works in literature correlates the elastic properties in the three scale levels at the bone nanoscale. The main goal of this work is to estimate the elastic properties of the bone tissue in a multiscale approach including a sensitivity analysis of the elastic behaviour at each length scale. This proposal is achieved by means of a novel hybrid multiscale modelling that involves neural network (NN) computations and finite elements method (FEM) analysis. The elastic properties are estimated using a neural network simulation that previously has been trained with the database results of the finite element models. In the results of this work, parametric analysis and averaged elastic constants for each length scale are provided. Likewise, the influence of the elastic constants of the tissue constituents is also depicted. Results highlight
A theory of finite strain magneto-poromechanics
NASA Astrophysics Data System (ADS)
Nedjar, B.
2015-11-01
The main purpose of this paper is the multi-physics modeling of magnetically sensitive porous materials. We develop for this a magneto-poromechanics formulation suitable for the description of such a coupling. More specifically, we show how the current state of the art in the mathematical modeling of magneto-mechanics can easily be integrated within the unified framework of continuum thermodynamics of open media, which is crucial in setting the convenient forms of the state laws to fully characterize the behavior of porous materials. Moreover, due to the soft nature of these materials in general, the formulation is directly developed within the finite strain range. In a next step, a modeling example is proposed and detailed for the particular case of magneto-active foams with reversible deformations. In particular, due to their potentially high change in porosity, a nonlinear porosity law recently proposed is used to correctly describe the fluid flow through the interconnected pores when the solid skeleton is finitely strained causing fluid release or reabsorption. From the numerical point of view, the variational formulation together with an algorithmic design is described for an easy implementation within the context of the finite element method. Finally, a set of numerical simulations is presented to illustrate the effectiveness of the proposed framework.
NASA Astrophysics Data System (ADS)
Namani, Ravi
Mechanical properties are essential for understanding diseases that afflict various soft tissues, such as osteoarthritic cartilage and hypertension which alters cardiovascular arteries. Although the linear elastic modulus is routinely measured for hard materials, standard methods are not available for extracting the nonlinear elastic, linear elastic and time-dependent properties of soft tissues. Consequently, the focus of this work is to develop indentation methods for soft biological tissues; since analytical solutions are not available for the general context, finite element simulations are used. First, parametric studies of finite indentation of hyperelastic layers are performed to examine if indentation has the potential to identify nonlinear elastic behavior. To answer this, spherical, flat-ended conical and cylindrical tips are examined and the influence of thickness is exploited. Also the influence of the specimen/substrate boundary condition (slip or non-slip) is clarified. Second, a new inverse method---the hyperelastic extraction algorithm (HPE)---was developed to extract two nonlinear elastic parameters from the indentation force-depth data, which is the basic measurement in an indentation test. The accuracy of the extracted parameters and the influence of noise in measurements on this accuracy were obtained. This showed that the standard Berkovitch tip could only extract one parameter with sufficient accuracy, since the indentation force-depth curve has limited sensitivity to both nonlinear elastic parameters. Third, indentation methods for testing tissues from small animals were explored. New methods for flat-ended conical tips are derived. These account for practical test issues like the difficulty in locating the surface or soft specimens. Also, finite element simulations are explored to elucidate the influence of specimen curvature on the indentation force-depth curve. Fourth, the influence of inhomogeneity and material anisotropy on the extracted
NASA Astrophysics Data System (ADS)
Neff, Patrizio; Ghiba, Ionel-Dumitrel
2016-03-01
We investigate an immediate application in finite strain multiplicative plasticity of the family of isotropic volumetric-isochoric decoupled strain energies F mapsto W_eH(F):= widehat{W}_eH(U) := μ/k e^{k | dev_n log {U}|^2}+κ/2 {widehat{k}} e^{widehat{k} [ tr(log U)]^2}&quad if& det F > 0, + ∞ & quad if & det F ≤ 0, based on the Hencky-logarithmic (true, natural) strain tensor {log U} . Here, {μ > 0} is the infinitesimal shear modulus, {κ=2 μ+3λ/3 > 0} is the infinitesimal bulk modulus with λ the first Lamé constant, {k,widehat{k}} are additional dimensionless material parameters, {F=nabla \\varphi} is the gradient of deformation, {U=√{F^T F}} is the right stretch tensor, and dev n {log {U} =log {U}-1/n tr(log {U})\\cdot{1}} is the deviatoric part of the strain tensor {log U} . Based on the multiplicative decomposition {F=F_e F_p} , we couple these energies with some isotropic elasto-plastic flow rules {F_p {dt}/[F_p^{-1}]in-partial χ(dev_3 Σe)} defined in the plastic distortion F p , where {partial χ} is the subdifferential of the indicator function {χ} of the convex elastic domain {E_e({Σe},1/3{σ}_{y}^2)} in the mixed-variant {Σe} -stress space, {Σe=F_e^T D_{F_e}W_iso(F_e)} , and {W_iso(F_e)} represents the isochoric part of the energy. While {W_eH} may loose ellipticity, we show that loss of ellipticity is effectively prevented by the coupling with plasticity, since the ellipticity domain of {W_eH} on the one hand and the elastic domain in {Σe} -stress space on the other hand are closely related. Thus, the new formulation remains elliptic in elastic unloading at any given plastic predeformation. In addition, in this domain, the true stress-true strain relation remains monotone, as observed in experiments.
Vibration band gaps for elastic metamaterial rods using wave finite element method
NASA Astrophysics Data System (ADS)
Nobrega, E. D.; Gautier, F.; Pelat, A.; Dos Santos, J. M. C.
2016-10-01
Band gaps in elastic metamaterial rods with spatial periodic distribution and periodically attached local resonators are investigated. New techniques to analyze metamaterial systems are using a combination of analytical or numerical method with wave propagation. One of them, called here wave spectral element method (WSEM), consists of combining the spectral element method (SEM) with Floquet-Bloch's theorem. A modern methodology called wave finite element method (WFEM), developed to calculate dynamic behavior in periodic acoustic and structural systems, utilizes a similar approach where SEM is substituted by the conventional finite element method (FEM). In this paper, it is proposed to use WFEM to calculate band gaps in elastic metamaterial rods with spatial periodic distribution and periodically attached local resonators of multi-degree-of-freedom (M-DOF). Simulated examples with band gaps generated by Bragg scattering and local resonators are calculated by WFEM and verified with WSEM, which is used as a reference method. Results are presented in the form of attenuation constant, vibration transmittance and frequency response function (FRF). For all cases, WFEM and WSEM results are in agreement, provided that the number of elements used in WFEM is sufficient to convergence. An experimental test was conducted with a real elastic metamaterial rod, manufactured with plastic in a 3D printer, without local resonance-type effect. The experimental results for the metamaterial rod with band gaps generated by Bragg scattering are compared with the simulated ones. Both numerical methods (WSEM and WFEM) can localize the band gap position and width very close to the experimental results. A hybrid approach combining WFEM with the commercial finite element software ANSYS is proposed to model complex metamaterial systems. Two examples illustrating its efficiency and accuracy to model an elastic metamaterial rod unit-cell using 1D simple rod element and 3D solid element are
Bouvier, Adeline; Deleaval, Flavien; Doyley, Marvin M; Yazdani, Saami K; Finet, Gérard; Le Floc'h, Simon; Cloutier, Guy; Pettigrew, Roderic I; Ohayon, Jacques
2016-01-01
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. PMID:24240392
NASA Astrophysics Data System (ADS)
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.
Finite Strain Behavior of Polyurea for a Wide Range of Strain Rates
2010-02-01
R.W. (1984) Non-linear Elastic Deformations, New York, NY, Ellis Horwood Limited, p.209. [75] Othman, R. and Gary, G. (2007) "Testing aluminum alloy ...elastomer that features fast setting time as well as good chemical and fire resistance. It has also good mechanical properties such as its high...nylon bar system (700/s to 1200/s) and an aluminum bar system (2300/s to 3700/s). Lastly, the rate-sensitivity for intermediate strain rates (10/s to
Derivation of a variational principle for plane strain elastic-plastic silk biopolymers
NASA Astrophysics Data System (ADS)
He, J. H.; Liu, F. J.; Cao, J. H.; Zhang, L.
2014-01-01
Silk biopolymers, such as spider silk and Bombyx mori silk, behave always elastic-plastically. An elastic-plastic model is adopted and a variational principle for the small strain, rate plasticity problem is established by semi-inverse method. A trial Lagrangian is constructed where an unknown function is included which can be identified step by step.
2009-03-01
finite shear strains associated with slip and deformation twinning and improper lattice rotations across twin boundaries . Nonlinear anisotropic...of (2) results from gradients in twin fractions, e.g. interface dislocations at tapered twin boundaries . Disclination models of twins (Clayton et
NASA Astrophysics Data System (ADS)
Matveev, A. D.
2016-11-01
To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.
NASA Astrophysics Data System (ADS)
Jian, Wang; Xiaohong, Meng; Hong, Liu; Wanqiu, Zheng; Yaning, Liu; Sheng, Gui; Zhiyang, Wang
2017-03-01
Full waveform inversion and reverse time migration are active research areas for seismic exploration. Forward modeling in the time domain determines the precision of the results, and numerical solutions of finite difference have been widely adopted as an important mathematical tool for forward modeling. In this article, the optimum combined of window functions was designed based on the finite difference operator using a truncated approximation of the spatial convolution series in pseudo-spectrum space, to normalize the outcomes of existing window functions for different orders. The proposed combined window functions not only inherit the characteristics of the various window functions, to provide better truncation results, but also control the truncation error of the finite difference operator manually and visually by adjusting the combinations and analyzing the characteristics of the main and side lobes of the amplitude response. Error level and elastic forward modeling under the proposed combined system were compared with outcomes from conventional window functions and modified binomial windows. Numerical dispersion is significantly suppressed, which is compared with modified binomial window function finite-difference and conventional finite-difference. Numerical simulation verifies the reliability of the proposed method.
NASA Astrophysics Data System (ADS)
Lederer, M.; Khatibi, G.
2017-01-01
It is a well known fact that linear elastic fracture mechanics (LEFM) predicts stress singularities at the tips of sharp cracks, at sharp edges, at corners and at the surface of material transitions. However, from the viewpoint of the strengths of atomic bonds it is clear that only finite forces may be present at the tip of a stable crack. Therefore, theories of strain gradient elasticity were developed which reduce the values of stress concentrations. Within these theories a bending modulus is postulated which introduces an increased stiffness of the crystal lattice against bending. In the present study, the value of this bending modulus is evaluated on the basis of the electrostatic energy of a bent crystal lattice. This is done for the face centred cubic structure of NaCl. In fact, results for the bending modulus could be obtained although they depend on the crystal size.
NASA Technical Reports Server (NTRS)
Kim, H. Alicia; Hardie, Robert; Yamakov, Vesselin; Park, Cheol
2015-01-01
This paper is the second part of a two-part series where the first part presents a molecular dynamics model of a single Boron Nitride Nanotube (BNNT) and this paper scales up to multiple BNNTs in a polymer matrix. This paper presents finite element (FE) models to investigate the effective elastic and piezoelectric properties of (BNNT) nanocomposites. The nanocomposites studied in this paper are thin films of polymer matrix with aligned co-planar BNNTs. The FE modelling approach provides a computationally efficient way to gain an understanding of the material properties. We examine several FE models to identify the most suitable models and investigate the effective properties with respect to the BNNT volume fraction and the number of nanotube walls. The FE models are constructed to represent aligned and randomly distributed BNNTs in a matrix of resin using 2D and 3D hollow and 3D filled cylinders. The homogenisation approach is employed to determine the overall elastic and piezoelectric constants for a range of volume fractions. These models are compared with an analytical model based on Mori-Tanaka formulation suitable for finite length cylindrical inclusions. The model applies to primarily single-wall BNNTs but is also extended to multi-wall BNNTs, for which preliminary results will be presented. Results from the Part 1 of this series can help to establish a constitutive relationship for input into the finite element model to enable the modeling of multiple BNNTs in a polymer matrix.
On the mechanism of bandgap formation in locally resonant finite elastic metamaterials
NASA Astrophysics Data System (ADS)
Sugino, Christopher; Leadenham, Stephen; Ruzzene, Massimo; Erturk, Alper
2016-10-01
Elastic/acoustic metamaterials made from locally resonant arrays can exhibit bandgaps at wavelengths much longer than the lattice size for various applications spanning from low-frequency vibration/sound attenuation to wave guiding and filtering in mechanical and electromechanical devices. For an effective use of such locally resonant metamaterial concepts in finite structures, it is required to bridge the gap between the lattice dispersion characteristics and modal behavior of the host structure with its resonators. To this end, we develop a novel argument for bandgap formation in finite-length elastic metamaterial beams, relying on the modal analysis and the assumption of infinitely many resonators. We show that the dual problem to wave propagation through an infinite periodic beam is the modal analysis of a finite beam with an infinite number of resonators. A simple formula that depends only on the resonator natural frequency and total mass ratio is derived for placing the bandgap in a desired frequency range, yielding an analytical insight and a rule of thumb for design purposes. A method for understanding the importance of a resonator location and mass is discussed in the context of a Riemann sum approximation of an integral, and a method for determining the optimal number of resonators for a given set of boundary conditions and target frequency is introduced. The simulations of the theoretical framework are validated by experiments for bending vibrations of a locally resonant cantilever beam.
A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation.
Bou Matar, Olivier; Guerder, Pierre-Yves; Li, YiFeng; Vandewoestyne, Bart; Van Den Abeele, Koen
2012-05-01
A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb's problem and plane wave nonlinear propagation.
Mixed boundary conditions for FFT-based homogenization at finite strains
NASA Astrophysics Data System (ADS)
Kabel, Matthias; Fliegener, Sascha; Schneider, Matti
2016-02-01
In this article we introduce a Lippmann-Schwinger formulation for the unit cell problem of periodic homogenization of elasticity at finite strains incorporating arbitrary mixed boundary conditions. Such problems occur frequently, for instance when validating computational results with tensile tests, where the deformation gradient in loading direction is fixed, as is the stress in the corresponding orthogonal plane. Previous Lippmann-Schwinger formulations involving mixed boundary can only describe tensile tests where the vector of applied force is proportional to a coordinate direction. Utilizing suitable orthogonal projectors we develop a Lippmann-Schwinger framework for arbitrary mixed boundary conditions. The resulting fixed point and Newton-Krylov algorithms preserve the positive characteristics of existing FFT-algorithms. We demonstrate the power of the proposed methods with a series of numerical examples, including continuous fiber reinforced laminates and a complex nonwoven structure of a long fiber reinforced thermoplastic, resulting in a speed-up of some computations by a factor of 1000.
A fourth order accurate finite difference scheme for the computation of elastic waves
NASA Technical Reports Server (NTRS)
Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.
1986-01-01
A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.
An Elastic Plastic Contact Model with Strain Hardening for the LAMMPS Granular Package
Kuhr, Bryan; Brake, Matthew Robert; Lechman, Jeremy B.
2015-03-01
The following details the implementation of an analytical elastic plastic contact model with strain hardening for normal im pacts into the LAMMPS granular package. The model assumes that, upon impact, the co llision has a period of elastic loading followed by a period of mixed elastic plas tic loading, with contributions to each mechanism estimated by a hyperbolic seca nt weight function. This function is implemented in the LAMMPS source code as the pair style gran/ep/history. Preliminary tests, simulating the pouring of pure nickel spheres, showed the elastic/plastic model took 1.66x as long as similar runs using gran/hertz/history.
Ho, Kai-Yu; Keyak, Joyce H; Powers, Christopher M
2014-01-03
Elevated bone principal strain (an indicator of potential bone injury) resulting from reduced cartilage thickness has been suggested to contribute to patellofemoral symptoms. However, research linking patella bone strain, articular cartilage thickness, and patellofemoral pain (PFP) remains limited. The primary purpose was to determine whether females with PFP exhibit elevated patella bone strain when compared to pain-free controls. A secondary objective was to determine the influence of patella cartilage thickness on patella bone strain. Ten females with PFP and 10 gender, age, and activity-matched pain-free controls participated. Patella bone strain fields were quantified utilizing subject-specific finite element (FE) models of the patellofemoral joint (PFJ). Input parameters for the FE model included (1) PFJ geometry, (2) elastic moduli of the patella bone, (3) weight-bearing PFJ kinematics, and (4) quadriceps muscle forces. Using quasi-static simulations, peak and average minimum principal strains as well as peak and average maximum principal strains were quantified. Cartilage thickness was quantified by computing the perpendicular distance between opposing voxels defining the cartilage edges on axial plane magnetic resonance images. Compared to the pain-free controls, individuals with PFP exhibited increased peak and average minimum and maximum principal strain magnitudes in the patella. Additionally, patella cartilage thickness was negatively associated with peak minimum principal patella strain and peak maximum principal patella strain. The elevated bone strain magnitudes resulting from reduced cartilage thickness may contribute to patellofemoral symptoms and bone injury in persons with PFP.
NASA Technical Reports Server (NTRS)
Endo, T.; Oden, J. T.; Becker, E. B.; Miller, T.
1984-01-01
Finite element methods for the analysis of bifurcations, limit-point behavior, and unilateral frictionless contact of elastic bodies undergoing finite deformation are presented. Particular attention is given to the development and application of Riks-type algorithms for the analysis of limit points and exterior penalty methods for handling the unilateral constraints. Applications focus on the problem of finite axisymmetric deformations, snap-through, and inflation of thick rubber spherical shells.
NASA Technical Reports Server (NTRS)
Kishoni, Doron; Taasan, Shlomo
1994-01-01
Solution of the wave equation using techniques such as finite difference or finite element methods can model elastic wave propagation in solids. This requires mapping the physical geometry into a computational domain whose size is governed by the size of the physical domain of interest and by the required resolution. This computational domain, in turn, dictates the computer memory requirements as well as the calculation time. Quite often, the physical region of interest is only a part of the whole physical body, and does not necessarily include all the physical boundaries. Reduction of the calculation domain requires positioning an artificial boundary or region where a physical boundary does not exist. It is important however that such a boundary, or region, will not affect the internal domain, i.e., it should not cause reflections that propagate back into the material. This paper concentrates on the issue of constructing such a boundary region.
Finite-element modelling of elastic wave propagation and scattering within heterogeneous media
NASA Astrophysics Data System (ADS)
Van Pamel, A.; Sha, G.; Rokhlin, S. I.; Lowe, M. J. S.
2017-01-01
The scattering treated here arises when elastic waves propagate within a heterogeneous medium defined by random spatial fluctuation of its elastic properties. Whereas classical analytical studies are based on lower-order scattering assumptions, numerical methods conversely present no such limitations by inherently incorporating multiple scattering. Until now, studies have typically been limited to two or one dimension, however, owing to computational constraints. This article seizes recent advances to realize a finite-element formulation that solves the three-dimensional elastodynamic scattering problem. The developed methodology enables the fundamental behaviour of scattering in terms of attenuation and dispersion to be studied. In particular, the example of elastic waves propagating within polycrystalline materials is adopted, using Voronoi tessellations to randomly generate representative models. The numerically observed scattering is compared against entirely independent but well-established analytical scattering theory. The quantitative agreement is found to be excellent across previously unvisited scattering regimes; it is believed that this is the first quantitative validation of its kind which provides significant support towards the existence of the transitional scattering regime and facilitates future deployment of numerical methods for these problems.
Micro-CT based finite element models for elastic properties of glass-ceramic scaffolds.
Tagliabue, Stefano; Rossi, Erica; Baino, Francesco; Vitale-Brovarone, Chiara; Gastaldi, Dario; Vena, Pasquale
2017-01-01
In this study, the mechanical properties of porous glass-ceramic scaffolds are investigated by means of three-dimensional finite element models based on micro-computed tomography (micro-CT) scan data. In particular, the quantitative relationship between the morpho-architectural features of the obtained scaffolds, such as macroscopic porosity and strut thickness, and elastic properties, is sought. The macroscopic elastic properties of the scaffolds have been obtained through numerical homogenization approaches using the mechanical characteristics of the solid walls of the scaffolds (assessed through nanoindentation) as input parameters for the numerical simulations. Anisotropic mechanical properties of the produced scaffolds have also been investigated by defining a suitable anisotropy index. A comparison with morphological data obtained through the micro-CT scans is also presented. The proposed study shows that the produced glass-ceramic scaffolds exhibited a macroscopic porosity ranging between 29% and 97% which corresponds to an average stiffness ranging between 42.4GPa and 36MPa. A quantitative estimation of the isotropy of the macroscopic elastic properties has been performed showing that the samples with higher solid fractions were those closest to an isotropic material.
Elastic bending modulus of single-layer molybdenum disulfide (MoS2): finite thickness effect.
Jiang, Jin-Wu; Qi, Zenan; Park, Harold S; Rabczuk, Timon
2013-11-01
We derive, from an empirical interaction potential, an analytic formula for the elastic bending modulus of single-layer MoS2 (SLMoS2). By using this approach, we do not need to define or estimate a thickness value for SLMoS2, which is important due to the substantial controversy in defining this value for two-dimensional or ultrathin nanostructures such as graphene and nanotubes. The obtained elastic bending modulus of 9.61 eV in SLMoS2 is significantly higher than the bending modulus of 1.4 eV in graphene, and is found to be within the range of values that are obtained using thin shell theory with experimentally obtained values for the elastic constants of SLMoS2. This increase in bending modulus as compared to monolayer graphene is attributed, through our analytic expression, to the finite thickness of SLMoS2. Specifically, while each monolayer of S atoms contributes 1.75 eV to the bending modulus, which is similar to the 1.4 eV bending modulus of monolayer graphene, the additional pairwise and angular interactions between out of plane Mo and S atoms contribute 5.84 eV to the bending modulus of SLMoS2.
Finite-element modelling of elastic wave propagation and scattering within heterogeneous media
Sha, G.; Rokhlin, S. I.; Lowe, M. J. S.
2017-01-01
The scattering treated here arises when elastic waves propagate within a heterogeneous medium defined by random spatial fluctuation of its elastic properties. Whereas classical analytical studies are based on lower-order scattering assumptions, numerical methods conversely present no such limitations by inherently incorporating multiple scattering. Until now, studies have typically been limited to two or one dimension, however, owing to computational constraints. This article seizes recent advances to realize a finite-element formulation that solves the three-dimensional elastodynamic scattering problem. The developed methodology enables the fundamental behaviour of scattering in terms of attenuation and dispersion to be studied. In particular, the example of elastic waves propagating within polycrystalline materials is adopted, using Voronoi tessellations to randomly generate representative models. The numerically observed scattering is compared against entirely independent but well-established analytical scattering theory. The quantitative agreement is found to be excellent across previously unvisited scattering regimes; it is believed that this is the first quantitative validation of its kind which provides significant support towards the existence of the transitional scattering regime and facilitates future deployment of numerical methods for these problems. PMID:28265198
Noise and finite size effects in multiferroics with strong elastic interactions
NASA Astrophysics Data System (ADS)
Salje, E. K. H.; Ding, X.; Zhao, Z.
2013-04-01
The size dependence of yield point assisted ferroelastic switching is dominated by the appearance of a minimum size where the domain switching by external strain is swamped by noise which is determined by internal jamming processes. The lower ferroelastic lateral cut-off size was found in computer simulations to be 200 × 202 unit cells for hard materials and 40 × 42 unit cells for soft materials. The corresponding length scales are 16 nm and 4 nm, respectively. These lengths are greater than the minimum length to sustain a twinned sample (˜1 nm). Elastic interactions modify the switching behavior of multiferroics at larger lengths but do not prevent elastic switching above these noise cut-offs.
NASA Technical Reports Server (NTRS)
Sanfeliz, Jose G.
1993-01-01
Micromechanical modeling via elastic-plastic finite element analyses were performed to investigate the effects that the residual stresses and the degree of matrix work hardening (i.e., cold-worked, annealed) have upon the behavior of a 9 vol percent, unidirectional W/Cu composite, undergoing tensile loading. The inclusion of the residual stress-containing state as well as the simulated matrix material conditions proved to be significant since the Cu matrix material exhibited plastic deformation, which affected the subsequent tensile response of the composite system. The stresses generated during cooldown to room temperature from the manufacturing temperature were more of a factor on the annealed-matrix composite, since they induced the softened matrix to plastically flow. This event limited the total load-carrying capacity of this matrix-dominated, ductile-ductile type material system. Plastic deformation of the hardened-matrix composite during the thermal cooldown stage was not considerable, therefore, the composite was able to sustain a higher stress before showing any appreciable matrix plasticity. The predicted room temperature, stress-strain response, and deformation stages under both material conditions represented upper and lower bounds characteristic of the composite's tensile behavior. The initial deformation stage for the hardened material condition showed negligible matrix plastic deformation while for the annealed state, its initial deformation stage showed extensive matrix plasticity. Both material conditions exhibited a final deformation stage where the fiber and matrix were straining plastically. The predicted stress-strain results were compared to the experimental, room temperature, tensile stress-strain curve generated from this particular composite system. The analyses indicated that the actual thermal-mechanical state of the composite's Cu matrix, represented by the experimental data, followed the annealed material condition.
W.R. Solonick
2003-04-01
Rapidly applied transient dynamic loads produce stresses and deflections in structures that typically exceed those from static loading conditions. Previous acceptance criteria for structures designed for rapidly applied transient dynamic loading limited stresses to those determined from elastic analysis. Different stress limits were established for different grades of structure depending upon the amount of permanent set considered acceptable. Structure allowed to sustain very limited permanent set is designed to stress limits not significantly greater than yield stress. Greater permanent set in structure under rapidly applied transient dynamic loading conditions is permitted by establishing stress limits that are significantly greater than yield stress but still provide adequate safety margin (with respect to failure). This paper presents a strain-based elastic-plastic (i.e., inelastic) analysis criterion developed as an alternative to the more conservative stress-based elastic analysis stress criterion for structures subjected to rapidly applied transient dynamic loading. The strain limits established are based on material ductility considerations only and are set as a fraction of the strain at ultimate stress obtained from an engineering stress/strain curve of the material. Strains limits are categorized by type as membrane or surface and by region as general, local , or concentrated. The application of the elastic-plastic criterion provides a more accurate, less conservative design/analysis basis for structures than that used in elastic stress-based analysis criteria, while still providing adequate safety margins.
Solonick, W.
1996-11-01
Rapidly applied transient dynamic loads produce stresses and deflections in structures that typically exceed those from static loading conditions. Previous acceptance criteria for structures designed for rapidly applied transient dynamic loading limited stresses to those determined from elastic analysis. Different stress limits were established for different grades of structure depending upon the amount of permanent set considered acceptable. Structure allowed to sustain very limited permanent set is designed to stress limits not significantly greater than yield stress. Greater permanent set in structure under rapidly applied transient dynamic loading conditions is permitted by establishing stress limits that are significantly greater than yield stress but still provide adequate safety margin (with respect to failure). This paper presents a strain-based elastic-plastic (i.e., inelastic) analysis criterion developed as an alternative to the more conservative stress-based elastic analysis stress criterion for structures subjected to rapidly applied transient dynamic loading. The strain limits established are based on a fraction of the strain at ultimate stress obtained from an engineering stress/strain curve of the material. Strains limits are categorized by type as membrane or surface and by region as general, local, or concentrated. The application of the elastic-plastic criterion provides a more accurate, less conservative design/analysis basis for structures than that used in elastic stress-based analysis criteria, while still providing adequate safety margins.
NASA Astrophysics Data System (ADS)
Heyden, S.; Li, B.; Weinberg, K.; Conti, S.; Ortiz, M.
2015-01-01
We formulate a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. We show that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain elasticity and failure regularized by means of fractional strain-gradient elasticity. In particular, we derive optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely, the critical energy-release rate of the material, and micromechanical parameters pertaining to the elasticity and strength of the polymer chains and to the strain-gradient elasticity regularization. We show how the critical energy-release rate of specific materials can be determined from test data. Finally, we demonstrate the scope and fidelity of the model by means of an example of application, namely, Taylor-impact experiments of polyurea 1000 rods.
NASA Astrophysics Data System (ADS)
Vohar, B.; Kegl, M.; Ren, Z.
2008-12-01
Theoretical and practical aspects of an absolute nodal coordinate formulation (ANCF) beam finite element implementation are considered in the context of dynamic transient response optimization of elastic manipulators. The proposed implementation is based on the introduction of new nodal degrees of freedom, which is achieved by an adequate nonlinear mapping between the original and new degrees of freedom. This approach preserves the mechanical properties of the ANCF beam, but converts it into a conventional finite element so that its nodal degrees of freedom are initially always equal to zero and never depend explicitly on the design variables. Consequently, the sensitivity analysis formulas can be derived in the usual manner, except that the introduced nonlinear mapping has to be taken into account. Moreover, the adjusted element can also be incorporated into general finite element analysis and optimization software in the conventional way. The introduced design variables are related to the cross-section of the beam, to the shape of the (possibly) skeletal structure of the manipulator and to the drive functions. The layered cross-section approach and the design element technique are utilized to parameterize the shape of individual elements and the whole structure. A family of implicit time integration methods is adopted for the response and sensitivity analysis. Based on this assumption, the corresponding sensitivity formulas are derived. Two numerical examples illustrate the performance of the proposed element implementation.
Liu, Yanjie; Zhang, Wen; Pan, Yao; Zhang, Wei; Zhang, Changqing; Zeng, Bingfang; Chen, Yunfeng
2015-01-01
Background The biomechanical characteristics of midshaft clavicular fractures treated with titanium elastic nail (TEN) is unclear. This study aimed to present a biomechanical finite element analysis of biomechanical characteristics involved in TEN fixation and reconstruction plate fixation for midshaft clavicular fractures. Methods Finite element models of the intact clavicle and of midshaft clavicular fractures fixed with TEN and with a reconstruction plate were built. The distal clavicle displacement, peak stress, and stress distribution on the 3 finite element models were calculated under the axial compression and cantilever bending. Results In both loading configurations, TEN generated the highest displacement of the distal clavicle, followed by the intact clavicle and the reconstruction plate. TEN showed higher peak bone and implant stresses, and is more likely to fail in both loading configurations compared with the reconstruction plate. TEN led to a stress distribution similar to that of the intact clavicle in both loading configurations, whereas the stress distribution with the reconstruction plate was nonphysiological in cantilever bending. Conclusions TEN is generally preferable for treating simple displaced fractures of the midshaft clavicle, because it showed a stress distribution similar to the intact clavicle. However, TEN provides less stability, and excessive exercise of and weight bearing on the ipsilateral shoulder should be avoided in the early postoperative period. Fixation with a reconstruction plate was more stable but showed obvious stress shielding. Therefore, for patients with a demand for early return to activity, reconstruction plate fixation may be preferred. PMID:25965409
Finite Element Modeling of the Behavior of Armor Materials Under High Strain Rates and Large Strains
NASA Astrophysics Data System (ADS)
Polyzois, Ioannis
For years high strength steels and alloys have been widely used by the military for making armor plates. Advances in technology have led to the development of materials with improved resistance to penetration and deformation. Until recently, the behavior of these materials under high strain rates and large strains has been primarily based on laboratory testing using the Split Hopkinson Pressure Bar apparatus. With the advent of sophisticated computer programs, computer modeling and finite element simulations are being developed to predict the deformation behavior of these metals for a variety of conditions similar to those experienced during combat. In the present investigation, a modified direct impact Split Hopkinson Pressure Bar apparatus was modeled using the finite element software ABAQUS 6.8 for the purpose of simulating high strain rate compression of specimens of three armor materials: maraging steel 300, high hardness armor (HHA), and aluminum alloy 5083. These armor materials, provided by the Canadian Department of National Defence, were tested at the University of Manitoba by others. In this study, the empirical Johnson-Cook visco-plastic and damage models were used to simulate the deformation behavior obtained experimentally. A series of stress-time plots at various projectile impact momenta were produced and verified by comparison with experimental data. The impact momentum parameter was chosen rather than projectile velocity to normalize the initial conditions for each simulation. Phenomena such as the formation of adiabatic shear bands caused by deformation at high strains and strain rates were investigated through simulations. It was found that the Johnson-Cook model can accurately simulate the behavior of body-centered cubic (BCC) metals such as steels. The maximum shear stress was calculated for each simulation at various impact momenta. The finite element model showed that shear failure first occurred in the center of the cylindrical specimen and
NASA Technical Reports Server (NTRS)
Levy, R.
1991-01-01
Post-processing algorithms are given to compute the vibratory elastic-rigid coupling matrices and the modal contributions to the rigid-body mass matrices and to the effective modal inertias and masses. Recomputation of the elastic-rigid coupling matrices for a change in origin is also described. A computational example is included. The algorithms can all be executed by using standard finite-element program eigenvalue analysis output with no changes to existing code or source programs.
Revealing ultralarge and localized elastic lattice strains in Nb nanowires embedded in NiTi matrix.
Zang, Ketao; Mao, Shengcheng; Cai, Jixiang; Liu, Yinong; Li, Haixin; Hao, Shijie; Jiang, Daqiang; Cui, Lishan
2015-12-02
Freestanding nanowires have been found to exhibit ultra-large elastic strains (4 to 7%) and ultra-high strengths, but exploiting their intrinsic superior mechanical properties in bulk forms has proven to be difficult. A recent study has demonstrated that ultra-large elastic strains of ~6% can be achieved in Nb nanowires embedded in a NiTi matrix, on the principle of lattice strain matching. To verify this hypothesis, this study investigated the elastic deformation behavior of a Nb nanowire embedded in NiTi matrix by means of in situ transmission electron microscopic measurement during tensile deformation. The experimental work revealed that ultra-large local elastic lattice strains of up to 8% are induced in the Nb nanowire in regions adjacent to stress-induced martensite domains in the NiTi matrix, whilst other parts of the nanowires exhibit much reduced lattice strains when adjacent to the untransformed austenite in the NiTi matrix. These observations provide a direct evidence of the proposed mechanism of lattice strain matching, thus a novel approach to designing nanocomposites of superior mechanical properties.
Revealing ultralarge and localized elastic lattice strains in Nb nanowires embedded in NiTi matrix
Zang, Ketao; Mao, Shengcheng; Cai, Jixiang; Liu, Yinong; Li, Haixin; Hao, Shijie; Jiang, Daqiang; Cui, Lishan
2015-01-01
Freestanding nanowires have been found to exhibit ultra-large elastic strains (4 to 7%) and ultra-high strengths, but exploiting their intrinsic superior mechanical properties in bulk forms has proven to be difficult. A recent study has demonstrated that ultra-large elastic strains of ~6% can be achieved in Nb nanowires embedded in a NiTi matrix, on the principle of lattice strain matching. To verify this hypothesis, this study investigated the elastic deformation behavior of a Nb nanowire embedded in NiTi matrix by means of in situ transmission electron microscopic measurement during tensile deformation. The experimental work revealed that ultra-large local elastic lattice strains of up to 8% are induced in the Nb nanowire in regions adjacent to stress-induced martensite domains in the NiTi matrix, whilst other parts of the nanowires exhibit much reduced lattice strains when adjacent to the untransformed austenite in the NiTi matrix. These observations provide a direct evidence of the proposed mechanism of lattice strain matching, thus a novel approach to designing nanocomposites of superior mechanical properties. PMID:26625854
NASA Astrophysics Data System (ADS)
Baxevanis, T.; Chemisky, Y.; Lagoudas, D. C.
2012-09-01
The plane strain mechanical fields near a stationary crack tip in a pseudoelastic shape memory alloy (SMA) are analyzed via the finite element method. The small scale transformation assumption is employed for the calculations using displacement boundary conditions on a circular region that encloses the stress-induced phase transformation zone. The constitutive law used adopts the classical rate-independent small strain flow theory for the evolution equations of both the transformation and plastic strains. Results on the size and shape of the stress-induced transformation and plastic zone formed near the stationary crack are obtained and a fracture toughness criterion based on the J-integral is discussed in view of the observed path-dependence of J. Moreover, the obtained results are discussed in relation to results for stationary cracks in conventional elastic-plastic materials.
Elastic rods with incompatible strain: Macroscopic versus microscopic buckling
NASA Astrophysics Data System (ADS)
Lestringant, Claire; Audoly, Basile
2017-06-01
We consider the buckling of a long prismatic elastic solid under the combined effect of a pre-stress that is inhomogeneous in the cross-section, and of a prescribed displacement of its endpoints. A linear bifurcation analysis is carried out using different structural models (namely a double beam, a rectangular thin plate, and a hyper-elastic prismatic solid in 3-d): it yields the buckling mode and the wavenumber qc that are first encountered when the end-to-end displacement is progressively decreased with fixed pre-stress. For all three structural models, we find a transition from a long-wavelength (qc = 0) to a short-wavelength first buckling mode (qc ≠ 0) when the inhomogeneous pre-stress is increased past a critical value. A method for calculating the critical inhomogeneous pre-stress is proposed based on a small-wavenumber expansion of the buckling mode. Overall, our findings explain the formation of multiple perversions in elastomer strips, as well as the large variations in the number of perversions as a function of pre-stress and cross-sectional geometry, as reported by Liu et al. (2014).
Fuhr, Javier
2015-01-01
Summary Elastically mediated interactions between surface domains are classically described in terms of point forces. Such point forces lead to local strain divergences that are usually avoided by introducing a poorly defined cut-off length. In this work, we develop a self-consistent approach in which the strain field induced by the surface domains is expressed as the solution of an integral equation that contains surface elastic constants, S ij. For surfaces with positive S ij the new approach avoids the introduction of a cut-off length. The classical and the new approaches are compared in case of 1-D periodic ribbons. PMID:25821670
Application Of Elastic Perfectly Plastic Cyclic Analysis To Assessment Of Creep Strain
Carter, Peter; Jetter, Robert I; Sham, Sam
2012-01-01
A cyclic elastic-perfectly plastic analysis method is proposed which provides a conservative estimate to cyclic creep strain accumulation within the ratchet boundary. The method is to check for ratcheting based on an elastic-perfectly material with a temperature-dependent pseudo yield stress defined by temperature, time and stress to give 1% creep strain. It does not require stress classification and is also applicable to a full range of temperature above and below the creep regime. This simplified method could be used as a rapid screening calculation, with full time-dependent creep analysis used if necessary.
NASA Astrophysics Data System (ADS)
Lim, C. W.; Zhang, G.; Reddy, J. N.
2015-05-01
In recent years there have been many papers that considered the effects of material length scales in the study of mechanics of solids at micro- and/or nano-scales. There are a number of approaches and, among them, one set of papers deals with Eringen's differential nonlocal model and another deals with the strain gradient theories. The modified couple stress theory, which also accounts for a material length scale, is a form of a strain gradient theory. The large body of literature that has come into existence in the last several years has created significant confusion among researchers about the length scales that these various theories contain. The present paper has the objective of establishing the fact that the length scales present in nonlocal elasticity and strain gradient theory describe two entirely different physical characteristics of materials and structures at nanoscale. By using two principle kernel functions, the paper further presents a theory with application examples which relates the classical nonlocal elasticity and strain gradient theory and it results in a higher-order nonlocal strain gradient theory. In this theory, a higher-order nonlocal strain gradient elasticity system which considers higher-order stress gradients and strain gradient nonlocality is proposed. It is based on the nonlocal effects of the strain field and first gradient strain field. This theory intends to generalize the classical nonlocal elasticity theory by introducing a higher-order strain tensor with nonlocality into the stored energy function. The theory is distinctive because the classical nonlocal stress theory does not include nonlocality of higher-order stresses while the common strain gradient theory only considers local higher-order strain gradients without nonlocal effects in a global sense. By establishing the constitutive relation within the thermodynamic framework, the governing equations of equilibrium and all boundary conditions are derived via the variational
NASA Astrophysics Data System (ADS)
DeLuca, R.
2006-03-01
Repeated elastic collisions of point particles on a finite frictionless linear track with perfectly reflecting endpoints are considered. The problem is analysed by means of an elementary linear algebra approach. It is found that, starting with a state consisting of a projectile particle in motion at constant velocity and a target particle at rest in a fixed known position, the points at which collisions occur on track, when plotted versus progressive numerals, corresponding to the collisions themselves, show periodic patterns for a rather large choice of values of the initial position x(0) and on the mass ratio r. For certain values of these parameters, however, only regular behaviour over a large number of collisions is detected.
NASA Technical Reports Server (NTRS)
Gyekenyesi, J. P.; Mendelson, A.
1975-01-01
The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement distributions in various bodies containing cracks. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The results obtained show a considerable potential for using this method in the three-dimensional analysis of finite geometry solids and suggest a possible extension of this technique to nonlinear material behavior.
NASA Technical Reports Server (NTRS)
Gyekenyesi, J. P.; Mendelson, A.
1974-01-01
The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement distributions in various bodies containing cracks. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The results obtained show a considerable potential for using this method in the three-dimensional analysis of finite geometry solids and suggest a possible extension of this technique to nonlinear material behavior.
Analytical phase-tracking-based strain estimation for ultrasound elasticity.
Yuan, Lili; Pedersen, Peder C
2015-01-01
A new strain estimator for quasi-static elastography is presented, based on tracking of the analytical signal phase as a function of the external force. Two implementations are introduced: zero-phase search with moving window (SMW) and zero-phase band tracking using connected component labeling (CCL). Low analytical signal amplitude caused by local destructive interference is associated with large error in the phase trajectories, and amplitude thresholding can thus be used to terminate the phase tracking along a particular path. Interpolation is then applied to estimate displacement in the eliminated path. The paper describes first a mathematical analysis based on 1-D multi-scatter modeling, followed by a statistical study of the displacement and strain error. Simulation and experiment with an inhomogeneous phantom indicate that SMW and CCL are capable of reliably estimating tissue displacement and strain over a larger range of deformation than standard timedomain cross-correlation (SCC). Results also show that SMW is roughly 40 times faster than SCC with comparable or even better accuracy. CCL is slower than SMW, but more noise robust. Simulation assessment at compression level 3% and 6% with SNR 20 dB demonstrates average strain error for SMW and CCL of 10%, whereas SCC achieves 18%.
NASA Technical Reports Server (NTRS)
Oline, L.; Medaglia, J.
1972-01-01
The dynamic finite element method was used to investigate elastic stress waves in a plate. Strain displacement and stress strain relations are discussed along with the stiffness and mass matrix. The results of studying point load, and distributed load over small, intermediate, and large radii are reported. The derivation of finite element matrices, and the derivation of lumped and consistent matrices for one dimensional problems with Laplace transfer solutions are included. The computer program JMMSPALL is also included.
Finite element simulation for damage detection of surface rust in steel rebars using elastic waves
NASA Astrophysics Data System (ADS)
Tang, Qixiang; Yu, Tzuyang
2016-04-01
Steel rebar corrosion reduces the integrity and service life of reinforced concrete (RC) structures and causes their gradual and sudden failures. Early stage detection of steel rebar corrosion can improve the efficiency of routine maintenance and prevent sudden failures from happening. In this paper, detecting the presence of surface rust in steel rebars is investigated by the finite element method (FEM) using surface-generated elastic waves. Simulated wave propagation mimics the sensing scheme of a fiber optic acoustic generator mounted on the surface of steel rebars. Formation of surface rust in steel rebars is modeled by changing material's property at local elements. In this paper, various locations of a fiber optic acoustic transducer and a receiver were considered. Megahertz elastic waves were used and different sizes of surface rust were applied. Transient responses of surface displacement and pressure were studied. It is found that surface rust is most detectable when the rust location is between the transducer and the receiver. Displacement response of intact steel rebar is needed in order to obtain background-subtracted response with a better signal-to-noise ratio. When the size of surface rust increases, reduced amplitude in displacement was obtained by the receiver.
Converting strain maps into elasticity maps for materials with small contrast
NASA Astrophysics Data System (ADS)
Bellis, Cédric
2017-01-01
This study addresses the question of the quantitative reconstruction of heterogeneous distributions of isotropic elastic moduli from full strain field data. This parameter identification problem exposes the need for a local reconstruction procedure that is investigated here in the case of materials with small contrast. To begin with the integral formulation framework for the periodic linear elasticity problem, first- and second-order asymptotics are retained for the strain field solution and the effective elasticity tensor. Properties of the featured Green's tensor are investigated to characterize its decomposition into an isotropic term and an orthogonal part. The former is then shown to define a local contribution to the volume integral equations considered. Based on this property, then the combination of multiple strain field solutions corresponding to well-chosen applied macroscopic strains is shown to lead to a set of local and uncoupled identities relating, respectively, the bulk and shear moduli to the spherical and deviatoric components of the strain fields. Valid at the first-order in the weak contrast limit, such relations permit point-wise conversions of strain maps into elasticity maps. Furthermore, it is also shown that for macroscopically isotropic material configurations a single strain field solution is actually sufficient to reconstruct either the bulk or the shear modulus distribution. Those results are then revisited in the case of bounded media. Finally, some sets of analytical and numerical examples are provided for comparison and to illustrate the relevance of the obtained strain-modulus local equations for a parameter identification method based on full-field data.
Klöppel, Thomas; Wall, Wolfgang A
2011-07-01
A novel finite element approach is presented to simulate the mechanical behavior of human red blood cells (RBC, erythrocytes). As the RBC membrane comprises a phospholipid bilayer with an intervening protein network, we propose to model the membrane with two distinct layers. The fairly complex characteristics of the very thin lipid bilayer are represented by special incompressible solid shell elements and an anisotropic viscoelastic constitutive model. Properties of the protein network are modeled with an isotropic hyperelastic third-order material. The elastic behavior of the model is validated with existing optical tweezers studies with quasi-static deformations. Employing material parameters consistent with literature, simulation results are in excellent agreement with experimental data. Available models in literature neglect either the surface area conservation of the RBC membrane or realistic loading conditions of the optical tweezers experiments. The importance of these modeling assumptions, that are both included in this study, are discussed and their influence quantified. For the simulation of the dynamic motion of RBC, the model is extended to incorporate the cytoplasm. This is realized with a monolithic fully coupled fluid-structure interaction simulation, where the fluid is described by the incompressible Navier-Stokes equations in an arbitrary Lagrangian Eulerian framework. It is shown that both membrane viscosity and cytoplasm viscosity have significant influence on simulation results. Characteristic recovery times and energy dissipation for varying strain rates in dynamic laser trap experiments are calculated for the first time and are found to be comparable with experimental data.
Frequency, pressure and strain dependence of nonlinear elasticity in Berea Sandstone
Riviere, Jacques; Johnson, Paul Allan; Marone, Chris; Pimienta, Lucas; Scuderi, Marco; Candela, Thibault; Shokouhi, Parisa; Schubnel, Alexandre; Fortin, Jerome
2016-04-14
Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi-static ( f → 0) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2–3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1f appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. Furthermore, these findings can be used to improve theories relating the macroscopic elastic response to microstructural features.
Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels
Nam, Sungmin; Hu, Kenneth H.; Chaudhuri, Ovijit
2016-01-01
The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell culture models of tissue. One of the most striking features of these gels is that they exhibit nonlinear elasticity, undergoing strain stiffening. However, these gels are also viscoelastic and exhibit stress relaxation, with the resistance of the gel to a deformation relaxing over time. Recent studies have suggested that cells sense and respond to both nonlinear elasticity and viscoelasticity of ECM, yet little is known about the connection between nonlinear elasticity and viscoelasticity. Here, we report that, as strain is increased, not only do biopolymer gels stiffen but they also exhibit faster stress relaxation, reducing the timescale over which elastic energy is dissipated. This effect is not universal to all biological gels and is mediated through weak cross-links. Mechanistically, computational modeling and atomic force microscopy (AFM) indicate that strain-enhanced stress relaxation of collagen gels arises from force-dependent unbinding of weak bonds between collagen fibers. The broader effect of strain-enhanced stress relaxation is to rapidly diminish strain stiffening over time. These results reveal the interplay between nonlinear elasticity and viscoelasticity in collagen gels, and highlight the complexity of the ECM mechanics that are likely sensed through cellular mechanotransduction. PMID:27140623
Elastic precursor shock waves in tantalum at very high strain rates
NASA Astrophysics Data System (ADS)
Crowhurst, Jonathan; Armstrong, Michael; Gates, Sean; Radousky, Harry; Zaug, Joseph
2015-06-01
We have obtained data from micron-thick tantalum films using our ultrafast laser shock platform. By measuring free surface velocity time histories at breakout, and shock wave arrival times at different film thicknesses, we have been able to estimate the dependence of particle and shock velocities on propagation distances and strain rates. We will show how elastic precursor shock waves depend on strain rate in the regime up to and above 109 s-1. We find that while elastic amplitudes are very large at very early times decay occurs rapidly as propagation distance increases. Finally we will consider the prospects for using these data to obtain the dynamic strength of tantalum at these very high strain rates. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 with Laboratory directed Research and Development funding (12ERD042).
Elastic precursor shock waves in tantalum at very high strain rates
NASA Astrophysics Data System (ADS)
Crowhurst, Jonathan; Armstrong, Michael; Radousky, Harry; Zaug, Joseph; Gates, Sean
2015-03-01
We have obtained data from micron-thick tantalum films using our ultrafast laser shock platform. By measuring free surface velocity time histories at breakout, and shock wave arrival times at different film thicknesses, we have been able to estimate the dependence of particle and shock velocities on propagation distances and strain rates. We will show how elastic precursor shock waves depend on strain rate in the regime up to and above 109 s-1. We find that while elastic amplitudes are very large at very early times decay occurs rapidly as propagation distance increases. Finally we will consider the prospects for using these data to obtain the dynamic strength of tantalum at these very high strain rates. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 with Laboratory directed Research and Development funding (12ERD042).
Development of Ti-Nb-Zr alloys with high elastic admissible strain for temporary orthopedic devices.
Ozan, Sertan; Lin, Jixing; Li, Yuncang; Ipek, Rasim; Wen, Cuie
2015-07-01
A new series of beta Ti-Nb-Zr (TNZ) alloys with considerable plastic deformation ability during compression test, high elastic admissible strain, and excellent cytocompatibility have been developed for removable bone tissue implant applications. TNZ alloys with nominal compositions of Ti-34Nb-25Zr, Ti-30Nb-32Zr, Ti-28Nb-35.4Zr and Ti-24.8Nb-40.7Zr (wt.% hereafter) were fabricated using the cold-crucible levitation technique, and the effects of alloying element content on their microstructures, mechanical properties (tensile strength, yield strength, compressive yield strength, Young's modulus, elastic energy, toughness, and micro-hardness), and cytocompatibilities were investigated and compared. Microstructural examinations revealed that the TNZ alloys consisted of β phase. The alloy samples displayed excellent ductility with no cracking, or fracturing during compression tests. Their tensile strength, Young's modulus, elongation at rupture, and elastic admissible strain were measured in the ranges of 704-839 MPa, 62-65 GPa, 9.9-14.8% and 1.08-1.31%, respectively. The tensile strength, Young's modulus and elongation at rupture of the Ti-34Nb-25Zr alloy were measured as 839 ± 31.8 MPa, 62 ± 3.6 GPa, and 14.8 ± 1.6%, respectively; this alloy exhibited the elastic admissible strain of approximately 1.31%. Cytocompatibility tests indicated that the cell viability ratios (CVR) of the alloys are greater than those of the control group; thus the TNZ alloys possess excellent cytocompatibility.
On the isotropic moduli of 2D strain-gradient elasticity
NASA Astrophysics Data System (ADS)
Auffray, Nicolas
2015-01-01
In the present paper, the simplest model of strain-gradient elasticity will be considered, that is, the isotropy in a bidimensional space. Paralleling the definition of the classic elastic moduli, our aim is to introduce second-order isotropic moduli having a mechanical interpretation. A general construction process of these moduli will be proposed. As a result, it appears that many sets can be defined, each of them constituted of 4 moduli: 3 associated with 2 distinct mechanisms and the last one coupling these mechanisms. We hope that these moduli (and the construction process) might be useful for forthcoming investigations on generalized continuum mechanics.
A 2D wavelet-based spectral finite element method for elastic wave propagation
NASA Astrophysics Data System (ADS)
Pahlavan, L.; Kassapoglou, C.; Suiker, A. S. J.; Gürdal, Z.
2012-10-01
A wavelet-based spectral finite element method (WSFEM) is presented that may be used for an accurate and efficient analysis of elastic wave propagation in two-dimensional (2D) structures. The approach is characterised by a temporal transformation of the governing equations to the wavelet domain using a wavelet-Galerkin approach, and subsequently performing the spatial discretisation in the wavelet domain with the finite element method (FEM). The final solution is obtained by transforming the nodal displacements computed in the wavelet domain back to the time domain. The method straightforwardly eliminates artificial temporal edge effects resulting from the discrete wavelet transform and allows for the modelling of structures with arbitrary geometries and boundary conditions. The accuracy and applicability of the method is demonstrated through (i) the analysis of a benchmark problem on axial and flexural waves (Lamb waves) propagating in an isotropic layer, and (ii) the study of a plate subjected to impact loading. The wave propagation response for the impact problem is compared to the result computed with standard FEM equipped with a direct time-integration scheme. The effect of anisotropy on the response is demonstrated by comparing the numerical result for an isotropic plate to that of an orthotropic plate, and to that of a plate made of two dissimilar materials, with and without a cut-out at one of the plate corners. The decoupling of the time-discretised equations in the wavelet domain makes the method inherently suitable for parallel computation, and thus an appealing candidate for efficiently studying high-frequency wave propagation in engineering structures with a large number of degrees of freedom.
NASA Astrophysics Data System (ADS)
Grilo, Tiago J.; Vladimirov, Ivaylo N.; Valente, Robertt A. F.; Reese, Stefanie
2016-06-01
In the present paper, a finite strain model for complex combined isotropic-kinematic hardening is presented. It accounts for finite elastic and finite plastic strains and is suitable for any anisotropic yield criterion. In order to model complex cyclic hardening phenomena, the kinematic hardening is described by several back stress components. To that end, a new procedure is proposed in which several multiplicative decompositions of the plastic part of the deformation gradient are considered. The formulation incorporates a completely general format of the yield function, which means that any yield function can by employed by following a procedure that ensures the principle of material frame indifference. The constitutive equations are derived in a thermodynamically consistent way and numerically integrated by means of a backward-Euler algorithm based on the exponential map. The performance of the constitutive model is assessed via numerical simulations of industry-relevant sheet metal forming processes (U-channel forming and draw/re-draw of a panel benchmarks), the results of which are compared to experimental data. The comparison between numerical and experimental results shows that the use of multiple back stress components is very advantageous in the description of springback. This holds in particular if one carries out a comparison with the results of using only one component. Moreover, the numerically obtained results are in excellent agreement with the experimental data.
Finite element analysis of the high strain rate testing of polymeric materials
NASA Astrophysics Data System (ADS)
Gorwade, C. V.; Alghamdi, A. S.; Ashcroft, I. A.; Silberschmidt, V. V.; Song, M.
2012-08-01
Advanced polymer materials are finding an increasing range of industrial and defence applications. Ultra-high molecular weight polymers (UHMWPE) are already used in lightweight body armour because of their good impact resistance with light weight. However, a broader use of such materials is limited by the complexity of the manufacturing processes and the lack of experimental data on their behaviour and failure evolution under high-strain rate loading conditions. The current study deals with an investigation of the internal heat generation during tensile of UHMWPE. A 3D finite element (FE) model of the tensile test is developed and validated the with experimental work. An elastic-plastic material model is used with adiabatic heat generation. The temperature and stresses obtained with FE analysis are found to be in a good agreement with the experimental results. The model can be used as a simple and cost effective tool to predict the thermo-mechanical behaviour of UHMWPE part under various loading conditions.
Elastic strains at interfaces in InAs/AlSb multilayer structures for quantum cascade lasers
NASA Astrophysics Data System (ADS)
Nicolai, J.; Gatel, Ch.; Warot-Fonrose, B.; Teissier, R.; Baranov, A. N.; Magen, C.; Ponchet, A.
2014-01-01
InAs/AlSb multilayers similar to those used in quantum cascade lasers have been grown by molecular beam epitaxy on (001) InAs substrates. Elastic strain is investigated by high resolution transmission electron microscopy. Thin interfacial regions with lattice distortions significantly different from the strain of the AlSb layers themselves are revealed from the geometrical phase analysis. Strain profiles are qualitatively compared to the chemical contrast of high angle annular dark field images obtained by scanning transmission electron microscopy. The strain and chemical profiles are correlated with the growth sequences used to form the interfaces. Tensile strained AlAs-like interfaces tend to form predominantly due to the high thermal stability of AlAs. Strongly asymmetric interfaces, AlAs-rich and (Al, In)Sb, respectively, can also be achieved by using appropriate growth sequences.
Elastic strains at interfaces in InAs/AlSb multilayer structures for quantum cascade lasers
Nicolai, J.; Gatel, Ch.; Warot-Fonrose, B.; Ponchet, A.; Teissier, R.; Baranov, A. N.; Magen, C.
2014-01-20
InAs/AlSb multilayers similar to those used in quantum cascade lasers have been grown by molecular beam epitaxy on (001) InAs substrates. Elastic strain is investigated by high resolution transmission electron microscopy. Thin interfacial regions with lattice distortions significantly different from the strain of the AlSb layers themselves are revealed from the geometrical phase analysis. Strain profiles are qualitatively compared to the chemical contrast of high angle annular dark field images obtained by scanning transmission electron microscopy. The strain and chemical profiles are correlated with the growth sequences used to form the interfaces. Tensile strained AlAs-like interfaces tend to form predominantly due to the high thermal stability of AlAs. Strongly asymmetric interfaces, AlAs-rich and (Al, In)Sb, respectively, can also be achieved by using appropriate growth sequences.
Eberle, Sebastian; Göttlinger, Michael; Augat, Peter
2013-09-03
In a previous study on subject-specific finite-element-models, we found that appropriate density-elasticity relationships to compute the mechanical behavior of femurs seem to be subject-specific. The purpose of this study was to test the hypothesis that the predictive error of a cohort of subject-specific finite element-models is lower with subject-specific density-elasticity relationships than with a cohort-specific density-elasticity relationship. Finite-element-analysis and inverse optimization based on response surface methodology were employed to test the hypothesis. Subject-specific FE-models of 17 human femurs and corresponding experimental data from biomechanical tests were taken from a previous study. A power function for the relation between radiological bone density and elastic modulus was set up with the optimization variables a and b: E(MPa)=aρqCT(b)(gK2HPO4/cm(3)). The goal of the optimization was to minimize the root-mean-square error in percent (RMSE%) between computational and experimental results. A Wilcoxon test (p=0.05) was performed on all absolute relative errors between the two groups (subject-specific functions vs. cohort-specific function). The subject-specific functions resulted in a 6% lower overall prediction error and a 6% lower RMSE% than the cohort-specific function (p<0.001). The determined subject-specific relations were mostly linear, with variable a ranging from 9307 to 15673 and variable b ranging from 0.68 to 1.40. For the cohort-specific relation, the following power law was obtained: E(MPa)=12486ρqCT(1.16)(gK2HPO4/cm(3)). We conclude that individual density-elasticity relationships improve the accuracy of subject-specific finite element models. Future subject-specific finite-element-analyses of bones should include the individuality of the elastic properties by a stochastic density-elasticity relationship with mean and standard deviation of a and b.
NASA Astrophysics Data System (ADS)
McLaskey, Gregory C.; Glaser, Steven D.
2009-03-01
Experimental studies were performed using high-fidelity broadband Glaser-NIST conical transducers to quantify stress waves produced by the elastic collision of a tiny ball and a massive plate. These sensors are sensitive to surface-normal displacements down to picometers in amplitude, in a frequency range of 20 kHz to over 1 MHz. Both the collision and the resulting transient elastic waves are modeled with the finite element program ABAQUS and described theoretically through a marriage of the Hertz theory of contact and a full elastodynamic Green's function found using generalized ray theory. The calculated displacements were compared to those measured through the Glaser-NIST sensors.
Validation of composite finite elements efficiently simulating elasticity of trabecular bone.
Schwen, Lars Ole; Wolfram, Uwe
2014-01-01
Patient-specific analyses of the mechanical properties of bones become increasingly important for the management of patients with osteoporosis. The potential of composite finite elements (CFEs), a novel FE technique, to assess the apparent stiffness of vertebral trabecular bone is investigated in this study. Segmented volumes of cylindrical specimens of trabecular bone are compared to measured volumes. Elasticity under uniaxial loading conditions is simulated; apparent stiffnesses are compared to experimentally determined values. Computational efficiency is assessed and recommendations for simulation parameters are given. Validating apparent uniaxial stiffnesses results in concordance correlation coefficients 0.69 ≤ r(c) ≤ 0.92 for resolutions finer than 168 μm, and an average error of 5.8% between experimental and numerical results at 24 μm resolution. As an application, the code was used to compute local, macroscopic stiffness tensors for the trabecular structure of a lumbar vertebra. The presented technique allows for computing stiffness using smooth FE meshes at resolutions that are well achievable in peripheral high resolution quantitative CT. Therefore, CFEs could be a valuable tool for the patient-specific assessment of bone stiffness.
NASA Astrophysics Data System (ADS)
Ballandras, S.; Lardat, R.; Wilm, M.; Pastureaud, Th.; Reinhardt, A.; Champavert, N.; Steichen, W.; Daniau, W.; Laude, V.; Armati, R.; Martin, G.
2009-01-01
The development of new surface acoustic wave devices exhibiting complicated electrode patterns or layered excitation transducers has been favored by an intense innovative activity in this area. For instance, devices exhibiting interdigital transducers covered by piezoelectric or dielectric layers have been fabricated and tested, but the design of such structures requires simulation tools capable to accurately take into account the actual shape of the wave guide elements. A modeling approach able to address complicated surface acoustic wave periodic structures (defined in the saggital plane) exhibiting any geometry then has been developed and implemented. It is based on the combination of a finite element analysis and a boundary element method. A first validation of the computation is reported by comparison with standard surface wave devices. Surface transverse wave resonators covered by amorphous silica have been built and consequently used for theory/experiment assessment. Also the case of recessed electrodes has been considered. The proposed model offers large opportunities for modeling any two-dimensional periodic elastic wave guide.
Stress and strain distribution in demineralized enamel: A micro-CT based finite element study.
Neves, Aline Almeida; Coutinho, Eduardo; Alves, Haimon Diniz Lopes; de Assis, Joaquim Teixeira
2015-10-01
Physiological oral mechanical forces may play a role on the progression of enamel carious lesions to cavitation. Thus, the aim of this study was to describe, by 3D finite element analysis, stress, and strain patterns in sound and carious enamel after a simulated occlusal load. Micro-CT based models were created and meshed with tetrahedral elements (based on an extracted third molar), namely: a sound (ST) and a carious tooth (CT). For the CT, enamel material properties were assigned according to the micro-CT gray values. Below the threshold corresponding to the enamel lesion (2.5 g/cm(3) ) lower and isotropic elastic modulus was assigned (E = 18 GPa against E1 = 80 GPa, E2 = E3 = 20 GPa for sound enamel). Both models were imported into a FE solver where boundary conditions were assigned and a pressure load (500 MPa) was applied at the occlusal surface. A linear static analysis was performed, considering anisotropy in sound enamel. ST showed a more efficient transfer of maximum principal stress from enamel to the dentin layer, while for the CT, enamel layer was subjected to higher and concentrated loads. Maximum principal strain distributions were seen at the carious enamel surface, especially at the central fossa, correlating to the enamel cavity seen at the original micro-CT model. It is possible to conclude that demineralized enamel compromises appropriate stress transfer from enamel to dentin, contributing to the odds of fracture and cavitation. Enamel fracture over a dentin lesion may happen as one of the normal pathways to caries progression and may act as a confounding factor during clinical diagnostic decisions.
Groger, Roman1; Lockman, Turab; Saxena, Avadh
2008-01-01
In dislocation-free martensites the components of the elastic strain tensor are constrained by the Saint-Venant compatibility condition which guarantees continuity of the body during external loading. However, in dislocated materials the plastic part of the distortion tensor introduces a displacement mismatch that is removed by elastic relaxation. The elastic strains are then no longer compatible in the sense of the Saint-Venant law and the ensuing incompatibility tensor is shown to be proportional to the gradients of the Nye dislocation density tensor. We demonstrate that the presence of this incompatibility gives rise to an additional long-range contribution in the inhomogeneous part of the Landau energy functional and to the corresponding stress fields. Competition among the local and long-range interactions results in frustration in the evolving order parameter (elastic) texture. We show how the Peach-Koehler forces and stress fields for any distribution of dislocations in arbitrarily anisotropic media can be calculated and employed in a Fokker-Planck dynamics for the dislocation density. This approach represents a self-consistent scheme that yields the evolutions of both the order parameter field and the continuous dislocation density. We illustrate our method by studying the effects of dislocations on microstructure, particularly twinned domain walls, in an Fe-Pd alloy undergoing a martensitic transformation.
NASA Astrophysics Data System (ADS)
Gröger, R.; Lookman, T.; Saxena, A.
2008-11-01
In dislocation-free martensites the components of the elastic strain tensor are constrained by the Saint-Venant compatibility condition which guarantees continuity of the body during external loading. However, in dislocated materials the plastic part of the distortion tensor introduces a displacement mismatch that is removed by elastic relaxation. The elastic strains are then no longer compatible in the sense of the Saint-Venant law and the ensuing incompatibility tensor is shown to be proportional to the gradients of the Nye dislocation density tensor. We demonstrate that the presence of this incompatibility gives rise to an additional long-range contribution in the inhomogeneous part of the Landau energy functional and to the corresponding stress fields. Competition among the local and long-range interactions results in frustration in the evolving order parameter (elastic) texture. We show how the Peach-Koehler forces and stress fields for any distribution of dislocations in arbitrarily anisotropic media can be calculated and employed in a Fokker-Planck dynamics for the dislocation density. This approach represents a self-consistent scheme that yields the evolutions of both the order parameter field and the continuous dislocation density. We illustrate our method by studying the effects of dislocations on microstructure, particularly twinned domain walls, in an Fe-Pd alloy undergoing a martensitic transformation.
Hutula, D.N.
1980-03-01
A finite element procedure is presented for finite deformation analysis of continuum structures with time-dependent anisotropic elastic-plastic material behavior. An updated Lagrangian formulation is used to describe the kinematics of deformation. Anisotropic constitutive relations are referred, at each material point, to a set of three mutually orthogonal axes which rotate as a unit with an angular velocity equal to the spin at the point. The time-history of the solution is generated by using a linear incremental procedure with residual force correction, along with an automatic time step control algorithm which chooses time step sizes to control the accuracy and numerical stability of the solution.
Zhan, Yu; Liu, Changsheng; Zhang, Fengpeng; Qiu, Zhaoguo
2016-07-01
The laser ultrasonic generation of Rayleigh surface wave and longitudinal wave in an elastic plate is studied by experiment and finite element method. In order to eliminate the measurement error and the time delay of the experimental system, the linear fitting method of experimental data is applied. The finite element analysis software ABAQUS is used to simulate the propagation of Rayleigh surface wave and longitudinal wave caused by laser excitation on a sheet metal sample surface. The equivalent load method is proposed and applied. The pulsed laser is equivalent to the surface load in time and space domain to meet the Gaussian profile. The relationship between the physical parameters of the laser and the load is established by the correction factor. The numerical solution is in good agreement with the experimental result. The simple and effective numerical and experimental methods for laser ultrasonic measurement of the elastic constants are demonstrated.
A 3D Orthotropic Strain-Rate Dependent Elastic Damage Material Model.
English, Shawn Allen
2014-09-01
A three dimensional orthotropic elastic constitutive model with continuum damage and cohesive based fracture is implemented for a general polymer matrix composite lamina. The formulation assumes the possibility of distributed (continuum) damage followed b y localized damage. The current damage activation functions are simply partially interactive quadratic strain criteria . However, the code structure allows for changes in the functions without extraordinary effort. The material model formulation, implementation, characterization and use cases are presented.
A highly elastic, capacitive strain gauge based on percolating nanotube networks.
Cohen, Daniel J; Mitra, Debkishore; Peterson, Kevin; Maharbiz, Michel M
2012-04-11
We present a highly elastic strain gauge based on capacitive sensing of parallel, carbon nanotube-based percolation electrodes separated by a dielectric elastomer. The fabrication, relying on vacuum filtration of single-walled carbon nanotubes and hydrophobic patterning of silicone, is both rapid and inexpensive. We demonstrate reliable, linear performance over thousands of cycles at up to 100% strain with less than 3% variability and the highest reported gauge factor for a device of this class (0.99). We further demonstrate use of this sensor in a robotics context to transduce joint angles.
A semi-implicit finite strain shell algorithm using in-plane strains based on least-squares
NASA Astrophysics Data System (ADS)
Areias, P.; Rabczuk, T.; de Sá, J. César; Natal Jorge, R.
2015-04-01
The use of a semi-implicit algorithm at the constitutive level allows a robust and concise implementation of low-order effective shell elements. We perform a semi-implicit integration in the stress update algorithm for finite strain plasticity: rotation terms (highly nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the (in this case evolving) reference configuration and relative Green-Lagrange strains (quadratic) are used to account for change in the equilibrium configuration implicitly. We parametrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use a common configuration. A finite strain quadrilateral element with least-squares assumed in-plane shear strains (in curvilinear coordinates) and classical transverse shear assumed strains is introduced. It is an alternative to enhanced-assumed-strain (EAS) formulations and, contrary to this, produces an element satisfying ab-initio the Patch test. No additional degrees-of-freedom are present, contrasting with EAS. Least-squares fit allows the derivation of invariant finite strain elements which are both in-plane and out-of-plane shear-locking free and amenable to standardization in commercial codes. Two thickness parameters per node are adopted to reproduce the Poisson effect in bending. Metric components are fully deduced and exact linearization of the shell element is performed. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.
A Finite Element Study of Elastically-Accommodated Grain Boundary Sliding
NASA Astrophysics Data System (ADS)
Lee, L.; Jackson, I.; Morris, S.; Zohdi, T.
2007-12-01
θ=30°; close to the value 0.09 found by Ghahremani (1980) in his finite element study of elastically--accommodated grain boundary sliding in an array of hexagonal crystals. As suggested by Faul et al. (2002), we also find that because sharp corners inhibit sliding by inducing stress concentrations, increasing N inhibits sliding, and so causes the maximum value of L to decrease; increasing N from 1 to 100 reduces L by about 4--fold. We are now adding diffusion to our numerical solution of the Raj-Ashby model.
Unified ab initio formulation of flexoelectricity and strain-gradient elasticity
NASA Astrophysics Data System (ADS)
Stengel, Massimiliano
2016-06-01
The theory of flexoelectricity and that of nonlocal elasticity are closely related, and are often considered together when modeling strain-gradient effects in solids. Here I show, based on a first-principles lattice-dynamical analysis, that their relationship is much more intimate than previously thought, and their consistent simultaneous treatment is crucial for obtaining correct physical answers. In particular, I identify a gauge invariance in the theory, whereby the energies associated to strain-gradient elasticity and flexoelectrically induced electric fields are individually reference dependent, and only when summed up they yield a well-defined result. To illustrate this, I construct a minimal thermodynamic functional incorporating strain-gradient effects, and establish a formal link between the continuum description and ab initio phonon dispersion curves to calculate the relevant tensor quantities. As a practical demonstration, I apply such a formalism to bulk SrTiO3, where I find an unusually strong contribution of nonlocal elasticity, mediated by the interaction between the ferroelectric soft mode and the transverse acoustic branches. These results have important implications towards the construction of well-defined thermodynamic theories where flexoelectricity and ferroelectricity coexist. More generally, they open exciting new avenues for the implementation of hierarchical multiscale concepts in the first-principles simulation of crystalline insulators.
Elastic Strain Energy Storage and Neighboring Organ Assistance for Fluid Propulsion
NASA Astrophysics Data System (ADS)
Arun, C. P.
2003-11-01
Storage of elastic strain energy by non-muscular structures such as tendons and ligaments, is a common scheme employed by jumping animals. Also, since skeletal muscle is attached to bone, mechanical advantage is obtained, allowing a burst of power that is unobtainable by muscle contraction alone. This is important at launch since force may be applied for only the brief period when the legs are in contact with the ground. Liquid propelling structures such as the urinary bladder and the heart face the similar problem of being able to impart force to the content only as long as the wall is in a stretched state. Using data from videocystometry and cardiac catheterisation we show that the means employed to achieve liquid propulsion appears to involve a combination of isometric contraction (contraction against a closed sphincter or valve) with hyperelastic stretch of the wall, elastic strain energy storage by the wall, overshoot past the undistended state and neighboring organ assistance (NOA). Thus, the heart, a partially collapsible thick muscular shell without the benefit of NOA manages an ejection fraction of about 70%. Using all of the above means, the collapsible urinary bladder is able to nearly always empty. Elastic strain energy storage and NOA appear to be important strategies for liquid propulsion employed by hollow viscera.
Mathieu, Pattie S; Bodle, Josephine C; Loboa, Elizabeth G
2014-06-27
Human adipose-derived stem cells (hASC) exhibit multilineage differentiation potential with lineage specification that is dictated by both the chemical and mechanical stimuli to which they are exposed. We have previously shown that 10% cyclic tensile strain increases hASC osteogenesis and cell-mediated calcium accretion. We have also recently shown that primary cilia are present on hASC and that chemically-induced lineage specification of hASC concurrently results in length and conformation changes of the primary cilia. Further, we have observed cilia length changes in hASC cultured within a collagen I gel in response to 10% cyclic tensile strain. We therefore hypothesize that primary cilia may play a key mechanotransduction role for hASC exposed to tensile strain. The goal of this study was to use finite element analysis (FEA) to determine strains occurring within the ciliary membrane in response to 10% tensile strain applied parallel, or perpendicular, to cilia orientation. To elucidate the mechanical environment experienced by the cilium, several lengths were modeled and evaluated based on cilia lengths measured on hASC grown under varied culture conditions. Principal tensile strains in both hASC and ciliary membranes were calculated using FEA, and the magnitude and location of maximum principal tensile strain determined. We found that maximum principal tensile strain was concentrated at the base of the cilium. In the linear elastic model, applying strain perpendicular to the cilium resulted in maximum strains within the ciliary membrane from 150% to 200%, while applying strain parallel to the cilium resulted in much higher strains, approximately 400%. In the hyperelastic model, applying strain perpendicular to the cilium resulted in maximum strains within the ciliary membrane around 30%, while applying strain parallel to the cilium resulted in much higher strains ranging from 50% to 70%. Interestingly, FEA results indicated that primary cilium length was not
Mathieu, Pattie S.; Bodle, Josephine C.; Loboa, Elizabeth G.
2014-01-01
Human adipose-derived stem cells (hASC) exhibit multilineage differentiation potential with lineage specification that is dictated by both the chemical and mechanical stimuli to which they are exposed. We have previously shown that 10% cyclic tensile strain increases hASC osteogenesis and cell-mediated calcium accretion. We have also recently shown that primary cilia are present on hASC and that chemically-induced lineage specification of hASC concurrently results in length and conformation changes of the primary cilia. Further, we have observed cilia length changes on hASC cultured within a collagen I gel in response to 10% cyclic tensile strain. We therefore hypothesize that primary cilia may play a key mechanotransduction role for hASC exposed to tensile strain. The goal of this study was to use finite element analysis (FEA) to determine strains occurring within the ciliary membrane in response to 10% tensile strain applied parallel, or perpendicular, to cilia orientation. To elucidate the mechanical environment experienced by the cilium, several lengths were modeled and evaluated based on cilia lengths measured on hASC grown under varied culture conditions. Principal tensile strains in both hASC and ciliary membranes were calculated using FEA, and the magnitude and location of maximum principal tensile strain determined. We found that maximum principal tensile strain was concentrated at the base of the cilium. In the linear elastic model, applying strain perpendicular to the cilium resulted in maximum strains within the ciliary membrane from 150 to 200%, while applying strain parallel to the cilium resulted in much higher strains, approximately 400%. In the hyperelastic model, applying strain perpendicular to the cilium resulted in maximum strains within the ciliary membrane around 30%, while applying strain parallel to the cilium resulted in much higher strains ranging from 50% to 70% . Interestingly, FEA results indicated that primary cilium length was not
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.
Non-conforming curved finite element schemes for time-dependent elastic-acoustic coupled problems
NASA Astrophysics Data System (ADS)
Rodríguez-Rozas, Ángel; Diaz, Julien
2016-01-01
High-order numerical methods for solving time-dependent acoustic-elastic coupled problems are introduced. These methods, based on Finite Element techniques, allow for a flexible coupling between the fluid and the solid domain by using non-conforming meshes and curved elements. Since characteristic waves travel at different speeds through different media, specific levels of granularity for the mesh discretization are required on each domain, making impractical a possible conforming coupling in between. Advantageously, physical domains may be independently discretized in our framework due to the non-conforming feature. Consequently, an important increase in computational efficiency may be achieved compared to other implementations based on conforming techniques, namely by reducing the total number of degrees of freedom. Differently from other non-conforming approaches proposed so far, our technique is relatively simpler and requires only a geometrical adjustment at the coupling interface at a preprocessing stage, so that no extra computations are necessary during the time evolution of the simulation. On the other hand, as an advantage of using curvilinear elements, the geometry of the coupling interface between the two media of interest is faithfully represented up to the order of the scheme used. In other words, higher order schemes are in consonance with higher order approximations of the geometry. Concerning the time discretization, we analyze both explicit and implicit schemes. These schemes are energy conserving and, for the explicit case, the stability is guaranteed by a CFL condition. In order to illustrate the accuracy and convergence of these methods, a set of representative numerical tests are presented.
A comparison of strain calculation using digital image correlation and finite element software
NASA Astrophysics Data System (ADS)
Iadicola, M.; Banerjee, D.
2016-08-01
Digital image correlation (DIC) data are being extensively used for many forming applications and for comparisons with finite element analysis (FEA) simulated results. The most challenging comparisons are often in the area of strain localizations just prior to material failure. While qualitative comparisons can be misleading, quantitative comparisons are difficult because of insufficient information about the type of strain output. In this work, strains computed from DIC displacements from a forming limit test are compared to those from three commercial FEA software. Quantitative differences in calculated strains are assessed to determine if the scale of variations seen between FEA and DIC calculated strains constitute real behavior or just calculation differences.
Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin
2015-04-14
It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.
Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin
2015-08-15
It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.
Gao, Kai; Fu, Shubin; Gibson, Richard L.; ...
2015-04-14
It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less
NASA Astrophysics Data System (ADS)
Contreras, M.; Tassara, A.; Araya, R.; Bataille, K.
2012-04-01
We implemented a two-dimensional finite element model that simulates the accumulation of crustal deformation due to the tectonic loading on a locked subduction fault and applied this model to study the seismic cycle of the Mw8.8 2010 Maule (Central Chile) earthquake. Our goal is to gain insigth into the fundamental factors controling elastic strain build-up and release in subduction zones and to evaluate different approaches proposed for modeling surface deformation as observed by GPS-based crustal velocities. By applying the finite element technique we developed a linear elasticity solver that allows us to assess a realistic plate geometry, rheology and relative velocity of subducting plate in a coupled seismic zone. Constraining parameters such as convergence velocity as well as the geometry of the subduction zone are supported by independent geophysical data so we concentrate on the influence of mechanical slab thickness, variations in the updip and downdip limit, degree of coupling and rheology. We have introduced idealized geometric models, noting that our numerical solution reproduce the analytical solution for an elastic half-space and that the surface displacement field obtained for a curved fault and non-zero slab thickness model mimics the predictions of a simple backslip model when the slab thickness tends to zero. We compared model predictions with GPS observations in a EW profile crossing the Maule earthquake rupture area in an attempt for determining the parameters of the seismogenic zone most suitable for this region. Our preliminary results, that consider a realistic geometry and uniform convergence velocity, suggest little influence of the subducting plate thickness for the same downdip limit and the fit to observations is only locally achieved within the margin of error of GPS speeds. We will show results for the inter- and co-seismic phases of the seismic cycle.
Finite element stress analysis of polymers at high strains
NASA Technical Reports Server (NTRS)
Durand, M.; Jankovich, E.
1973-01-01
A numerical analysis is presented for the problem of a flat rectangular rubber membrane with a circular rigid inclusion undergoing high strains due to the action of an axial load. The neo-hookean constitutive equations are introduced into the general purpose TITUS program by means of equivalent hookean constants and initial strains. The convergence is achieved after a few iterations. The method is not limited to any specific program. The results are in good agreement with those of a company sponsored photoelastic stress analysis. The theoretical and experimental deformed shapes also agree very closely with one another. For high strains it is demonstrated that using the conventional HOOKE law the stress concentration factor obtained is unreliable in the case of rubberlike material.
Giant elastic tunability in strained BiFeO3 near an electrically induced phase transition
Yu, Pu; Vasudevan, Rama K.; Tselev, Alexander; ...
2015-01-01
Elastic anomalies are signatures of phase transitions in condensed matters and have traditionally been studied using various techniques spanning from neutron scattering to static mechanical testing. Here, using band-excitation elastic/piezoresponse spectroscopy, we probed sub-MHz elastic dynamics of a tip bias-induced rhombohedral–tetragonal phase transition of strained (001)-BiFeO3 (rhombohedral) ferroelectric thin films from ~103 nm3 sample volumes. Near this transition, we observed that the Young's modulus intrinsically softens by over 30% coinciding with 2-3 folds enhancement of local piezoresponse. Coupled with phase-field modeling, we also addressed the influence of polarization switching and mesoscopic structural heterogeneities (e.g., domain walls) on the kinetics ofmore » this phase transition, thereby providing fresh insights into the morphotropic phase boundary (MPB) in ferroelectrics. Moreover, the giant electrically tunable elastic stiffness and corresponding electromechanical properties observed here suggest potential applications of BiFeO3 in next-generation frequency-agile electroacoustic devices, based on utilization of the soft modes underlying successive ferroelectric phase transitions.« less
Effect of the elastic modulus of the matrix on magnetostrictive strain in composites
Chen, Y.; Snyder, J.E.; Schwichtenberg, C.R.; Dennis, K.W.; Falzgraf, D.K.; McCallum, R.W.; Jiles, D.C.
1999-02-01
The effect of the matrix material on the magnetostriction of composites containing highly magnetostrictive particles has been studied. Experimental results showed that the elastic modulus of the matrix is an important factor determining the bulk magnetostriction of the composite. For a series of composites with the same volume fraction of magnetostrictive particles but different matrix materials, the bulk magnetostriction was found to increase systematically with decreasing elastic modulus of the matrix. A model theory for the magnetostriction of such composites has been developed, based on two limiting assumptions: uniform strain or uniform stress inside the composite. The theory was then used to predict the magnetostriction of the entire material from the volume fractions of the components, their elastic moduli and magnetostrictions. These predictions were in agreement with the experimental results. It is concluded that to obtain a high magnetostriction and adequate mechanical properties of a composite, the elastic moduli of the magnetostrictive phase and the matrix should be as close as possible in value. {copyright} {ital 1999 American Institute of Physics.}
Giant elastic tunability in strained BiFeO3 near an electrically induced phase transition
Li, Q; Cao, Y.; Yu, P.; Vasudevan, R. K.; Laanait, N.; Tselev, A.; Xue, F.; Chen, L. Q.; Maksymovych, P.; Kalinin, S. V.; Balke, N.
2015-01-01
Elastic anomalies are signatures of phase transitions in condensed matters and have traditionally been studied using various techniques spanning from neutron scattering to static mechanical testing. Here, using band-excitation elastic/piezoresponse spectroscopy, we probed sub-MHz elastic dynamics of a tip bias-induced rhombohedral−tetragonal phase transition of strained (001)-BiFeO3 (rhombohedral) ferroelectric thin films from ∼103 nm3 sample volumes. Near this transition, we observed that the Young's modulus intrinsically softens by over 30% coinciding with two- to three-fold enhancement of local piezoresponse. Coupled with phase-field modelling, we also addressed the influence of polarization switching and mesoscopic structural heterogeneities (for example, domain walls) on the kinetics of this phase transition, thereby providing fresh insights into the morphotropic phase boundary in ferroelectrics. Furthermore, the giant electrically tunable elastic stiffness and corresponding electromechanical properties observed here suggest potential applications of BiFeO3 in next-generation frequency-agile electroacoustic devices, based on the utilization of the soft modes underlying successive ferroelectric phase transitions. PMID:26597483
Frequency, pressure and strain dependence of nonlinear elasticity in Berea Sandstone
Riviere, Jacques; Johnson, Paul Allan; Marone, Chris; ...
2016-04-14
Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi-static ( f → 0) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2–3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1fmore » appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. Furthermore, these findings can be used to improve theories relating the macroscopic elastic response to microstructural features.« less
Wang, Huamiao; Clausen, Bjorn; Capolungo, Laurent; ...
2015-07-16
Continuous mechanical tests with strain holds (stress relaxation) and with stress holds (strain relaxation) are performed simultaneously with in-situ neutron measurements to analyze the mechanisms of stress and strain relaxation in Mg AZ31 rolled plate. A dislocation activity based constitutive model, accounting for internal stress statistical distributions, is proposed and implemented into an elastic viscoplastic self-consistent (EVPSC) framework to simultaneously describe both stress and strain relaxation. The model captures the experimental data in terms of macroscopic stress strain curves, evolution of stress and strain during holding, as well as evolution of the internal elastic strains. Model results indicate that themore » magnitude of the stress relaxed during strain holding is dependent on both, the magnitude of the flow stress and the spread of the resolved shear stress distribution. The magnitude of strain accumulated during stress holding is, on the other hand, dependent on the magnitude of the hardening rate and on the spread of the resolved shear stress distribution. Furthermore, the internal elastic strains are directly correlated with the stress state, and hence the stress relaxation during strain holds has a greater influence on the lattice strains than strain relaxation during stress holds.« less
In vivo bone strain and finite element modeling of the mandible of Alligator mississippiensis
Porro, Laura B; Metzger, Keith A; Iriarte-Diaz, Jose; Ross, Callum F
2013-01-01
Forces experienced during feeding are thought to strongly influence the morphology of the vertebrate mandible; in vivo strain data are the most direct evidence for deformation of the mandible induced by these loading regimes. Although many studies have documented bone strains in the mammalian mandible, no information is available on strain magnitudes, orientations or patterns in the sauropsid lower jaw during feeding. Furthermore, strain gage experiments record the mechanical response of bone at a few locations, not across the entire mandible. In this paper, we present bone strain data recorded at various sites on the lower jaw of Alligator mississippiensis during in vivo feeding experiments. These data are used to understand how changes in loading regime associated with changes in bite location are related to changes in strain regime on the working and balancing sides of the mandible. Our results suggest that the working side mandible is bent dorsoventrally and twisted about its long-axis during biting, and the balancing side experiences primarily dorsoventral bending. Strain orientations are more variable on the working side than on the balancing side with changes in bite point and between experiments; the balancing side exhibits higher strain magnitudes. In the second part of this paper, we use principal strain orientations and magnitudes recorded in vivo to evaluate a finite element model of the alligator mandible. Our comparison demonstrates that strain orientations and mandibular deformation predicted by the model closely match in vivo results; however, absolute strain magnitudes are lower in the finite element model. PMID:23855772
Applications of meshless methods for damage computations with finite strains
NASA Astrophysics Data System (ADS)
Pan, Xiaofei; Yuan, Huang
2009-06-01
Material defects such as cavities have great effects on the damage process in ductile materials. Computations based on finite element methods (FEMs) often suffer from instability due to material failure as well as large distortions. To improve computational efficiency and robustness the element-free Galerkin (EFG) method is applied in the micro-mechanical constitute damage model proposed by Gurson and modified by Tvergaard and Needleman (the GTN damage model). The EFG algorithm is implemented in the general purpose finite element code ABAQUS via the user interface UEL. With the help of the EFG method, damage processes in uniaxial tension specimens and notched specimens are analyzed and verified with experimental data. Computational results reveal that the damage which takes place in the interior of specimens will extend to the exterior and cause fracture of specimens; the damage is a fast procedure relative to the whole tensing process. The EFG method provides more stable and robust numerical solution in comparing with the FEM analysis.
Constructing generalized Cesàro formulas for finite plane strains
NASA Astrophysics Data System (ADS)
Georgievskii, D. V.
2014-05-01
The problem of finding the displacement vector from a system of nonlinear differential equations which includes displacement gradient components is studied. Expressions on the right side of this system for certain parameter values have the kinematic sense of Lagrange and Euler finite strain tensors. The task is to construct generalized Cesàro formulas for finite strains. The construction of the solution consists of two stages (algebraic and differential), and the second is performed for space whose dimension is greater than or equal to two. An algorithm for the inversion of the original system is proposed, and analytical constructions for the case of two-dimensional space are performed. The problem is solved at the first (algebraic) stage, i.e., an exact analytical expression for the displacement vector components is derived through the known finite strain tensor and an unknown scalar function having the kinematic sense of rotation. Necessary conditions for the existence of this relationship are formulated.
NASA Technical Reports Server (NTRS)
Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)
2002-01-01
Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.
(In)stability of quasi-static paths of some finite dimensional smooth or elastic-plastic systems
NASA Astrophysics Data System (ADS)
Martins, J. A. C.; Monteiro Marques, M. D. P.; Petrov, A.; Rebrova, N. V.; Sobolev, V. A.; Coelho, I.
2005-01-01
In this paper we discuss some mathematical issues related to the stability of quasistatic paths of finite dimensional mechanical systems that have a smooth or an elastic-plastic behavior. The concept of stability of quasi-static paths used here is essentially a continuity property relatively to the size of the initial perturbations (as in Lyapunov stability) and to the smallness of the rate of application of the external forces (which here plays the role of the small parameter in singular perturbation problems). A related concept of attractiveness is also proposed. Sufficient conditions for attractiveness or for instability of quasi-static paths of smooth systems are presented. The Ziegler column and other examples illustrate these situations. Mathematical formulations (plus existence and uniqueness results) for dynamic and quasi-static elastic-plastic problems with linear hardening are recalled. A stability result is proved for the quasi-static evolution of these systems.
2013-01-01
Background The resistance of the bone against damage by repairing itself and adapting to environmental conditions is its most important property. These adaptive changes are regulated by physiological process commonly called the bone remodeling. Better understanding this process requires that we apply the theory of elastic-damage under the hypothesis of small displacements to a bone structure and see its mechanical behavior. Results The purpose of the present study is to simulate a two dimensional model of a proximal femur by taking into consideration elastic-damage and mechanical stimulus. Here, we present a mathematical model based on a system of nonlinear ordinary differential equations and we develop the variational formulation for the mechanical problem. Then, we implement our mathematical model into the finite element method algorithm to investigate the effect of the damage. Conclusion The results are consistent with the existing literature which shows that the bone stiffness drops in damaged bone structure under mechanical loading. PMID:23663260
Extremely Elastic Wearable Carbon Nanotube Fiber Strain Sensor for Monitoring of Human Motion.
Ryu, Seongwoo; Lee, Phillip; Chou, Jeffrey B; Xu, Ruize; Zhao, Rong; Hart, Anastasios John; Kim, Sang-Gook
2015-06-23
The increasing demand for wearable electronic devices has made the development of highly elastic strain sensors that can monitor various physical parameters an essential factor for realizing next generation electronics. Here, we report an ultrahigh stretchable and wearable device fabricated from dry-spun carbon nanotube (CNT) fibers. Stretching the highly oriented CNT fibers grown on a flexible substrate (Ecoflex) induces a constant decrease in the conductive pathways and contact areas between nanotubes depending on the stretching distance; this enables CNT fibers to behave as highly sensitive strain sensors. Owing to its unique structure and mechanism, this device can be stretched by over 900% while retaining high sensitivity, responsiveness, and durability. Furthermore, the device with biaxially oriented CNT fiber arrays shows independent cross-sensitivity, which facilitates simultaneous measurement of strains along multiple axes. We demonstrated potential applications of the proposed device, such as strain gauge, single and multiaxial detecting motion sensors. These devices can be incorporated into various motion detecting systems where their applications are limited to their strain.
1992-12-01
1Nb matrix was attained using a bilinear elastic -plastic model with temperature dependent elastic and plastic moduli , yield stress and coefficient of...J., "Investigation of the Thermomechanical Response of a Titanium - Aluminide /Silicon-Carbide Composite using a Unified State Variable Model and the...Analysis of MMC Subjected to Thermomechanical Fatigue", Titanium Aluminide Composites, WL-TR-91- 4020, Wright Laboratory, Wright-Patterson AFB, Ohio
2015-04-01
Arch. Ration. Mech. Anal. 3, 97–119 (1959). [53] M. Lazar, An elastoplastic theory of dislocations as a physical field theory with torsion , J. Phys. A...considered in detail: the screw dislocation, the wedge disclination, and the point defect. New analytical solutions are obtained for elastic fields ...dislocation, the wedge disclination, and the point defect. New analytical solutions are obtained for elastic fields of these defects in isotropic solids of
Looking-Free Mixed hp Finite Element Methods for Linear and Geometrically Nonlinear Elasticity
1997-06-09
element method. Particu- lar areas of interest : hp versions, mixed methods , nearly incompressible materials, curvilinear domains, nonlinear elasticity...1 Introduction 1 2 Preliminaries 10 2.1 The Standard and Mixed Methods for Linear Elasticity .......... 10 2.2 Locking...be used to denote pressure, we use k to denote polynomial degree. 4 Mixed methods have also been used to avoid locking. In these methods, an aux
Gao, Hao; Carrick, David; Berry, Colin; Griffith, Boyce E.; Luo, Xiaoyu
2016-01-01
Detailed models of the biomechanics of the heart are important both for developing improved interventions for patients with heart disease and also for patient risk stratification and treatment planning. For instance, stress distributions in the heart affect cardiac remodelling, but such distributions are not presently accessible in patients. Biomechanical models of the heart offer detailed three-dimensional deformation, stress and strain fields that can supplement conventional clinical data. In this work, we introduce dynamic computational models of the human left ventricle (LV) that are derived from clinical imaging data obtained from a healthy subject and from a patient with a myocardial infarction (MI). Both models incorporate a detailed invariant-based orthotropic description of the passive elasticity of the ventricular myocardium along with a detailed biophysical model of active tension generation in the ventricular muscle. These constitutive models are employed within a dynamic simulation framework that accounts for the inertia of the ventricular muscle and the blood that is based on an immersed boundary (IB) method with a finite element description of the structural mechanics. The geometry of the models is based on data obtained non-invasively by cardiac magnetic resonance (CMR). CMR imaging data are also used to estimate the parameters of the passive and active constitutive models, which are determined so that the simulated end-diastolic and end-systolic volumes agree with the corresponding volumes determined from the CMR imaging studies. Using these models, we simulate LV dynamics from enddiastole to end-systole. The results of our simulations are shown to be in good agreement with subject-specific CMR-derived strain measurements and also with earlier clinical studies on human LV strain distributions. PMID:27041786
Elastic-Plastic Finite Element Analysis of Fatigue Crack Growth in Mode 1 and Mode 2 Conditions
NASA Technical Reports Server (NTRS)
Nakagaki, M.; Atluri, S. N.
1978-01-01
Presented is an alternate cost-efficient and accurate elastic-plastic finite element procedure to analyze fatigue crack closure and its effects under general spectrum loading. Both Modes 1 and 2 type cycling loadings are considered. Also presented are the results of an investigation, using the newly developed procedure, of various factors that cause crack growth acceleration or retardation and delay effects under high-to-low, low-to-high, single overload, and constant amplitude type cyclic loading in a Mode 1 situation. Further, the results of an investigation of a centercracked panel under external pure shear (Mode 2) cyclic loading, of constant amplitude, are reported.
NASA Astrophysics Data System (ADS)
Zingerman, K. M.; Shavyrin, D. A.
2016-06-01
The approximate analytical solution of a quasi-static plane problem of the theory of viscoelasticity is obtained under finite strains. This is the problem of the stress-strain state in an infinite body with circular viscoelastic inclusion. The perturbation technique, Laplace transform, and complex Kolosov-Muskhelishvili's potentials are used for the solution. The numerical results are presented. The nonlinear effects and the effects of viscosity are estimated.
NASA Astrophysics Data System (ADS)
Stebner, Aaron Paul
Empirical investigations and first principles calculations performed in the years since shape memory alloy (SMA) model development efforts began have unveiled contradictions between the microstructural deformation mechanisms at play within these materials and the phenomenological appearance of SMA deformations, which are used to develop constitutive models. Thus, in this work theoretical calculations, numerical modeling, and neutron diffraction experiments were performed to elucidate relationships between phenomenological appearance and mechanistic activity of SMA deformations, in particular Nickel-Titanium. Numerical methods and improvements were derived to allow for robust finite element implementation of a phenomenological SMA constitutive model. New methodologies were also developed to verify and validate mechanistic SMA constitutive model predictions of microstructure evolution for the first time. In depth neutron diffraction empirical studies investigated in situ non-proportional compression as well as large-deformation uniaxial tension and compression of bulk martensitic NiTi. From these studies, insights were gained as to the partitioning of both macroscopic stresses and strains realized of elasticity, recoverable and deformation twinning, and slip within populations of orientation-specific martensite plates. The implications these empirical findings have toward both the models presented in this work as well as future development of SMA constitutive models are documented.
Stability of elastic and viscoelastic plates in a gas flow taking into account shear strains
NASA Astrophysics Data System (ADS)
Potapov, V. D.
2004-09-01
It is well known that the internal friction in a material can have a considerable destabilizing effect on the stability of non-conservative systems. Apart from the Voigt model, the viscoelastic body model is sometimes utilized to describe material damping. This relates the stability problem for non-conservative elastic systems with that for viscoelastic system. The Bubnov-Galerkin method is usually applied for solving the problems. In this case, the displacement functions are represented by series in terms of natural vibration modes ϕ i( x) of the elastic system. To provide a high degree of accuracy for the solution, one should involve a fairly large number of modes. For a viscoelastic plate, the number of terms to be kept in the expansion of the deflection can be substantially more. One should bear in mind, however, that as the number of modes preserved in the expansion increases, the influence of shear strains and rotational inertia on the behavior of the solution becomes more pronounced. In view of this, it is important to study the stability of non-conservative viscoelastic systems with the shear strain and rotational inertia being taken into account. In the present paper this problem is solved for a viscoelastic plate in a supersonic gas flow.
Re-computing palaeopoles for the effects of tectonic finite strain
NASA Astrophysics Data System (ADS)
Borradaile, Graham J.; Hamilton, Thomas D.
2009-03-01
The pre-Messinian limestone cover (˜ 58-8 Ma) to the Troodos ophiolite (˜ 88 Ma) of southern Cyprus is penetratively strained as shown by ubiquitous magnetic fabrics and, in many sites, stylolitic cleavage. These define a gently N-dipping foliation and an N-plunging extension. South-vergent folding and thrusting is well known in very localized whereas the bulk of the strained limestone cover dips gently south, disturbed by faulting. The magnetic fabrics and stylolitic cleavage define the axes of finite strain in all sites studied, and the calcite matrix was suitably ductile to permit the original palaeomagnetic directions to be de-strained assuming continuum behaviour. The optimum de-straining (30-40% shortening in a flattening strain) is compatible with the stylolitic cleavage development, restores bedding to the near-horizontal, and restores the characteristic remanent magnetization vectors (ChRMs) to concentrated, symmetrical Fisherian distributions. The strain-corrected ChRMs yield more reasonable palaeopole locations for the Lefkara and Pakhna Limestone and more uniform micro-plate rotation rates. Corrected palaeopoles reveal a relatively uniform anticlockwise rotation of the Troodos plate since the creation of the late Cretaceous (˜ 88 Ma) ocean lithosphere. It did not accelerate during the deposition of the limestone cover as required by palaeopoles calculated from data not corrected for finite strain but turned at ˜ 1.5° Ma - 1 since ˜ 58 Ma.
Skin-like pressure and strain sensors based on transparent elastic films of carbon nanotubes.
Lipomi, Darren J; Vosgueritchian, Michael; Tee, Benjamin C-K; Hellstrom, Sondra L; Lee, Jennifer A; Fox, Courtney H; Bao, Zhenan
2011-10-23
Transparent, elastic conductors are essential components of electronic and optoelectronic devices that facilitate human interaction and biofeedback, such as interactive electronics, implantable medical devices and robotic systems with human-like sensing capabilities. The availability of conducting thin films with these properties could lead to the development of skin-like sensors that stretch reversibly, sense pressure (not just touch), bend into hairpin turns, integrate with collapsible, stretchable and mechanically robust displays and solar cells, and also wrap around non-planar and biological surfaces such as skin and organs, without wrinkling. We report transparent, conducting spray-deposited films of single-walled carbon nanotubes that can be rendered stretchable by applying strain along each axis, and then releasing this strain. This process produces spring-like structures in the nanotubes that accommodate strains of up to 150% and demonstrate conductivities as high as 2,200 S cm(-1) in the stretched state. We also use the nanotube films as electrodes in arrays of transparent, stretchable capacitors, which behave as pressure and strain sensors.
Skin-like pressure and strain sensors based on transparent elastic films of carbon nanotubes
NASA Astrophysics Data System (ADS)
Lipomi, Darren J.; Vosgueritchian, Michael; Tee, Benjamin C.-K.; Hellstrom, Sondra L.; Lee, Jennifer A.; Fox, Courtney H.; Bao, Zhenan
2011-12-01
Transparent, elastic conductors are essential components of electronic and optoelectronic devices that facilitate human interaction and biofeedback, such as interactive electronics, implantable medical devices and robotic systems with human-like sensing capabilities. The availability of conducting thin films with these properties could lead to the development of skin-like sensors that stretch reversibly, sense pressure (not just touch), bend into hairpin turns, integrate with collapsible, stretchable and mechanically robust displays and solar cells, and also wrap around non-planar and biological surfaces such as skin and organs, without wrinkling. We report transparent, conducting spray-deposited films of single-walled carbon nanotubes that can be rendered stretchable by applying strain along each axis, and then releasing this strain. This process produces spring-like structures in the nanotubes that accommodate strains of up to 150% and demonstrate conductivities as high as 2,200 S cm-1 in the stretched state. We also use the nanotube films as electrodes in arrays of transparent, stretchable capacitors, which behave as pressure and strain sensors.
A variational justification of the assumed natural strain formulation of finite elements
NASA Technical Reports Server (NTRS)
Militello, Carmelo; Felippa, Carlos A.
1991-01-01
The objective is to study the assumed natural strain (ANS) formulation of finite elements from a variational standpoint. The study is based on two hybrid extensions of the Reissner-type functional that uses strains and displacements as independent fields. One of the forms is a genuine variational principle that contains an independent boundary traction field, whereas the other one represents a restricted variational principle. Two procedures for element level elimination of the strain field are discussed, and one of them is shown to be equivalent to the inclusion of incompatible displacement modes. Also, the 4-node C(exp 0) plate bending quadrilateral element is used to illustrate applications of this theory.
NASA Astrophysics Data System (ADS)
De Basabe, Jonás D.; Sen, Mrinal K.
2010-04-01
We investigate the stability of some high-order finite element methods, namely the spectral element method and the interior-penalty discontinuous Galerkin method (IP-DGM), for acoustic or elastic wave propagation that have become increasingly popular in the recent past. We consider the Lax-Wendroff method (LWM) for time stepping and show that it allows for a larger time step than the classical leap-frog finite difference method, with higher-order accuracy. In particular the fourth-order LWM allows for a time step 73 per cent larger than that of the leap-frog method; the computational cost is approximately double per time step, but the larger time step partially compensates for this additional cost. Necessary, but not sufficient, stability conditions are given for the mentioned methods for orders up to 10 in space and time. The stability conditions for IP-DGM are approximately 20 and 60 per cent more restrictive than those for SEM in the acoustic and elastic cases, respectively.
Petersson, N. Anders; Sjogreen, Bjorn
2015-07-20
We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-field technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.
Petersson, N. Anders; Sjogreen, Bjorn
2015-07-20
We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-fieldmore » technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.« less
Weickenmeier, J; Jabareen, M
2014-11-01
The characteristic highly nonlinear, time-dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic-viscoplastic constitutive equations. The specific elastic-viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic-viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative deformation gradient-the deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery.
Dohrmann, C.R.; Heinstein, M.W.; Jung, J.; Key, S.W.
1999-01-01
This report documents a collection of papers on a family of uniform strain tetrahedral finite elements and their connection to different element types. Also included in the report are two papers which address the general problem of connecting dissimilar meshes in two and three dimensions. Much of the work presented here was motivated by the development of the tetrahedral element described in the report "A Suitable Low-Order, Eight-Node Tetrahedral Finite Element For Solids," by S. W. Key {ital et al.}, SAND98-0756, March 1998. Two basic issues addressed by the papers are: (1) the performance of alternative tetrahedral elements with uniform strain and enhanced uniform strain formulations, and (2) the proper connection of tetrahedral and other element types when two meshes are "tied" together to represent a single continuous domain.
Paul, Shirshendu; Katiyar, Amit; Sarkar, Kausik; Chatterjee, Dhiman; Shi, William T.; Forsberg, Flemming
2010-01-01
Two nonlinear interfacial elasticity models—interfacial elasticity decreasing linearly and exponentially with area fraction—are developed for the encapsulation of contrast microbubbles. The strain softening (decreasing elasticity) results from the decreasing association between the constitutive molecules of the encapsulation. The models are used to find the characteristic properties (surface tension, interfacial elasticity, interfacial viscosity and nonlinear elasticity parameters) for a commercial contrast agent. Properties are found using the ultrasound attenuation measured through a suspension of contrast agent. Dynamics of the resulting models are simulated, compared with other existing models and discussed. Imposing non-negativity on the effective surface tension (the encapsulation experiences no net compressive stress) shows “compression-only” behavior. The exponential and the quadratic (linearly varying elasticity) models result in similar behaviors. The validity of the models is investigated by comparing their predictions of the scattered nonlinear response for the contrast agent at higher excitations against experimental measurement. All models predict well the scattered fundamental response. The nonlinear strain softening included in the proposed elastic models of the encapsulation improves their ability to predict subharmonic response. They predict the threshold excitation for the initiation of subharmonic response and its subsequent saturation. PMID:20550283
The stability of elastically strained nanorings and the formation of quantum dot molecules
NASA Astrophysics Data System (ADS)
Gill, Simon P. A.
2015-05-01
Self-assembled nanorings have recently been identified in a number of heteroepitaxially strained material systems. Under some circumstances these rings have been observed to break up into ring-shaped quantum dot molecules. A general non-linear model for the elastic strain energy of non-axisymmetric epitaxially strained nanostructures beyond the small slope assumption is developed. This model is then used to investigate the stability of strained nanorings evolving via surface diffusion subject to perturbations around their circumference. An expression for the fastest growing mode is determined and related to experimental observations. The model predicts a region of stability for rings below a critical radius, and also a region for larger rings which have a proportionally small thickness. The predictions of the model are shown to be consistent with the available results. For the heteroepitaxial InP on In0.5Ga0.5P system investigated by Jevasuwan et al. (2013), the nanorings are found to be stable below a certain critical size. This is in good quantitative agreement with the model predictions. At larger sizes, the rings are unstable. The number of dots in the resulting quantum dot molecule is similar to the mode number for the fastest growing mode. Second order terms show that the number of dots is expected to reduce as the height of the ring increases in proportion to its thickness. The strained In0.4Ga0.6As on GaAs nanorings of Hanke et al. (2007) are always stable and this is in accordance with the findings of the analysis. The Au nanorings of Ruffino et al. (2011) are stable as well, even as they expand during annealing. This observation is also shown to be consistent with the proposed model, which is expected to be useful in the design and tailoring of heteroepitaxial systems for the self-organisation of quantum dot molecules.
On the origins of anomalous elastic moduli and failure strains of GaP nanowires.
Yashinski, M S; Gutiérrez, H R; Muhlstein, C L
2017-02-10
Previous reports suggest that Raman peaks in uniaxially loaded nanowires with diamond cubic and zinc blende crystal structures shift at rates that are significantly different from bulk specimens. We have investigated the first order Raman scattering from individual, free-standing, [111] oriented GaP nanowires ranging from 75 to 180 nm in diameter at uniaxial tensile stresses up to 5 GPa. All of the phonon modes were shifted to frequencies lower than previously reported for bulk GaP, and significant splitting of the degenerate transverse optical mode was observed. A general analysis method using single and double Lorentzian fits of the Raman peaks is presented and used to report more accurate values of the phonon deformation potentials (PDPs) that relate uniaxial strains to Raman peak shifts in GaP. A new set of PDPs determined from the nanowires revealed that the they have elastic moduli and failure strains that are consistent with bulk GaP. The analysis method eliminated the anomalous, inconsistent deformation behavior commonly reported in Raman-based strain measurements of nanowires, and can be extended to other materials systems with degenerate phonons.
On the origins of anomalous elastic moduli and failure strains of GaP nanowires
NASA Astrophysics Data System (ADS)
Yashinski, M. S.; Gutiérrez, H. R.; Muhlstein, C. L.
2017-02-01
Previous reports suggest that Raman peaks in uniaxially loaded nanowires with diamond cubic and zinc blende crystal structures shift at rates that are significantly different from bulk specimens. We have investigated the first order Raman scattering from individual, free-standing, [111] oriented GaP nanowires ranging from 75 to 180 nm in diameter at uniaxial tensile stresses up to 5 GPa. All of the phonon modes were shifted to frequencies lower than previously reported for bulk GaP, and significant splitting of the degenerate transverse optical mode was observed. A general analysis method using single and double Lorentzian fits of the Raman peaks is presented and used to report more accurate values of the phonon deformation potentials (PDPs) that relate uniaxial strains to Raman peak shifts in GaP. A new set of PDPs determined from the nanowires revealed that the they have elastic moduli and failure strains that are consistent with bulk GaP. The analysis method eliminated the anomalous, inconsistent deformation behavior commonly reported in Raman-based strain measurements of nanowires, and can be extended to other materials systems with degenerate phonons.
The Elastic Behaviour of Sintered Metallic Fibre Networks: A Finite Element Study by Beam Theory
Bosbach, Wolfram A.
2015-01-01
Background The finite element method has complimented research in the field of network mechanics in the past years in numerous studies about various materials. Numerical predictions and the planning efficiency of experimental procedures are two of the motivational aspects for these numerical studies. The widespread availability of high performance computing facilities has been the enabler for the simulation of sufficiently large systems. Objectives and Motivation In the present study, finite element models were built for sintered, metallic fibre networks and validated by previously published experimental stiffness measurements. The validated models were the basis for predictions about so far unknown properties. Materials and Methods The finite element models were built by transferring previously published skeletons of fibre networks into finite element models. Beam theory was applied as simplification method. Results and Conclusions The obtained material stiffness isn’t a constant but rather a function of variables such as sample size and boundary conditions. Beam theory offers an efficient finite element method for the simulated fibre networks. The experimental results can be approximated by the simulated systems. Two worthwhile aspects for future work will be the influence of size and shape and the mechanical interaction with matrix materials. PMID:26569603
Benchmark solution of the dynamic response of a spherical shell at finite strain
Versino, Daniele; Brock, Jerry S.
2016-09-28
Our paper describes the development of high fidelity solutions for the study of homogeneous (elastic and inelastic) spherical shells subject to dynamic loading and undergoing finite deformations. The goal of the activity is to provide high accuracy results that can be used as benchmark solutions for the verification of computational physics codes. Furthermore, the equilibrium equations for the geometrically non-linear problem are solved through mode expansion of the displacement field and the boundary conditions are enforced in a strong form. Time integration is performed through high-order implicit Runge–Kutta schemes. Finally, we evaluate accuracy and convergence of the proposed method by means of numerical examples with finite deformations and material non-linearities and inelasticity.
Benchmark solution of the dynamic response of a spherical shell at finite strain
Versino, Daniele; Brock, Jerry S.
2016-09-28
Our paper describes the development of high fidelity solutions for the study of homogeneous (elastic and inelastic) spherical shells subject to dynamic loading and undergoing finite deformations. The goal of the activity is to provide high accuracy results that can be used as benchmark solutions for the verification of computational physics codes. Furthermore, the equilibrium equations for the geometrically non-linear problem are solved through mode expansion of the displacement field and the boundary conditions are enforced in a strong form. Time integration is performed through high-order implicit Runge–Kutta schemes. Finally, we evaluate accuracy and convergence of the proposed method bymore » means of numerical examples with finite deformations and material non-linearities and inelasticity.« less
Xian, Cory J.
2015-01-01
Osteocytes, the major type of bone cells which reside in their lacunar and canalicular system within the bone matrix, function as biomechanosensors and biomechanotransducers of the bone. Although biomechanical behaviour of the osteocyte-lacunar-canalicular system has been investigated in previous studies mostly using computational 2-dimensional (2D) geometric models, only a few studies have used the 3-dimensional (3D) finite element (FE) model. In the current study, a 3D FE model was used to predict the responses of strain distributions of osteocyte-lacunar-canalicular system analyzed under static and cyclic loads. The strain amplification factor was calculated for all simulations. Effects on the strain of the osteocyte system were investigated under 500, 1500, 2000, and 3000 microstrain loading magnitudes and 1, 5, 10, 40, and 100 Hz loading frequencies. The maximum strain was found to change with loading magnitude and frequency. It was observed that maximum strain under 3000-microstrain loading was higher than those under 500, 1500, and 2000 microstrains. When the loading strain reached the maximum magnitude, the strain amplification factor of 100 Hz was higher than those of the other frequencies. Data from this 3D FE model study suggests that the strain amplification factor of the osteocyte-lacunar-canalicular system increases with loading frequency and loading strain increasing. PMID:25664319
Wrinkling of a stiff thin film bonded to a pre-strained, compliant substrate with finite thickness
NASA Astrophysics Data System (ADS)
Ma, Yinji; Xue, Yeguang; Jang, Kyung-In; Feng, Xue; Rogers, John A.; Huang, Yonggang
2016-08-01
A stiff thin film bonded to a pre-strained, compliant substrate wrinkles into a sinusoidal form upon release of the pre-strain. Many analytical models developed for the critical pre-strain for wrinkling assume that the substrate is semi-infinite. This critical pre-strain is actually much smaller than that for a substrate with finite thickness (Ma Y et al. 2016 Adv. Funct. Mater. (doi:10.1002/adfm.201600713)). An analytical solution of the critical pre-strain for a system of a stiff film bonded to a pre-strained, finite-thickness, compliant substrate is obtained, and it agrees well with the finite-element analysis. The finite-thickness effect is significant when the substrate tensile stiffness cannot overwhelm the film tensile stiffness.
Wrinkling of a stiff thin film bonded to a pre-strained, compliant substrate with finite thickness.
Ma, Yinji; Xue, Yeguang; Jang, Kyung-In; Feng, Xue; Rogers, John A; Huang, Yonggang
2016-08-01
A stiff thin film bonded to a pre-strained, compliant substrate wrinkles into a sinusoidal form upon release of the pre-strain. Many analytical models developed for the critical pre-strain for wrinkling assume that the substrate is semi-infinite. This critical pre-strain is actually much smaller than that for a substrate with finite thickness (Ma Y et al. 2016 Adv. Funct. Mater. (doi:10.1002/adfm.201600713)). An analytical solution of the critical pre-strain for a system of a stiff film bonded to a pre-strained, finite-thickness, compliant substrate is obtained, and it agrees well with the finite-element analysis. The finite-thickness effect is significant when the substrate tensile stiffness cannot overwhelm the film tensile stiffness.
Spectral Modeling of Residual Stress and Stored Elastic Strain Energy in Thermal Barrier Coatings
Donegan, Sean; Rolett, Anthony
2013-12-31
Solutions to the thermoelastic problem are important for characterizing the response under temperature change of refractory systems. This work extends a spectral fast Fourier transform (FFT) technique to analyze the thermoelastic behavior of thermal barrier coatings (TBCs), with the intent of probing the local origins of failure in TBCs. The thermoelastic FFT (teFFT) approach allows for the characterization of local thermal residual stress and strain fields, which constitute the origins of failure in TBC systems. A technique based on statistical extreme value theory known as peaks-over-threshold (POT) is developed to quantify the extreme values ("hot spots") of stored elastic strain energy (i.e., elastic energy density, or EED). The resolution dependence of the teFFT method is assessed through a sensitivity study of the extreme values in EED. The sensitivity study is performed both for the local (point-by-point) eld distributions as well as the grain scale eld distributions. A convergence behavior to a particular distribution shape is demonstrated for the local elds. The grain scale fields are shown to exhibit a possible convergence to a maximum level of EED. To apply the teFFT method to TBC systems, 3D synthetic microstructures are created to approximate actual TBC microstructures. The morphology of the grains in each constituent layer as well as the texture is controlled. A variety of TBC materials, including industry standard materials and potential future materials, are analyzed using the teFFT. The resulting hot spots are quantified using the POT approach. A correlation between hot spots in EED and interface rumpling between constituent layers is demonstrated, particularly for the interface between the bond coat (BC) and the thermally grown oxide (TGO) layer.
Nonlinear visco-elastic finite element analysis of different porcelain veneers configuration.
Sorrentino, Roberto; Apicella, Davide; Riccio, Carlo; Gherlone, Enrico; Zarone, Fernando; Aversa, Raffaella; Garcia-Godoy, Franklin; Ferrari, Marco; Apicella, Antonio
2009-11-01
This study is aimed at evaluating the biomechanical behavior of feldspathic versus alumina porcelain veneers. A 3D numerical model of a maxillary central incisor, with the periodontal ligament (PDL) and the alveolar bone was generated. Such model was made up of four main volumes: dentin, enamel, cement layer and veneer. Incisors restored with alumina and feldspathic porcelain veneers were compared with a natural sound tooth (control). Enamel, cementum, cancellous and cortical bone were considered as isotropic elastic materials; on the contrary, the tubular structure of dentin was designed as elastic orthotropic. The nonlinear visco-elatic behavior of the PDL was considered. The veneer volumes were coupled with alumina and feldspathic porcelain mechanical properties. The adhesive layers were modeled in the FE environment using spring elements. A 50N load applied at 60 degrees angle with tooth longitudinal axis was applied and validated. Compressive stresses were concentrated on the external surface of the buccal side of the veneer close to the incisal margin; such phenomenon was more evident in the presence of alumina. Tensile stresses were negligible when compared to compressive ones. Alumina and feldspathic ceramic were characterized by a different biomechanical behavior in terms of elastic deformations and stress distributions. The ultimate strength of both materials was not overcome in the performed analysis.
Mourad, Hashem M; Bronkhorst, Curt A; Addessio, Francis L
2010-12-16
An explicit finite element formulation, used to study the behavior and failure mechanisms of metallic materials under high strain rate loading, is presented. The formulation is based on the assumed-strain approach of Fish and Belytschko [1988], which allows localization bands to be embedded within an element, thereby alleviating mesh sensitivity and reducing the required computational effort. The behavior of the material outside localization bands (and of the virgin material prior to the onset of strain localization) is represented using a Gurson-type coupled plasticity-damage model based on the work of Johnson and Addessio [1988]. Assuming adiabatic conditions, the response of the localization band material is represented by a set of constitutive equations for large elasticviscoplastic deformations in metals at high strain rates and high homologous temperatures (see Brown et al. [1989]). Computational results are compared to experimental data for different metallic alloys to illustrate the advantages of the proposed modeling strategy.
Do reduction spots predate finite strain? A magnetic diagnosis of Cambrian slates in North Wales
NASA Astrophysics Data System (ADS)
Nakamura, Norihiro; Borradaile, Graham
2001-10-01
The purple Cambrian slates of North Wales contain green-colored, irregular patches drawn out along cleavage and the more familiar ellipsoidal reduction spots that are parallel to cleavage. Because parallelism of pre-strain ellipsoids could only be produced by extremely high strain, we reject the hypothesis that these are strain markers. Here, we use magnetic methods to resolve this argument. The magnetic analysis reveals that the magnetic fabric of purple slate differs from the green variety of the slate only in the oxidation state, and indicates that the reduction process postdates cleavage. This suggests that the shape of reduction spots reflects the anisotropy of diffusion during reduction, not finite strain and alignment of an initially ellipsoidal object in the slates.
Wu, Yuan; Stoica, Alexandru Dan; Ren, Yang; ...
2015-09-03
In situ high-energy synchrotron X-ray diffraction was conducted on elastically and plastically bent bulk metallic glass (BMG) thin plates, from which distinct local elastic strain fields were mapped spatially. These directly measured residual strain fields can be nicely interpreted by our stress analysis, and also validate a previously proposed indirect residual-stress-measurement method by relating nanoindentation hardness to residual stresses. Local shear strain variations on the cross sections of these thin plates were found in the plastically bent BMG, which however cannot be determined from the indirect indentation method. As a result, this study has important implications in designing and manipulatingmore » internal strain fields in BMGs for the purpose of ductility enhancement.« less
Wu, Yuan; Stoica, Alexandru Dan; Ren, Yang; Ma, Dong; Gao, Yanfei F.; Bei, Hongbin
2015-09-03
In situ high-energy synchrotron X-ray diffraction was conducted on elastically and plastically bent bulk metallic glass (BMG) thin plates, from which distinct local elastic strain fields were mapped spatially. These directly measured residual strain fields can be nicely interpreted by our stress analysis, and also validate a previously proposed indirect residual-stress-measurement method by relating nanoindentation hardness to residual stresses. Local shear strain variations on the cross sections of these thin plates were found in the plastically bent BMG, which however cannot be determined from the indirect indentation method. As a result, this study has important implications in designing and manipulating internal strain fields in BMGs for the purpose of ductility enhancement.
NASA Astrophysics Data System (ADS)
Zhang, Fan; Wang, Jianchuan; Liu, Shuhong; Du, Yong
2016-10-01
Sn and Sn-based compounds have been attracting a great interest as promising alternative materials for commercial anodes in lithium ion batteries. In this study, the phase evolution of the Li-Sn system during the lithiated processes and the effect of the elastic-strain energies caused by volume change on the phase transition are investigated by means of first-principles calculations. Our calculated results demonstrate that the distorted Li7Sn3 crystal tends to be formed in order to decrease the elastic-strain energy. In addition, our work indicates that the whole lithiated processes under the elastically constrained condition could be classified into two steps. The first step is the two-phase equilibrium process, in which the thermodynamic driving force is large enough to facilitate the phase transition and the plateau voltage could be established. The second step is considered to be the selective equilibrium, in which the thermodynamic driving force is not enough to facilitate the nucleation of the new equilibrium phase due to the elastically constrained conditions and the plateau voltage unformed. Besides, we find that in the Li0.4Sn matrix the nucleation of the αSn is more preferential than the βSn due to the effects of the elastic-strain energies.
NASA Technical Reports Server (NTRS)
Vazquez, Sixto L.; Tessler, Alexander; Quach, Cuong C.; Cooper, Eric G.; Parks, Jeffrey; Spangler, Jan L.
2005-01-01
In an effort to mitigate accidents due to system and component failure, NASA s Aviation Safety has partnered with industry, academia, and other governmental organizations to develop real-time, on-board monitoring capabilities and system performance models for early detection of airframe structure degradation. NASA Langley is investigating a structural health monitoring capability that uses a distributed fiber optic strain system and an inverse finite element method for measuring and modeling structural deformations. This report describes the constituent systems that enable this structural monitoring function and discusses results from laboratory tests using the fiber strain sensor system and the inverse finite element method to demonstrate structural deformation estimation on an instrumented test article
Karmakar, Smarajit; Lerner, Edan; Procaccia, Itamar; Zylberg, Jacques
2010-09-01
The effect of finite temperature T and finite strain rate γ on the statistical physics of plastic deformations in amorphous solids made of N particles is investigated. We recognize three regimes of temperature where the statistics are qualitatively different. In the first regime the temperature is very low, T
X-ray microbeam probing of elastic strains in patterned He+ implanted single-crystal LiNbO3
NASA Astrophysics Data System (ADS)
Djukic, Djordje; Roth, Ryan M.; Osgood, R. M.; Evans-Lutterodt, Kenneth; Bakhru, Hassaram; Bakhru, Sasha; Welch, David
2007-09-01
X-ray microprobing is used to investigate buried elastic strain resulting from deep He+ implantantion in LiNbO3. The implantation regions are defined lithographically and strain fields mapped with spatial- and energy-resolved x-ray microdiffraction to characterize the resulting structures. The structurally modified regions are found to retain their lateral lithographic definition, with the buried implantation being in strong compression.
NASA Astrophysics Data System (ADS)
Jayasekara, Vishara; Min, Kyung Ho; Noh, Jeong Hoon; Kim, Min Tae; Seo, Jeong Min; Lee, Ho Yong; Hwang, Beong Bok
2010-04-01
This article describes the joining of thin metal sheets by a single stroke clinching process. Elastic-plastic and rigid-plastic finite element analysis were applied by employing Coulomb friction and constant shear friction in order to investigate the behavior of the clinch joint formation process. Four process variables, such as die diameter, die depth, groove width, and groove corner radius were selected to investigate the parametric effect on the clinch joint. The strength of clinch joints were evaluated by examining the separation strengths, such as peel strength and tensile shear strength, respectively. A failure diagram was constructed that summarizes the analysis results. The simulation results showed that die diameter and depth were the most decisive parameters for controlling the quality of the clinch joint, while the bottom's thickness was the most important evaluation parameter to determine the separation strengths.
Application of Finite Element to Evaluate Material with Small Modulus of Elasticity
2013-03-01
14 Figure 8: Cross-sectional diagram of thorax highlighting the various muscle groups in the Hawkmoth and the interaction with Exoskeleton ...44 Figure 26: Partially Dissected Moth highlighting the point of incision of the exoskeleton (wings are removed...applications to the exoskeleton of the hawkmoth are examined. The formulation of these equations is discussed in Chapter 2 and the finite element model is
Finite Element Modeling of Plane Strain Toughness for 7085 Aluminum Alloy
NASA Astrophysics Data System (ADS)
Karabin, M. E.; Barlat, F.; Shuey, R. T.
2009-02-01
In this work, the constitutive model for 7085-T7X (overaged) aluminum alloy plate samples with controlled microstructures was developed. Different lengths of 2nd step aging times produced samples with similar microstructure but different stress-strain curves ( i.e., different nanostructure). A conventional phenomenological strain-hardening law with no strain gradient effects was proposed to capture the peculiar hardening behavior of the material samples investigated in this work. The classical Gurson-Tvergaard potential, which includes the influence of void volume fraction (VVF) on the plastic flow behavior, as well as an extension proposed by Leblond et al.,[3] were considered. Unlike the former, the latter is able to account for the influence of strain hardening on the VVF growth. All the constitutive coefficients used in this work were based on experimental stress-strain curves obtained in uniaxial tension and on micromechanical modeling results of a void embedded in a matrix. These material models were used in finite element (FE) simulations of a compact tension (CT) specimen. An engineering criterion based on the instability of plastic flow at a crack tip was used for the determination of plane strain toughness K Ic . The influence of the microstructure was lumped into a single state variable, the initial void volume fraction. The simulation results showed that the strain-hardening behavior has a significant influence on K Ic .
The effect of strain rate on fracture toughness of human cortical bone: a finite element study.
Ural, Ani; Zioupos, Peter; Buchanan, Drew; Vashishth, Deepak
2011-10-01
Evaluating the mechanical response of bone under high loading rates is crucial to understanding fractures in traumatic accidents or falls. In the current study, a computational approach based on cohesive finite element modeling was employed to evaluate the effect of strain rate on fracture toughness of human cortical bone. Two-dimensional compact tension specimen models were simulated to evaluate the change in initiation and propagation fracture toughness with increasing strain rate (range: 0.08-18 s(-1)). In addition, the effect of porosity in combination with strain rate was assessed using three-dimensional models of micro-computed tomography-based compact tension specimens. The simulation results showed that bone's resistance against the propagation of a crack decreased sharply with increase in strain rates up to 1 s(-1) and attained an almost constant value for strain rates larger than 1 s(-1). On the other hand, initiation fracture toughness exhibited a more gradual decrease throughout the strain rates. There was a significant positive correlation between the experimentally measured number of microcracks and the fracture toughness found in the simulations. Furthermore, the simulation results showed that the amount of porosity did not affect the way initiation fracture toughness decreased with increasing strain rates, whereas it exacerbated the same strain rate effect when propagation fracture toughness was considered. These results suggest that strain rates associated with falls lead to a dramatic reduction in bone's resistance against crack propagation. The compromised fracture resistance of bone at loads exceeding normal activities indicates a sharp reduction and/or absence of toughening mechanisms in bone during high strain conditions associated with traumatic fracture.
THE EFFECT OF STRAIN RATE ON FRACTURE TOUGHNESS OF HUMAN CORTICAL BONE: A FINITE ELEMENT STUDY
Ural, Ani; Zioupos, Peter; Buchanan, Drew; Vashishth, Deepak
2011-01-01
Evaluating the mechanical response of bone under high loading rates is crucial to understanding fractures in traumatic accidents or falls. In the current study, a computational approach based on cohesive finite element modeling was employed to evaluate the effect of strain rate on fracture toughness of human cortical bone. Two-dimensional compact tension specimen models were simulated to evaluate the change in initiation and propagation fracture toughness with increasing strain rate (range: 0.08 to 18 s−1). In addition, the effect of porosity in combination with strain rate was assessed using three-dimensional models of microcomputed tomography-based compact tension specimens. The simulation results showed that bone’s resistance against the propagation of fracture decreased sharply with increase in strain rates up to 1 s−1 and attained an almost constant value for strain rates larger than 1 s−1. On the other hand, initiation fracture toughness exhibited a more gradual decrease throughout the strain rates. There was a significant positive correlation between the experimentally measured number of microcracks and the fracture toughness found in the simulations. Furthermore, the simulation results showed that the amount of porosity did not affect the way initiation fracture toughness decreased with increasing strain rates, whereas it exacerbated the same strain rate effect when propagation fracture toughness was considered. These results suggest that strain rates associated with falls lead to a dramatic reduction in bone’s resistance against crack propagation. The compromised fracture resistance of bone at loads exceeding normal activities indicates a sharp reduction and/or absence of toughening mechanisms in bone during high strain conditions associated with traumatic fracture. PMID:21783112
Viscoplastic and Creep Crack Growth Analysis by the Finite Element Method.
1980-06-01
and Yoshimura, N. and Sakurai, T., "Plastic Stress-Strain Matrix and Its Application For The Solution of Elastic- Plastic Problems by the Finite...required to obtain displacements for the elastic structure. However, for elastic- plastic problems the coefficients in the stiffness matrix vary as a...solve small displacement elastic- plastic problems incrementally within a finite element computer program, may be divideu into two categories. In one
HEMP 3D -- a finite difference program for calculating elastic-plastic flow
Wilkins, M.L.
1993-05-26
The HEMP 3D program can be used to solve problems in solid mechanics involving dynamic plasticity and time dependent material behavior and problems in gas dynamics. The equations of motion, the conservation equations, and the constitutive relations are solved by finite difference methods following the format of the HEMP computer simulation program formulated in two space dimensions and time. Presented here is an update of the 1975 report on the HEMP 3D numerical technique. The present report includes the sliding surface routines programmed by Robert Gulliford.
Transitions in a compressible finite elastic sheet on a fluid substrate
NASA Astrophysics Data System (ADS)
Oshri, Oz; Diamant, Haim
2014-03-01
A thin elastic sheet, supported on a fluid substrate and uniaxially compressed, exhibits two critical transitions: From a flat state to sinusoidal wrinkles and from wrinkles to a localized fold. Previous theoretical studies treated the system in the limits of incompressible and infinite sheets. Both assumptions are relaxed in the current work to obtain details of the transitions and the phase diagram. Deriving an amplitude equation and using a variational approach, we show that the flat-to-wrinkle transition is second-order, whereas the wrinkle-to-fold one is first-order. The pressure-displacement relation is linear above the first transition and becomes parabolic after the second one, in agreement with numerical results. Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel.
NASA Technical Reports Server (NTRS)
Buczek, M. B.; Gregory, M. A.; Herakovich, C. T.
1983-01-01
CLFE2D is a two dimensional generalized plane strain finite element code, using a linear, four node, general quadrilateral, isoparametric element. The program is developed to calculate the displacements, strains, stresses, and strain energy densities in a finite width composite laminate. CLFE2D offers any combination of the following load types: nodal displacements, nodal forces, uniform normal strain, or hygrothermal. The program allows the user to input one set of three dimensional orthotropic material properties. The user can then specify the angle of material principal orientation for each element in the mesh. Output includes displacements, stresses, strains and strain densities at points selected by the user. An option is also available to plot the underformed and deformed finite element meshes.
Barabash, R. I.; Agarwal, V.; Koric, S.; Jasiuk, I.; Tischler, J. Z.
2016-01-01
The depth-dependent strain partitioning across the interfaces in the growth direction of the NiAl/Cr(Mo) nanocomposite between the Cr and NiAl lamellae was directly measured experimentally and simulated using a finite element method (FEM). Depth-resolved X-ray microdiffraction demonstrated that in the as-grown state both Cr and NiAl lamellae grow along the$>"\; separators="|">111$direction with the formation of as-grown distinct residual ~0.16% compressive strains for Cr lamellae and ~0.05% tensile strains for NiAl lamellae. Three-dimensional simulations were carried out using an implicit FEM. First simulation was designed to study residual strains in the composite due to cooling resulting in formation of crystals. Strains in the growth direction were computed and compared to those obtained from the microdiffraction experiments. Second simulation was conducted to understand the combined strains resulting from cooling and mechanical indentation of the composite. Numerical results in the growth direction of crystal were compared to experimental results confirming the experimentally observed trends.
Fu, Y B; Chui, C K; Teo, C L
2013-04-01
Biological soft tissue is highly inhomogeneous with scattered stress-strain curves. Assuming that the instantaneous strain at a specific stress varies according to a normal distribution, a nondeterministic approach is proposed to model the scattered stress-strain relationship of the tissue samples under compression. Material parameters of the liver tissue modeled using Mooney-Rivlin hyperelastic constitutive equation were represented by a statistical function with normal distribution. Mean and standard deviation of the material parameters were determined using inverse finite element method and inverse mean-value first-order second-moment (IMVFOSM) method respectively. This method was verified using computer simulation based on direct Monte-Carlo (MC) method. The simulated cumulative distribution function (CDF) corresponded well with that of the experimental stress-strain data. The resultant nondeterministic material parameters were able to model the stress-strain curves from other separately conducted liver tissue compression tests. Stress-strain data from these new tests could be predicted using the nondeterministic material parameters.
Barabash, R. I.; Agarwal, V.; Koric, S.; ...
2016-01-01
Tmore » he depth-dependent strain partitioning across the interfaces in the growth direction of the NiAl/Cr(Mo) nanocomposite between the Cr and NiAl lamellae was directly measured experimentally and simulated using a finite element method (FEM). Depth-resolved X-ray microdiffraction demonstrated that in the as-grown state both Cr and NiAl lamellae grow along the 111 direction with the formation of as-grown distinct residual ~0.16% compressive strains for Cr lamellae and ~0.05% tensile strains for NiAl lamellae.hree-dimensional simulations were carried out using an implicit FEM. First simulation was designed to study residual strains in the composite due to cooling resulting in formation of crystals. Strains in the growth direction were computed and compared to those obtained from the microdiffraction experiments. Second simulation was conducted to understand the combined strains resulting from cooling and mechanical indentation of the composite. Numerical results in the growth direction of crystal were compared to experimental results confirming the experimentally observed trends.« less
Key, S.W.; Krieg, R.D.
1980-01-01
A number of complex issues are addressed which will allow the incorporation of finite strain, inelastic material behavior into the piecewise numerical construction of solutions in solid mechanics. Without recourse to extensive continuum mechanics preliminaries, an elementary time independent plasticity model, an elementary time dependent creep model, and a viscoelastic model are introduced as examples of constitutive equations which are routinely used in engineering calculations. The constitutive equations are all suitable for problems involving large deformations and finite strains. The plasticity and creep models are in rate form and use the symmetric part of the velocity gradient or the stretching to compute the co-rotational time derivative of the Cauchy stress. The viscoelastic model computes the current value of the Cauchy stress from a hereditary integral of a materially invariant form of the stretching history. The current configuration is selected for evaluation of equilibrium as opposed to either the reference configuration or the last established equilibrium configuration. The process of strain incrementation is examined in some depth and the stretching evaluated at the midinterval multiplied by the time step is identified as the appropriate finite strain increment to use with the selected form of the constitutive equations. Discussed is the conversion of rotation rates based on the spin into incremental orthogonal rotations which are then used to update stresses and state variables due to rigid body rotation during the load increment. Comments and references to the literature are directed at numerical integration of the constitutive equations with an emphasis on doing this accurately, if not exactly, for any time step and stretching. This material taken collectively provides an approach to numerical implementation which is marked by its simplicity.
Latorre, Marcos; Peña, Estefanía; Montáns, Francisco J
2017-03-01
What-You-Prescribe-Is-What-You-Get (WYPIWYG) procedures are a novel and general phenomenological approach to modelling the behavior of soft materials, applicable to biological tissues in particular. For the hyperelastic case, these procedures solve numerically the nonlinear elastic material determination problem. In this paper we show that they can be applied to determine the stored energy density of superficial fascia. In contrast to the usual approach, in such determination no user-prescribed material parameters and no optimization algorithms are employed. The strain energy densities are computed solving the equilibrium equations of the set of experiments. For the case of superficial fascia it is shown that the mechanical behavior derived from such strain energies is capable of reproducing simultaneously the measured load-displacement curves of three experiments to a high accuracy.
McCarty, K.F. )
1999-09-01
We address whether the elastic strain-energy theory (minimizing the Gibbs energy of a stressed crystal) of McKenzie and co-workers [D. R. McKenzie and M. M. M. Bilek, J. Vac. Sci. Technol. A [bold 16], 2733 (1998)] adequately explains the preferred orientation observed in carbon and BN films. In the formalism, the Gibbs energy of the cubic materials diamond and cubic boron includes the strain that occurs when the phases form, through specific structural transformations, from graphitic precursors. This treatment violates the requirement of thermodynamics that the Gibbs energy be a path-independent, state function. If the cubic phases are treated using the same (path-independent) formalism applied to the graphitic materials, the crystallographic orientation of lowest Gibbs energy is not that observed experimentally. For graphitic (hexagonal) carbon and BN, an elastic strain approach seems inappropriate because the compressive stresses in energetically deposited films are orders of magnitude higher than the elastic limit of the materials. Furthermore, using the known elastic constants of either ordered or disordered graphitic materials, the theory does not predict the orientation observed by experiment. [copyright] [ital 1999 American Vacuum Society.
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
2005-01-01
A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.
Analysis of shear strain imaging for classifying breast masses: Finite element and phantom results
Xu, Haiyan; Varghese, Tomy; Madsen, Ernest L.
2011-01-01
Purpose: Features extracted from axial-shear strain images of breast masses have been previously utilized to differentiate and classify benign from malignant breast masses. In this paper, we compare shear strain patterns exhibited by both the full-shear (axial and lateral component) versus only the axial-shear strain component for differentiating between bound masses (malignant) when compared to unbound masses (benign). Methods: We examine different breast mass characteristics such as mass shape, asymmetric location of masses, stiffness variations, and mass bonding characteristics to background tissue to assess their impact on shear strain patterns generated due to a uniaxial applied deformation. Two-dimensional finite element simulations of both circular and elliptical inclusions embedded within a uniform background were utilized. Different degrees of bonding were characterized using friction coefficient values ranging from 0.01 to 100 denoting loosely bound to firmly bound masses. Single-inclusion tissue-mimicking phantoms mimicking firmly bound and loosely bound ellipsoidal masses oriented at four different angles to the applied deformation were studied to corroborate the mass differentiation performance. Results: Our results indicate that the normalized axial-shear strain and full-shear strain area features are larger for bound when compared to unbound masses. A higher stiffness ratio or contrast between the inclusion and background also improves differentiation. Larger applied deformations reduce the discrimination performance for masses with friction coefficients lower than 0.4, due to increased mass slippage with applied deformations. Potential errors with the use of these features would occur for unbound inclusions at larger applied deformations and for asymmetric mass positions within the background normal tissue. Conclusions: Finite element and tissue-mimicking phantom results demonstrate the feasibility of utilizing both the normalized axial-shear and
NASA Astrophysics Data System (ADS)
Ebrahimi, Farzad; Dabbagh, Ali
2017-02-01
Main object of the present research is an exact investigation of wave propagation responses of smart rotating magneto-electro-elastic (MEE) graded nanoscale plates. In addition, effective material properties of functionally graded (FG) nanoplate are presumed to be calculated using the power-law formulations. Also, it has been tried to cover both softening and stiffness-hardening behaviors of nanostructures by the means of employing nonlocal strain gradient theory (NSGT). Due to increasing the accuracy of the presented model in predicting shear deformation effects, a refined higher-order plate theory is introduced. In order to cover the most enormous circumstances, maximum amount of load generated by plate’s rotation is considered. Furthermore, utilizing a developed form of Hamilton’s principle, containing magneto-electric effects, the nonlocal governing equations of MEE-FG rotating nanoplates are derived. An analytical solution is obtained to solve the governing equations and validity of the solution method is proven by comparing results from present method with those of former attempts. At last, outcomes are plotted in the framework of some figures to show the influences of various parameters such as wave number, nonlocality, length scale parameter, magnetic potential, electric voltage, gradient index and angular velocity on wave frequency, phase velocity and escape frequency of the examined nanoplate.
NASA Astrophysics Data System (ADS)
Weil, K. S.; Koeppel, B. J.
One of the critical issues in designing and fabricating a high performance planar solid oxide fuel cell (pSOFC) stack is the development of the appropriate materials and techniques for hermetically sealing the metal and ceramic components. A second critical issue is ensuring that the brittle ceramic cell constituents, i.e. the electrodes and electrolyte, exhibit high mechanical reliability by mitigating potential sources of thermal-mechanically induced stresses that can lead to fracture during operation and/or shutdown. A foil-based sealing approach is currently being developed that appears to offer good hermeticity and mechanical integrity, while minimizing the generation of high stresses in either of the joint's substrate materials. Based on the concept's viability, demonstrated in prior experimental work, numerical analyses were conducted to evaluate the behavior and benefits of the seal in a configuration prototypic of current pSOFC stack designs. This paper presents recent results from finite element (FE) simulations of a planar cell using the foil-based seal, along with companion analyses of the more conventionally employed glass-ceramic and brazed joints. The stresses and deformations of the components were evaluated at isothermal operating and shutdown temperatures. The results indicate that the foil seal is able to accommodate a significant degree of thermal mismatch strain between the metallic support structure and the ceramic cell via elastic deformations of the foil and plasticity in the foil-to-cell braze layer. Consequently the cell stresses in this type of seal are predicted to be much lower than those in the glass-ceramic and brazed designs, which is expected to lead to improved stack reliability. This ability to accommodate large thermal strain mismatches allows the design requirement of thermal expansion matching between ceramic and metal stack components to be relaxed and expands the list of candidate materials that can be considered for the
NASA Astrophysics Data System (ADS)
Minakuchi, Shu; Sanada, Teruhisa; Takeda, Nobuo; Mitani, Shinji; Mizutani, Tadahito; Sasaki, Yoshinobu; Shinozaki, Keisuke
2014-05-01
Thermal strain significantly affects stability of fiber optic gyroscope (FOG) performance. This study investigates thermal strain development in a lightweight carbon fiber reinforced plastic (CFRP) FOG under thermal vacuum condition simulating space environment. First, we measure thermal strain distribution along an optical fiber in a CFRP FOG using a Brillouin-based high-spatial resolution system. The key strain profile is clarified and the strain development is simulated using finite element analysis. Finally, several constituent materials for FOG are quantitatively compared from the aspect of the maximum thermal strain and the density, confirming the clear advantage of CFRP.
Parallel computation in a three-dimensional elastic-plastic finite-element analysis
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Bigelow, C. A.; Newman, J. C., Jr.
1992-01-01
A CRAY parallel processing technique called autotasking was implemented in a three-dimensional elasto-plastic finite-element code. The technique was evaluated on two CRAY supercomputers, a CRAY 2 and a CRAY Y-MP. Autotasking was implemented in all major portions of the code, except the matrix equations solver. Compiler directives alone were not able to properly multitask the code; user-inserted directives were required to achieve better performance. It was noted that the connect time, rather than wall-clock time, was more appropriate to determine speedup in multiuser environments. For a typical example problem, a speedup of 2.1 (1.8 when the solution time was included) was achieved in a dedicated environment and 1.7 (1.6 with solution time) in a multiuser environment on a four-processor CRAY 2 supercomputer. The speedup on a three-processor CRAY Y-MP was about 2.4 (2.0 with solution time) in a multiuser environment.
NASA Astrophysics Data System (ADS)
Le Page, Yvon; Saxe, Paul
2002-03-01
A symmetry-general approach for the least-squares, therefore precise, extraction of elastic coefficients for strained materials is reported. It analyzes stresses calculated ab initio for properly selected strains. The problem, its implementation, and its solution strategy all differ radically from a previous energy-strain approach that we published last year, but the normal equations turn out to be amenable to the same constrainment scheme that makes both approaches symmetry general. The symmetry considerations governing the automated selection of appropriately strained models and their Cartesian systems are detailed. The extension to materials under general stress is discussed and implemented. VASP was used for ab initio calculation of stresses. A comprehensive range of examples includes a triclinic material (kyanite) and simple materials with a range of symmetries at zero pressure, MgO under hydrostatic pressure, Ti4As3 under [001] uniaxial strain, and Si under [001] uniaxial stress. The MgO case agrees with recent experimental work including elastic coefficients as well as their first and second derivatives. The curves of elastic coefficients for Si show a gradual increase in the 33 compliance coefficient, leading to a collapse of the material at -11.7 GPa, compared with -12.0 GPa experimentally. Interpretation of results for Be using two approximations [local density (LDA), generalized gradient (GGA)], two approaches (stress strain and energy strain), two potential types (projector augmented wave and ultrasoft), and two quantum engines (VASP and ORESTES) expose the utmost importance of the cell data used for the elastic calculations and the lesser importance of the other factors. For stiffness at relaxed cell data, differences are shown to originate mostly in the considerable overestimation of the residual compressive stresses at x-ray cell data by LDA, resulting in a smaller relaxed cell, thus larger values for diagonal stiffness coefficients. The symmetry
NASA Technical Reports Server (NTRS)
Chulya, Abhisak; Mullen, Robert L.
1989-01-01
A linear finite strip plate element based on Mindlin-Reissner plate theory is developed. The analysis is suitable for both thin and thick plates. In the formulation, new transverse shear strains are introduced and assumed constant in each two-node linear strip. The element stiffness matrix is explicitly formulated for efficient computation and computer implementation. Numerical results showing the efficiency and predictive capability of the element for the analysis of plates are presented for different support and loading conditions and a wide range of thicknesses. No sign of shear locking is observed with the newly developed element.
Nguyen, Ba Nghiep; Bapanapalli, Satish K.; Kunc, Vlastimil; Phelps, Jay; Tucker III, Charles L.
2009-01-26
This paper proposes a model to predict the elastic-plastic response of injection-molded long-fiber thermoplastics (LFTs). The model accounts for elastic fibers embedded in a thermoplastic resin that exhibits the elastic-plastic behavior obeying the Ramberg-Osgood relation and J-2 deformation theory of plasticity. It also accounts for fiber length and orientation distributions in the composite formed by the injection-molding process. Fiber orientation was predicted using the anisotropic rotary diffusion model recently developed by Phelps and Tucker for LFTs. An incremental procedure using the Eshelby’s equivalent inclusion method and the Mori-Tanaka model is proposed to compute the overall stress increment resulting from an overall strain increment for an aligned fiber composite that contains the same fiber volume fraction and length distribution as the actual composite. The incremental response of the later is then obtained from the solution for the aligned fiber composite that is averaged over all possible fiber orientations using the orientation averaging method. Failure during incremental loading is predicted using the Van Hattum-Bernado model. The elastic-plastic and strength prediction model for LFTs was validated against the experimental stress-strain results obtained for long glass fiber/polypropylene specimens.
Viscoplastic and Creep Crack Growth Analysis by the Finite Element Method.
1981-07-01
Strain Matrix and Its Application for the Solution of Elastic- Plastic Problems by the Finite Element Method," Int’l Journ. of Mechani- cal Sciences, Vol...constant. Therefore only one solution is required to obtain displacements for the elastic structure. However, for elastic- plastic problems the...form as dP= ;I.3 deP~i dEYi.. (A-28) 4. ELASTIC-PLASTIC SOLUTION TECHNIQUES The procedures used to solve small displacement elastic- plastic problems incrementally
NASA Astrophysics Data System (ADS)
Lafontaine, N. M.; Rossi, R.; Cervera, M.; Chiumenti, M.
2015-03-01
Low-order finite elements face inherent limitations related to their poor convergence properties. Such difficulties typically manifest as mesh-dependent or excessively stiff behaviour when dealing with complex problems. A recent proposal to address such limitations is the adoption of mixed displacement-strain technologies which were shown to satisfactorily address both problems. Unfortunately, although appealing, the use of such element technology puts a large burden on the linear algebra, as the solution of larger linear systems is needed. In this paper, the use of an explicit time integration scheme for the solution of the mixed strain-displacement problem is explored as an alternative. An algorithm is devised to allow the effective time integration of the mixed problem. The developed method retains second order accuracy in time and is competitive in terms of computational cost with the standard irreducible formulation.
Strain-Based Damage Determination Using Finite Element Analysis for Structural Health Management
NASA Technical Reports Server (NTRS)
Hochhalter, Jacob D.; Krishnamurthy, Thiagaraja; Aguilo, Miguel A.
2016-01-01
A damage determination method is presented that relies on in-service strain sensor measurements. The method employs a gradient-based optimization procedure combined with the finite element method for solution to the forward problem. It is demonstrated that strains, measured at a limited number of sensors, can be used to accurately determine the location, size, and orientation of damage. Numerical examples are presented to demonstrate the general procedure. This work is motivated by the need to provide structural health management systems with a real-time damage characterization. The damage cases investigated herein are characteristic of point-source damage, which can attain critical size during flight. The procedure described can be used to provide prognosis tools with the current damage configuration.
Levine, Lyle E.; Okoro, Chukwudi A.; Xu, Ruqing
2015-09-30
We report non-destructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 mm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positionsmore » were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components.« less
Levine, Lyle E.; Okoro, Chukwudi A.; Xu, Ruqing
2015-09-30
We report non-destructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 mm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components.
Levine, Lyle E.; Okoro, Chukwudi; Xu, Ruqing
2015-01-01
Nondestructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 µm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components. PMID:26594371
Levine, Lyle E; Okoro, Chukwudi; Xu, Ruqing
2015-11-01
Nondestructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 µm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components.
NASA Astrophysics Data System (ADS)
Wilkinson, Angus J.; Randman, David
2010-03-01
The deformation around a 500-nm deep Berkovich indent in a large grained Fe sample has been studied using high resolution electron back scatter diffraction (EBSD). EBSD patterns were obtained in a two-dimensional map around the indent on the free surface. A cross-correlation-based analysis of small shifts in many sub-regions of the EBSD patterns was used to determine the variation of elastic strain and lattice rotations across the map at a sensitivity of ∼±10-4. Elastic strains were smaller than lattice rotations, with radial strains found to be compressive and hoop strains tensile as expected. Several analyses based on Nye's dislocation tensor were used to estimate the distribution of geometrically necessary dislocations (GNDs) around the indent. The results obtained using different assumed dislocation geometries, optimisation routines and different contributions from the measured lattice rotation and strain fields are compared. Our favoured approach is to seek a combination of GND types which support the six measurable (of a possible nine) gradients of the lattice rotations after correction for the 10 measurable elastic strain gradients, and minimise the total GND line energy using an L1 optimisation method. A lower bound estimate for the noise on the GND density determination is ∼±1012 m-2 for a 200-nm step size, and near the indent densities as high as 1015 m-2 were measured. For comparison, a Hough-based analysis of the EBSD patterns has a much higher noise level of ∼±1014m-2 for the GND density.
Pavlov, D. A.; Bidus, N. V.; Bobrov, A. I.; Vikhrova, O. V.; Volkova, E. I.; Zvonkov, B. N.; Malekhonova, N. V.; Sorokin, D. S.
2015-01-15
The distribution of elastic strains in a system consisting of a quantum-dot layer and a buried GaAs{sub x}P{sub 1−x} layer is studied using geometric phase analysis. A hypothesis is offered concerning the possibility of controlling the process of the formation of InAs quantum dots in a GaAs matrix using a local isovalent phosphorus impurity.
Chávarri-Prado, David; Jiménez-Garrudo, Antonio; Solaberrieta-Méndez, Eneko; Diéguez-Pereira, Markel; Fernández-González, Felipe J.; Dehesa-Ibarra, Borja; Monticelli, Francesca
2016-01-01
The objective of the present study is to evaluate how the elastic properties of the fabrication material of dental implants influence peri-implant bone load transfer in terms of the magnitude and distribution of stress and deformation. A three-dimensional (3D) finite element analysis was performed; the model used was a section of mandibular bone with a single implant containing a cemented ceramic-metal crown on a titanium abutment. The following three alloys were compared: rigid (Y-TZP), conventional (Ti-6Al-4V), and hyperelastic (Ti-Nb-Zr). A 150-N static load was tested on the central fossa at 6° relative to the axial axis of the implant. The results showed no differences in the distribution of stress and deformation of the bone for any of the three types of alloys studied, mainly being concentrated at the peri-implant cortical layer. However, there were differences found in the magnitude of the stress transferred to the supporting bone, with the most rigid alloy (Y-TZP) transferring the least stress and deformation to cortical bone. We conclude that there is an effect of the fabrication material of dental implants on the magnitude of the stress and deformation transferred to peri-implant bone. PMID:27995137
Pérez-Pevida, Esteban; Brizuela-Velasco, Aritza; Chávarri-Prado, David; Jiménez-Garrudo, Antonio; Sánchez-Lasheras, Fernando; Solaberrieta-Méndez, Eneko; Diéguez-Pereira, Markel; Fernández-González, Felipe J; Dehesa-Ibarra, Borja; Monticelli, Francesca
2016-01-01
The objective of the present study is to evaluate how the elastic properties of the fabrication material of dental implants influence peri-implant bone load transfer in terms of the magnitude and distribution of stress and deformation. A three-dimensional (3D) finite element analysis was performed; the model used was a section of mandibular bone with a single implant containing a cemented ceramic-metal crown on a titanium abutment. The following three alloys were compared: rigid (Y-TZP), conventional (Ti-6Al-4V), and hyperelastic (Ti-Nb-Zr). A 150-N static load was tested on the central fossa at 6° relative to the axial axis of the implant. The results showed no differences in the distribution of stress and deformation of the bone for any of the three types of alloys studied, mainly being concentrated at the peri-implant cortical layer. However, there were differences found in the magnitude of the stress transferred to the supporting bone, with the most rigid alloy (Y-TZP) transferring the least stress and deformation to cortical bone. We conclude that there is an effect of the fabrication material of dental implants on the magnitude of the stress and deformation transferred to peri-implant bone.
Kim, Jeong Chul; Wang, Li; Shen, Dinggang; Lin, Weili
2016-01-01
The first year of life is the most critical time period for structural and functional development of the human brain. Combining longitudinal MR imaging and finite strain theory, this study aimed to provide new insights into normal brain development through a biomechanical framework. Thirty-three normal infants were longitudinally imaged using MRI from 2 weeks to 1 year of age. Voxel-wise Jacobian determinant was estimated to elucidate volumetric changes while Lagrange strains (both normal and shear strains) were measured to reveal directional growth information every 3 months during the first year of life. Directional normal strain maps revealed that, during the first 6 months, the growth pattern of gray matter is anisotropic and spatially inhomogeneous with higher left-right stretch around the temporal lobe and interhemispheric fissure, anterior-posterior stretch in the frontal and occipital lobes, and superior-inferior stretch in right inferior occipital and right inferior temporal gyri. In contrast, anterior lateral ventricles and insula showed an isotropic stretch pattern. Volumetric and directional growth rates were linearly decreased with age for most of the cortical regions. Our results revealed anisotropic and inhomogeneous brain growth patterns of the human brain during the first year of life using longitudinal MRI and a biomechanical framework. PMID:27910866
Bone stress and strain modification in diastema closure: 3D analysis using finite element method.
Geramy, Allahyar; Bouserhal, Joseph; Martin, Domingo; Baghaeian, Pedram
2015-09-01
The aim of this study was to analyse the stress and strain distribution in the alveolar bone between two central incisors in the process of diastema closure with a constant force. A 3-dimensional computer modeling based on finite element techniques was used for this purpose. A model of an anterior segment of the mandible containing cortical bone, spongy bone, gingivae, PDL and two central incisors with a bracket in the labial surface of each tooth were designed. The von Mises stress and strain was evaluated in alveolar bone along a path of nodes defined in a cresto-apical direction in the midline between two teeth. It was observed that stress and strain of alveolar bone increased in midline with a constant force to close the diastema regardless of the type of movement in gradual steps of diastema closure, however the stress was higher in the tipping movement than the bodily so it can be suggested that a protocol of force system modification should be introduced to compensate for the stress and strain changes caused by the reduced distance to avoid the unwanted stress alteration during the diastema closure.
Kim, Jeong Chul; Wang, Li; Shen, Dinggang; Lin, Weili
2016-12-02
The first year of life is the most critical time period for structural and functional development of the human brain. Combining longitudinal MR imaging and finite strain theory, this study aimed to provide new insights into normal brain development through a biomechanical framework. Thirty-three normal infants were longitudinally imaged using MRI from 2 weeks to 1 year of age. Voxel-wise Jacobian determinant was estimated to elucidate volumetric changes while Lagrange strains (both normal and shear strains) were measured to reveal directional growth information every 3 months during the first year of life. Directional normal strain maps revealed that, during the first 6 months, the growth pattern of gray matter is anisotropic and spatially inhomogeneous with higher left-right stretch around the temporal lobe and interhemispheric fissure, anterior-posterior stretch in the frontal and occipital lobes, and superior-inferior stretch in right inferior occipital and right inferior temporal gyri. In contrast, anterior lateral ventricles and insula showed an isotropic stretch pattern. Volumetric and directional growth rates were linearly decreased with age for most of the cortical regions. Our results revealed anisotropic and inhomogeneous brain growth patterns of the human brain during the first year of life using longitudinal MRI and a biomechanical framework.
Feng, Yuan; Lee, Chung-Hao; Sun, Lining; Ji, Songbai; Zhao, Xuefeng
2017-01-01
Characterizing the mechanical properties of white matter is important to understand and model brain development and injury. With embedded aligned axonal fibers, white matter is typically modeled as a transversely isotropic material. However, most studies characterize the white matter tissue using models with a single anisotropic invariant or in a small-strain regime. In this study, we combined a single experimental procedure - asymmetric indentation - with inverse finite element (FE) modeling to estimate the nearly incompressible transversely isotropic material parameters of white matter. A minimal form comprising three parameters was employed to simulate indentation responses in the large-strain regime. The parameters were estimated using a global optimization procedure based on a genetic algorithm (GA). Experimental data from two indentation configurations of porcine white matter, parallel and perpendicular to the axonal fiber direction, were utilized to estimate model parameters. Results in this study confirmed a strong mechanical anisotropy of white matter in large strain. Further, our results suggested that both indentation configurations are needed to estimate the parameters with sufficient accuracy, and that the indenter-sample friction is important. Finally, we also showed that the estimated parameters were consistent with those previously obtained via a trial-and-error forward FE method in the small-strain regime. These findings are useful in modeling and parameterization of white matter, especially under large deformation, and demonstrate the potential of the proposed asymmetric indentation technique to characterize other soft biological tissues with transversely isotropic properties.
In vivo bone strain and finite-element modeling of the craniofacial haft in catarrhine primates
Ross, Callum F; Berthaume, Michael A; Dechow, Paul C; Iriarte-Diaz, Jose; Porro, Laura B; Richmond, Brian G; Spencer, Mark; Strait, David
2011-01-01
Hypotheses regarding patterns of stress, strain and deformation in the craniofacial skeleton are central to adaptive explanations for the evolution of primate craniofacial form. The complexity of craniofacial skeletal morphology makes it difficult to evaluate these hypotheses with in vivo bone strain data. In this paper, new in vivo bone strain data from the intraorbital surfaces of the supraorbital torus, postorbital bar and postorbital septum, the anterior surface of the postorbital bar, and the anterior root of the zygoma are combined with published data from the supraorbital region and zygomatic arch to evaluate the validity of a finite-element model (FEM) of a macaque cranium during mastication. The behavior of this model is then used to test hypotheses regarding the overall deformation regime in the craniofacial haft of macaques. This FEM constitutes a hypothesis regarding deformation of the facial skeleton during mastication. A simplified verbal description of the deformation regime in the macaque FEM is as follows. Inferior bending and twisting of the zygomatic arches about a rostrocaudal axis exerts inferolaterally directed tensile forces on the lateral orbital wall, bending the wall and the supraorbital torus in frontal planes and bending and shearing the infraorbital region and anterior zygoma root in frontal planes. Similar deformation regimes also characterize the crania of Homo and Gorilla under in vitro loading conditions and may be shared among extant catarrhines. Relatively high strain magnitudes in the anterior root of the zygoma suggest that the morphology of this region may be important for resisting forces generated during feeding. PMID:21105871
NASA Astrophysics Data System (ADS)
Vitale, Stefano
2014-11-01
A new technique for estimating the finite strain of deformed elliptical markers is presented. This method is based on the property of the arithmetic mean Rfbar of the deformed object aspect ratios Rf to reach its minimum value in the undeformed state when they correspond to the initial aspect ratios Ri. The minimized Ribar (MIRi) iterative method furnishes the best results when, in the pre-strain state, the markers are uniformly orientated for every aspect ratio (Ri) class. A Matlab code, provided in this study, finds the best values of strain Rs and maximum stretching direction X that minimize the arithmetic mean Ribar by means of several iterations. In order to define the uncertainties of Rs and X, the code: (i) re-samples h-times the original (Ri, θ) dataset; (ii) assigns random values to the initial long axis angles θ; (iii) deforms newly the synthetic dataset; (iv) re-applies the MIRi method; and finally (v) estimates the standard deviation for the (Rs, X) values. Tests of the method on synthetic aggregates of elliptical markers and two naturally deformed rocks provide strain values that are compared with estimations from other available methods.
NASA Astrophysics Data System (ADS)
Balusu, K.; Huang, H.
2017-04-01
A combined dislocation fan-finite element (DF-FE) method is presented for efficient and accurate simulation of dislocation nodal forces in 3D elastically anisotropic crystals with dislocations intersecting the free surfaces. The finite domain problem is decomposed into half-spaces with singular traction stresses, an infinite domain, and a finite domain with non-singular traction stresses. As such, the singular and non-singular parts of the traction stresses are addressed separately; the dislocation fan (DF) method is introduced to balance the singular traction stresses in the half-spaces while the finite element method (FEM) is employed to enforce the non-singular boundary conditions. The accuracy and efficiency of the DF method is demonstrated using a simple isotropic test case, by comparing it with the analytical solution as well as the FEM solution. The DF-FE method is subsequently used for calculating the dislocation nodal forces in a finite elastically anisotropic crystal, which produces dislocation nodal forces that converge rapidly with increasing mesh resolutions. In comparison, the FEM solution fails to converge, especially for nodes closer to the surfaces.
Martin, F.; Jaouen, C.; Pacaud, J.; Abadias, G.; Djemia, Ph.; Ganot, F.
2005-01-15
The interdependence between the microstructure of sputter-deposited Ni(111)/Mo(110) superlattices and their elastic behavior is investigated as a function of the bilayer period ({lambda}). Brillouin light scattering measurements show that a drastic softening of the effective shear modulus occurs with decreasing {lambda}, until {lambda}=2 nm where it reaches -62%. Ion irradiation is here used to trigger stress relaxation and to induce, in a controlled way, interdiffusion and structural changes allowing us thus to investigate their influence on the elastic anomaly. At a very low irradiation dose (0.1 displacements per atom), the relief of the lattice expansion and associated compressive stresses does not induce any change of the elastic response, which indicates that the elastic behavior of the as-grown multilayers is not correlated with the presence of elastic strains. Furthermore, a detailed x-ray diffraction analysis shows that the unstrained lattice parameter of Mo layers exhibit a linear dependence with the interface density, while the Ni unstrained lattice parameter remains nearly unchanged in the same {lambda} range. This effect can be attributed to an interfacial mixing of a constant Ni amount ({approx}1.5 monolayers) into the Mo layers, as a consequence of a dynamic segregation of Ni atoms during growth. Thus, the formation of interfacial metastable and supersaturated solid solutions, structurally and mechanically unstable, appears as the origin of the huge elastic softening observed in this system. At high ion fluences, when the mixing process becomes dominant, the present study also provides experimental data on phase transformation in 'driven' alloys, by addressing the issue of the stability of out-of-equilibrium structures under irradiation.
Elsaadany, Mostafa; Yan, Karen Chang; Yildirim-Ayan, Eda
2017-01-16
Successful tissue engineering and regenerative therapy necessitate having extensive knowledge about mechanical milieu in engineered tissues and the resident cells. In this study, we have merged two powerful analysis tools, namely finite element analysis and stochastic analysis, to understand the mechanical strain within the tissue scaffold and residing cells and to predict the cell viability upon applying mechanical strains. A continuum-based multi-length scale finite element model (FEM) was created to simulate the physiologically relevant equiaxial strain exposure on cell-embedded tissue scaffold and to calculate strain transferred to the tissue scaffold (macro-scale) and residing cells (micro-scale) upon various equiaxial strains. The data from FEM were used to predict cell viability under various equiaxial strain magnitudes using stochastic damage criterion analysis. The model validation was conducted through mechanically straining the cardiomyocyte-encapsulated collagen constructs using a custom-built mechanical loading platform (EQUicycler). FEM quantified the strain gradients over the radial and longitudinal direction of the scaffolds and the cells residing in different areas of interest. With the use of the experimental viability data, stochastic damage criterion, and the average cellular strains obtained from multi-length scale models, cellular viability was predicted and successfully validated. This methodology can provide a great tool to characterize the mechanical stimulation of bioreactors used in tissue engineering applications in providing quantification of mechanical strain and predicting cellular viability variations due to applied mechanical strain.
Hanson, David E
2011-08-07
Based on recent molecular dynamics and ab initio simulations of small isoprene molecules, we propose a new ansatz for rubber elasticity. We envision a network chain as a series of independent molecular kinks, each comprised of a small number of backbone units, and the strain as being imposed along the contour of the chain. We treat chain extension in three distinct force regimes: (Ia) near zero strain, where we assume that the chain is extended within a well defined tube, with all of the kinks participating simultaneously as entropic elastic springs, (II) when the chain becomes sensibly straight, giving rise to a purely enthalpic stretching force (until bond rupture occurs) and, (Ib) a linear entropic regime, between regimes Ia and II, in which a force limit is imposed by tube deformation. In this intermediate regime, the molecular kinks are assumed to be gradually straightened until the chain becomes a series of straight segments between entanglements. We assume that there exists a tube deformation tension limit that is inversely proportional to the chain path tortuosity. Here we report the results of numerical simulations of explicit three-dimensional, periodic, polyisoprene networks, using these extension-only force models. At low strain, crosslink nodes are moved affinely, up to an arbitrary node force limit. Above this limit, non-affine motion of the nodes is allowed to relax unbalanced chain forces. Our simulation results are in good agreement with tensile stress vs. strain experiments.
Chi, Sheng-Wei; Hodgson, John; Chen, Jiun-Shyan; Reggie Edgerton, V; Shin, David D; Roiz, Ronald A; Sinha, Shantanu
2010-05-07
A finite element model was used to investigate the counter-intuitive experimental observation that some regions of the aponeuroses of a loaded and contracting muscle may shorten rather than undergo an expected lengthening. The model confirms the experimental findings and suggests that pennation angle plays a significant role in determining whether regions of the aponeuroses stretch or shorten. A smaller pennation angles (25 degrees ) was accompanied by aponeurosis lengthening whereas a larger pennation angle (47 degrees ) was accompanied by mixed strain effects depending upon location along the length of the aponeurosis. This can be explained by the Poisson effect during muscle contraction and a Mohr's circle analogy. Constant volume constraint requires that fiber cross sectional dimensions increase when a fiber shortens. The opposing influences of these two strains upon the aponeurosis combine in proportion to the pennation angle. Lower pennation angles emphasize the influence of fiber shortening upon the aponeurosis and thus favor aponeurosis compression, whereas higher pennation angles increase the influence of cross sectional changes and therefore favor aponeurosis stretch. The distance separating the aponeuroses was also found to depend upon pennation angle during simulated contractions. Smaller pennation angles favored increased aponeurosis separation larger pennation angles favored decreased separation. These findings caution that measures of the mechanical properties of aponeuroses in intact muscle may be affected by contributions from adjacent muscle fibers and that the influence of muscle fibers on aponeurosis strain will depend upon the fiber pennation angle.
Giant elastic tunability in strained BiFeO_{3} near an electrically induced phase transition
Yu, Pu; Vasudevan, Rama K.; Tselev, Alexander; Xue, Fei; Chen, Long -Qing; Maksymovych, Petro; Kalinin, Sergei V.; Balke, Nina; Li, Q.; Cao, Y.; Laanait, N.
2015-01-01
Elastic anomalies are signatures of phase transitions in condensed matters and have traditionally been studied using various techniques spanning from neutron scattering to static mechanical testing. Here, using band-excitation elastic/piezoresponse spectroscopy, we probed sub-MHz elastic dynamics of a tip bias-induced rhombohedral–tetragonal phase transition of strained (001)-BiFeO_{3} (rhombohedral) ferroelectric thin films from ~10^{3} nm^{3} sample volumes. Near this transition, we observed that the Young's modulus intrinsically softens by over 30% coinciding with 2-3 folds enhancement of local piezoresponse. Coupled with phase-field modeling, we also addressed the influence of polarization switching and mesoscopic structural heterogeneities (e.g., domain walls) on the kinetics of this phase transition, thereby providing fresh insights into the morphotropic phase boundary (MPB) in ferroelectrics. Moreover, the giant electrically tunable elastic stiffness and corresponding electromechanical properties observed here suggest potential applications of BiFeO_{3} in next-generation frequency-agile electroacoustic devices, based on utilization of the soft modes underlying successive ferroelectric phase transitions.
NASA Astrophysics Data System (ADS)
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.
Gao, Jing; Rubin, Jonathan M
2014-09-01
To determine whether ultrasound strain zero-crossing elasticity measurement can be used to discriminate moderate cortical fibrosis or inflammation in renal allografts, we prospectively assessed cortical hardness with quasi-static ultrasound elastography in 38 renal transplant patients who underwent kidney biopsy from January 2013 to June 2013. With the Banff score criteria for renal cortical fibrosis as gold standard, 38 subjects were divided into two groups: group 1 (n = 18) with ≤25% cortical fibrosis and group 2 (n = 20) with >26% cortical fibrosis. We then divided this population again into group 3 (n = 20) with ≤ 25% inflammation and group 4 (n = 18) with >26% inflammation based on the Banff score for renal parenchyma inflammation. To estimate renal cortical hardness in both population divisions, we propose an ultrasound strain relative zero-crossing elasticity measurement (ZC) method. In this technique, the relative return to baseline, that is zero strain, of strain in the renal cortex is compared with that of strain in reference soft tissue (between the abdominal wall and pelvic muscles). Using the ZC point on the reference strain decompression slope as standard, we determined when cortical strain crossed zero during decompression. ZC was negative when cortical strain did not return or returned after the reference, whereas ZC was positive when cortical strain returned ahead of the reference. Fisher's exact test was used to examine the significance of differences in ZC between groups 1 and 2 and between groups 3 and 4. The accuracy of ZC in determining moderate cortical fibrosis and moderate inflammation was examined by receiver operating characteristic analysis. The intra-class correlation coefficient and analysis of variance were used to test inter-rater reliability and reproducibility. ZC had good inter-observer agreement (ICC = 0.912) and reproducibility (p = 0.979). ZCs were negative in 18 of 18 cases in group 1 and positive in 19 of 20 cases in
NASA Technical Reports Server (NTRS)
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.
Wang, Huamiao; Clausen, Bjorn; Capolungo, Laurent; Beyerlein, Irene Jane; Wang, Jian; Tome, Carlos N.
2015-07-16
Continuous mechanical tests with strain holds (stress relaxation) and with stress holds (strain relaxation) are performed simultaneously with in-situ neutron measurements to analyze the mechanisms of stress and strain relaxation in Mg AZ31 rolled plate. A dislocation activity based constitutive model, accounting for internal stress statistical distributions, is proposed and implemented into an elastic viscoplastic self-consistent (EVPSC) framework to simultaneously describe both stress and strain relaxation. The model captures the experimental data in terms of macroscopic stress strain curves, evolution of stress and strain during holding, as well as evolution of the internal elastic strains. Model results indicate that the magnitude of the stress relaxed during strain holding is dependent on both, the magnitude of the flow stress and the spread of the resolved shear stress distribution. The magnitude of strain accumulated during stress holding is, on the other hand, dependent on the magnitude of the hardening rate and on the spread of the resolved shear stress distribution. Furthermore, the internal elastic strains are directly correlated with the stress state, and hence the stress relaxation during strain holds has a greater influence on the lattice strains than strain relaxation during stress holds.
NASA Astrophysics Data System (ADS)
Marino, Michele; Wriggers, Peter
2017-01-01
Composite materials reinforced by crimped fibers intervene in a number of advanced structural applications. Accordingly, constitutive equations describing their anisotropic behavior and explicitly accounting for fiber properties are needed for modeling and design purposes. To this aim, the finite strain response of crimped beams under uniaxial traction is herein addressed by obtaining analytical relationships based on the Principle of Virtual Works. The model is applied to collagen fibers in soft biological tissues, coupling geometric nonlinearities related to fiber crimp with material nonlinearities due to nanoscale mechanisms. Several numerical applications are presented, addressing the influence of geometric and material features. Available experimental data for tendons are reproduced, integrating the proposed approach within an optimization procedure for data fitting. The obtained results highlight the effectiveness of the proposed approach in correlating fibers structure with composite material mechanics.
A thermo-mechanically coupled finite strain model considering inelastic heat generation
NASA Astrophysics Data System (ADS)
Dunić, Vladimir; Busarac, Nenad; Slavković, Vukašin; Rosić, Bojana; Niekamp, Rainer; Matthies, Hermann; Slavković, Radovan; Živković, Miroslav
2016-07-01
The procedure for reuse of finite element method (FEM) programs for heat transfer and structure analysis to solve advanced thermo-mechanical problems is presented as powerful algorithm applicable for coupling of other physical fields (magnetic, fluid flow, etc.). In this case, nonlinear Block-Gauss-Seidel partitioned algorithm strongly couples the heat transfer and structural FEM programs by a component-based software engineering. Component template library provides possibility to exchange the data between the components which solve the corresponding subproblems. The structural component evaluates the dissipative energy induced by inelastic strain. The heat transfer component computes the temperature change due to the dissipation. The convergence is guaranteed by posing the global convergence criterion on the previously locally converged coupled variables. This enables reuse of software and allows the numerical simulation of thermo-sensitive problems.
Jia, Yunfei; Xuan, Fu-Zhen; Yang, Fuqian
2014-04-01
Tooth enamel is a complex structure, consisting of numerous enamel rods surrounded by a protein-rich sheath. Considering the possible effect of the protein-rich sheath on the indentation deformation of an enamel rod and the limitation of the Oliver-Pharr method in measuring the elastic modulus of the enamel rod, we used a finite element method to analyze the indentation deformation of an elastic-perfectly plastic cylinder surrounded by an elastic-perfectly plastic film. A concept of the threshold indentation depth was proposed, at which the percentage error of the measured modulus of the cylinder is ±10%. For the indentation depth less than the threshold indentation depth, the elastic modulus measured from the indentation test can be approximated as the intrinsic elastic modulus of the cylinder. The normalized threshold indentation depth strongly depends on the modulus ratio of the film to the cylinder and the ratio of the film thickness to the cylinder radius. The results can be used to guide the use of the Oliver-Pharr method in characterizing the mechanical properties of tooth enamel and bio-composites with core-shell structures.
NASA Astrophysics Data System (ADS)
Rout, Matruprasad; Pal, Surjya Kanta; Singh, Shiv Brat
2017-02-01
Studies on the effect of strain path during rolling has been carried out for a long time, but the same has not been done using Finite Element Analysis (FEA). Change in strain path affects the state variables in the rolled plate like stress, strain, temperature etc. In the current work, Finite Element Analysis for cross rolling of AISI 304 austenitic stainless steel has been carried out by rotating the plate by 90° in between the passes. To analyze stress and strain fields in the material for cross rolling, a full 3D model of work-roll and plate has been developed using rigid-viscoplastic finite element method. The stress and strain fields, considering von-Mises yield criteria, are calculated by using updated Lagrangian method. In addition to these, the model also calculates the normal pressure and strain rate distribution in the plate during cross rolling. The nature of the variations of stress and strain fields in the plate, predicted by the model, is in good agreement with the previously published works for unidirectional rolling.
NASA Astrophysics Data System (ADS)
Ziółkowski, Andrzej
2017-01-01
An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition
NASA Astrophysics Data System (ADS)
Malekan, Mohammad; Barros, Felicio Bruzzi
2016-11-01
Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning system of equations due to presence of blending elements. The local enrichment can be chosen from polynomial, singular, branch or numerical types. The so-called stable version of G/XFEM method provides a well-conditioning approach when only singular functions are used in the blending elements. This paper combines numeric enrichment functions obtained from global-local G/XFEM method with the polynomial enrichment along with a well-conditioning approach, stable G/XFEM, in order to show the robustness and effectiveness of the approach. In global-local G/XFEM, the enrichment functions are constructed numerically from the solution of a local problem. Furthermore, several enrichment strategies are adopted along with the global-local enrichment. The results obtained with these enrichments strategies are discussed in detail, considering convergence rate in strain energy, growth rate of condition number, and computational processing. Numerical experiments show that using geometrical enrichment along with stable G/XFEM for global-local strategy improves the convergence rate and the conditioning of the problem. In addition, results shows that using polynomial enrichment for global problem simultaneously with global-local enrichments lead to ill-conditioned system matrices and bad convergence rate.
Kim, Yoon Hyuk; Yao, Zhidong; Kim, Kyungsoo; Park, Won Man
2014-06-01
It may be assumed that the stability is affected when some ligaments are injured or loosened, and this joint instability causes sacroiliac joint pain. Several physical examinations have been used to diagnose sacroiliac pain and to isolate the source of the pain. However, more quantitative and objective information may be necessary to identify unstable or injured ligaments during these tests due to the lack of understanding of the quantitative relationship between the physical tests and the biomechanical parameters that may be related to pains in the sacroiliac joint and the surrounding ligaments. In this study, a three-dimensional finite element model of the sacroiliac joint was developed and the biomechanical conditions for six typical physical tests such as the compression test, distraction test, sacral apex pressure test, thigh thrust test, Patrick's test, and Gaenslen's test were modelled. The sacroiliac joint contact pressure and ligament strain were investigated for each test. The values of contact pressure and the combination of most highly strained ligaments differed markedly among the tests. Therefore, these findings in combination with the physical tests would be helpful to identify the pain source and to understand the pain mechanism. Moreover, the technology provided in this study might be a useful tool to evaluate the physical tests, to improve the present test protocols, or to develop a new physical test protocol.
NASA Technical Reports Server (NTRS)
Trice, R.; Warren, N.; Anderson, O. L.
1974-01-01
Linear strain measurements are presented for two lunar basalts, 14310,82 and 71055,15 and one breccia, 15498,23 to 5 kb hydrostatic pressure. Compressional and shear acoustic velocities to 5 kb are also presented for the basalts, 14310,82 and 71055,15. These elastic properties, along with geological, seismological and rock mechanics considerations are consistent with a model of the structure of the Taurus-Littrow valley as follows, a thin surface regolith overlying a fractured mixture of basalt flows and ejecta material which in turn overlies a coherent breccia of highland ejecta debris.
Albocher, U; Barbone, P E; Richards, M S; Oberai, A A; Harari, I
2014-01-01
We apply the adjoint weighted equation method (AWE) to the direct solution of inverse problems of incompressible plane strain elasticity. We show that based on untreated noisy displacements, the reconstruction of the shear modulus can be very poor. We link this poor performance to loss of coercivity of the weak form when treating problems with discontinuous coefficients. We demonstrate that by smoothing the displacements and appending a regularization term to the AWE formulation, a dramatic improvement in the reconstruction can be achieved. With these improvements, the advantages of the AWE method as a direct solution approach can be extended to a wider range of problems.
Albocher, U.; Barbone, P.E.; Richards, M.S.; Oberai, A.A.; Harari, I.
2014-01-01
We apply the adjoint weighted equation method (AWE) to the direct solution of inverse problems of incompressible plane strain elasticity. We show that based on untreated noisy displacements, the reconstruction of the shear modulus can be very poor. We link this poor performance to loss of coercivity of the weak form when treating problems with discontinuous coefficients. We demonstrate that by smoothing the displacements and appending a regularization term to the AWE formulation, a dramatic improvement in the reconstruction can be achieved. With these improvements, the advantages of the AWE method as a direct solution approach can be extended to a wider range of problems. PMID:25383085
Hilbert complexes of nonlinear elasticity
NASA Astrophysics Data System (ADS)
Angoshtari, Arzhang; Yavari, Arash
2016-12-01
We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.
NASA Technical Reports Server (NTRS)
Deng, Xiaomin; Newman, James C., Jr.
1997-01-01
ZIP2DL is a two-dimensional, elastic-plastic finte element program for stress analysis and crack growth simulations, developed for the NASA Langley Research Center. It has many of the salient features of the ZIP2D program. For example, ZIP2DL contains five material models (linearly elastic, elastic-perfectly plastic, power-law hardening, linear hardening, and multi-linear hardening models), and it can simulate mixed-mode crack growth for prescribed crack growth paths under plane stress, plane strain and mixed state of stress conditions. Further, as an extension of ZIP2D, it also includes a number of new capabilities. The large-deformation kinematics in ZIP2DL will allow it to handle elastic problems with large strains and large rotations, and elastic-plastic problems with small strains and large rotations. Loading conditions in terms of surface traction, concentrated load, and nodal displacement can be applied with a default linear time dependence or they can be programmed according to a user-defined time dependence through a user subroutine. The restart capability of ZIP2DL will make it possible to stop the execution of the program at any time, analyze the results and/or modify execution options and resume and continue the execution of the program. This report includes three sectons: a theoretical manual section, a user manual section, and an example manual secton. In the theoretical secton, the mathematics behind the various aspects of the program are concisely outlined. In the user manual section, a line-by-line explanation of the input data is given. In the example manual secton, three types of examples are presented to demonstrate the accuracy and illustrate the use of this program.
NASA Astrophysics Data System (ADS)
Rao, R. Ramji; Padmaja, A.
1988-06-01
The equation for elastic wave propagation in a homogeneously deformed crystal has been used to obtain the expressions for the effective second-order elastic constants of the seven crystal systems in terms of their natural second- and third-order elastic constants. These expressions are employed to obtain the pressure derivatives of the effective second-order elastic constants of some cubic crystals for which experimental data are available.
Brake, M. R. W.
2015-02-17
Impact between metallic surfaces is a phenomenon that is ubiquitous in the design and analysis of mechanical systems. We found that to model this phenomenon, a new formulation for frictional elastic–plastic contact between two surfaces is developed. The formulation is developed to consider both frictional, oblique contact (of which normal, frictionless contact is a limiting case) and strain hardening effects. The constitutive model for normal contact is developed as two contiguous loading domains: the elastic regime and a transitionary region in which the plastic response of the materials develops and the elastic response abates. For unloading, the constitutive model is based on an elastic process. Moreover, the normal contact model is assumed to only couple one-way with the frictional/tangential contact model, which results in the normal contact model being independent of the frictional effects. Frictional, tangential contact is modeled using a microslip model that is developed to consider the pressure distribution that develops from the elastic–plastic normal contact. This model is validated through comparisons with experimental results reported in the literature, and is demonstrated to be significantly more accurate than 10 other normal contact models and three other tangential contact models found in the literature.
Brake, M. R. W.
2015-02-17
Impact between metallic surfaces is a phenomenon that is ubiquitous in the design and analysis of mechanical systems. We found that to model this phenomenon, a new formulation for frictional elastic–plastic contact between two surfaces is developed. The formulation is developed to consider both frictional, oblique contact (of which normal, frictionless contact is a limiting case) and strain hardening effects. The constitutive model for normal contact is developed as two contiguous loading domains: the elastic regime and a transitionary region in which the plastic response of the materials develops and the elastic response abates. For unloading, the constitutive model ismore » based on an elastic process. Moreover, the normal contact model is assumed to only couple one-way with the frictional/tangential contact model, which results in the normal contact model being independent of the frictional effects. Frictional, tangential contact is modeled using a microslip model that is developed to consider the pressure distribution that develops from the elastic–plastic normal contact. This model is validated through comparisons with experimental results reported in the literature, and is demonstrated to be significantly more accurate than 10 other normal contact models and three other tangential contact models found in the literature.« less
Bedolla Pantoja, Marco A; Abbott, Nicholas L
2016-05-25
We report the fabrication of chemically patterned microwells that enable the rapid and facile preparation (by spin coating and patterned dewetting) of thin films of liquid crystals (LCs) that have precise thicknesses (0.7-30 μm), are supported on chemically defined substrates, and have free upper surfaces. We use these microwells to prepare elastically strained nematic LC films supported on silica glass, gold, or polystyrene substrates and thereby characterize the response of the strained LC films to vapors of toluene. We report that low concentrations of toluene vapor (<500 ppm) can partition into the LC to lower the anchoring energy of the LC on these substrates, thus allowing the elastic energy of the strained LC film to drive the LC films through an orientational transition. The central role of the toluene-induced change in surface anchoring energy is supported by additional experiments in which the response of the nematic LC to changes in film thickness and substrate identity are quantified. A simple thermodynamic model captures these trends and yielded estimates of anchoring energies (8-22 μJ/m(2)). Significantly, the orientational transitions observed in these strained LC thin films occur at concentrations of toluene vapor that are almost 1 order of magnitude below those which lead to bulk phase transitions, and they are not triggered by exposure to water vapor. Overall, these results hint at principles for the design of responsive LC-based materials that can be triggered by concentrations of aromatic, volatile organic compounds that are relevant to human health.
NASA Astrophysics Data System (ADS)
Klein, Claude A.; Miller, Richard P.
2000-03-01
Solid structures consisting of layers of different materials created at elevated temperatures usually exhibit substantial residual stresses. These stresses are caused by intrinsic strains in addition to thermal strains, and originate from the bonding of the layers, which generates internal forces and moments that must be balanced to achieve mechanical equilibrium. It is shown that the solution proposed by Townsend et al. [P. Townsend, D. Barnett, and T. Brunner, J. Appl. Phys. 62, 4438 (1987)] for describing elastic interactions in multilayered, elastically isotropic structures provides a powerful tool for evaluating the strains, the normal stresses off the edges, and the curvature of chemically vapor-deposited (CVD) laminates. The residual stresses acting in each layer are best expressed as follows: σi(z)=Ei'[(ɛi,0-ɛ0¯)+(zN-z)K], where z measures the distance from the bottom surface, Ei' is the biaxial modulus of the layer, (ɛi,0-ɛ0¯) characterizes the strain mismatch prior to any mechanical relaxation, and (zN-z)K defines the bending contribution, which depends linearly on the distance from the neutral plane and stems from the curvature K. For bilayered structures the curvature can be expressed in a relatively simple form. In conjunction with the proper expression for the average stress in the coating, it is seen that Stoney's equation holds for thickness ratios much larger than expected in the context of the thin-film approximation. The case of CVD laminates made of ZnS on ZnSe illustrates how the theory can be applied for designing structures that minimize the deformation and, thus, for obtaining optically desirable configurations. The stresses acting in bilayered ZnS/ZnSe structures are controlled by the strain differential Δɛ0=ɛcintr.+(αc¯-αs¯)ΔT, where ɛcintr. represents the intrinsic strain of the ZnS coating, and (αc¯-αs¯)ΔT defines the contribution originating from the thermal expansion mismatch. For ZnS deposited at 670
NASA Astrophysics Data System (ADS)
Wang, Dong; Wang, Chunrui; Zhang, Yao; Zhang, Shasha; Xu, Xiaofeng; Yang, Qinyu
2013-12-01
A new finite element method based on boundary conditions is proposed here to obtain the complete strains distribution in Ge/CdSe biaxial nanowires. The results show that the strains in nanowire is essentially uniform along the nanowire axis, whereas turn to be complex in cross-section. Additionally, Raman spectrum of Ge subnanowire was calculated on base of those strain data. Raman frequency shifts in Ge subnanowire in Ge/CdSe biaxial nanowires is a good agreement with that of Raman spectrum, which confirms the validity of this model.
Elastic and plastic strain measurement in high temperature environment using laser speckle
NASA Technical Reports Server (NTRS)
Chiang, Fu-Pen
1992-01-01
Two laser speckle methods are described to measure strain in high temperature environment and thermal strain caused by high temperature. Both are non-contact, non-destructive and remote sensing techniques that can be automated. The methods have different but overlapping ranges of application with one being more suitable for large plastic deformation.
Elastic strain relaxation in GaN/AlN nanowire superlattice
NASA Astrophysics Data System (ADS)
Landré, O.; Camacho, D.; Bougerol, C.; Niquet, Y. M.; Favre-Nicolin, V.; Renaud, G.; Renevier, H.; Daudin, B.
2010-04-01
The molecular-beam epitaxy growth of AlN/GaN nanowire superlattices has been studied by using a combination of in situ x-ray diffraction experiments, high-resolution electron-microscopy analysis and theoretical calculations performed in a valence force field approach. It is found that the nanowire superlattices are in elastic equilibrium, in contrast with the two-dimensional case but in line with the predicted increase in the critical thickness in the nanowire geometry.
Neuert, Mark A C; Dunning, Cynthia E
2013-09-01
Strain energy-based adaptive material models are used to predict bone resorption resulting from stress shielding induced by prosthetic joint implants. Generally, such models are governed by two key parameters: a homeostatic strain-energy state (K) and a threshold deviation from this state required to initiate bone reformation (s). A refinement procedure has been performed to estimate these parameters in the femur and glenoid; this study investigates the specific influences of these parameters on resulting density distributions in the distal ulna. A finite element model of a human ulna was created using micro-computed tomography (µCT) data, initialized to a homogeneous density distribution, and subjected to approximate in vivo loading. Values for K and s were tested, and the resulting steady-state density distribution compared with values derived from µCT images. The sensitivity of these parameters to initial conditions was examined by altering the initial homogeneous density value. The refined model parameters selected were then applied to six additional human ulnae to determine their performance across individuals. Model accuracy using the refined parameters was found to be comparable with that found in previous studies of the glenoid and femur, and gross bone structures, such as the cortical shell and medullary canal, were reproduced. The model was found to be insensitive to initial conditions; however, a fair degree of variation was observed between the six specimens. This work represents an important contribution to the study of changes in load transfer in the distal ulna following the implementation of commercial orthopedic implants.
Webster, Duncan; Schulte, Friederike A; Lambers, Floor M; Kuhn, Gisela; Müller, Ralph
2015-03-18
Huiskes et al. hypothesized that mechanical strains sensed by osteocytes residing in trabecular bone dictate the magnitude of load-induced bone formation. More recently, the mechanical environment in bone marrow has also been implicated in bone׳s response to mechanical stimulation. In this study, we hypothesize that trabecular load-induced bone formation can be predicted by mechanical signals derived from an integrative µFE model, incorporating a description of both the bone and marrow phase. Using the mouse tail loading model in combination with in vivo micro-computed tomography (µCT) we tracked load induced changes in the sixth caudal vertebrae of C57BL/6 mice to quantify the amount of newly mineralized and eroded bone volumes. To identify the mechanical signals responsible for adaptation, local morphometric changes were compared to micro-finite element (µFE) models of vertebrae prior to loading. The mechanical parameters calculated were strain energy density (SED) on trabeculae at bone forming and resorbing surfaces, SED in the marrow at the boundary between bone forming and resorbing surfaces, along with SED in the trabecular bone and marrow volumes. The gradients of each parameter were also calculated. Simple regression analysis showed mean SED gradients in the trabecular bone matrix to significantly correlate with newly mineralized and eroded bone volumes R(2)=0.57 and 0.41, respectively, p<0.001). Nevertheless, SED gradients in the marrow were shown to be the best predictor of osteoblastic and osteoclastic activity (R(2)=0.83 and 0.60, respectively, p<0.001). These data suggest that the mechanical environment of the bone marrow plays a significant role in determining osteoblast and osteoclast activity.
Hutula, D.N.; Wiancko, B.E.
1980-03-01
ACCEPT is a three-dimensional finite element computer program for analysis of large-deformation elastic-plastic-creep response of Zircaloy tubes subjected to temperature, surface pressures, and axial force. A twenty-mode, tri-quadratic, isoparametric element is used along with a Zircaloy materials model. A linear time-incremental procedure with residual force correction is used to solve for the time-dependent response. The program features an algorithm which automatically chooses the time step sizes to control the accuracy and numerical stability of the solution. A contact-separation capability allows modeling of interaction of reactor fuel rod cladding with fuel pellets or external supports.
NASA Astrophysics Data System (ADS)
Kazuhiro, Tanaka; Wolfgang, Bentz; Akito, Arima
1990-11-01
The quasi-elastic Coulomb response function of finite nuclei including vacuum polarization effects is investigated in the relativistic σ-ω model. For the consistent elimination of the Landau ghost in meson propagators, the description of the ground state and the response function of the system is formulated utilizing the effective action method, and the effects of the ghost elimination on the nuclear matter response function are discussed. Finite system calculations are performed for 12C (|q|= 300, 400, 550 MeV) and 40Ca (|q|= 410, 500, 550 MeV) , in which particle-hole continuum states are fully taken into account by the method of continuum RPA, while the vacuum polarization effects are included by the local density approximation. The effects of the particle-hole effective interaction and the medium modified single-nucleon form factor on the response function are also discussed.
DT-REFinD: diffusion tensor registration with exact finite-strain differential.
Yeo, B T Thomas; Vercauteren, Tom; Fillard, Pierre; Peyrat, Jean-Marc; Pennec, Xavier; Golland, Polina; Ayache, Nicholas; Clatz, Olivier
2009-12-01
In this paper, we propose the DT-REFinD algorithm for the diffeomorphic nonlinear registration of diffusion tensor images. Unlike scalar images, deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme. Current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently, these methods often approximate the gradient of the objective function. In the case of the finite-strain (FS) reorientation strategy, we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function. By utilizing the closed-form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms, the resulting registration algorithm is diffeomorphic and fast. We contrast the algorithm with a traditional FS alternative that ignores the reorientation in the gradient computation. We show that the exact gradient leads to significantly better registration at the cost of computation time. Independently of the choice of Euclidean or Log-Euclidean interpolation and sum of squared differences dissimilarity measure, the exact gradient achieves better alignment over an entire spectrum of deformation penalties. Alignment quality is assessed with a battery of metrics including tensor overlap, fractional anisotropy, inverse consistency and closeness to synthetic warps. The improvements persist even when a different reorientation scheme, preservation of principal directions, is used to apply the final deformations.
A comparative study of strain and shear-wave elastography in an elasticity phantom.
Carlsen, Jonathan F; Pedersen, Malene R; Ewertsen, Caroline; Săftoiu, Adrian; Lönn, Lars; Rafaelsen, Søren R; Nielsen, Michael B
2015-03-01
OBJECTIVE. The purpose of this study was to assess the diagnostic accuracy of strain and shear-wave elastography for determining targets of varying stiffness in a phantom. The effect of target diameter on elastographic assessments and the effect of depth on shear-wave velocity were also investigated. MATERIALS AND METHODS. We examined 20 targets of varying diameters (2.5-16.7 mm) and stiffnesses (8, 14, 45, and 80 kPa) with a 4-9-MHz linear-array transducer. Targets were evaluated 10 times with three different methods-shear-wave elastography, strain ratio, and strain histogram analysis-yielding 600 evaluations. AUCs were calculated for data divided between different stiffnesses. A 1.5-6-MHz curved-array transducer was used to assess the effect of depth (3.5 vs 6 cm) on shear-wave elastography in 80 scans. Mixed model analysis was performed to assess the effect of target diameter and depth. RESULTS. Strain ratio and strain histogram AUCs were higher than the shear-wave velocity AUC (p < 0.001) in data divided as 80 versus 45, 14, and 8 kPa. In data divided as 80 and 45 versus 14 and 8 kPa, the methods were equal (p = 0.959 and p = 1.000, respectively). Strain ratios were superior (p = 0.030), whereas strain histograms were not significantly better (p = 0.083) than shear-wave elastography in data divided as 80, 45, and 14 versus 8 kPa. Target diameter had an effect on all three methods (p = 0.001). Depth had an effect on shear-wave velocity (p = 0.001). CONCLUSION. The ability to discern different target stiffnesses varies between shear-wave and strain elastography. Target diameter affected all methods. Shear-wave elastography is affected by target depth.
Lu, Yongtao; Rosenau, Eike; Paetzold, Helge; Klein, Anke; Püschel, Klaus; Morlock, Michael M; Huber, Gerd
2013-12-01
The probability of fractures of the cortical shell of vertebral bodies increases as ageing progresses. Ageing involves all the spinal component changes. However, the effect of the spinal component ageing on the fracture risk of the cortical shell remains poorly understood. In this study, the influence of the ageing of the spinal components on cortical shell strain was investigated. A lumbar spinal specimen (L3-L5) was mechanically tested under a quasi-static axial compressive load. Clinical computed tomography images of the same specimen were used to create a corresponding finite element model. The material properties were determined by calibrating the finite element model using the L4 cortical shell strains of the anterior centre measurement site. The remaining experiment data (axial displacement, the intra-discal pressures, L4 cortical shell strain on the lateral measurement site) were used to evaluate the model. The individual ageing process of the six spinal components (cortical shell, cancellous bone, bony endplate, posterior elements, nucleus pulposus and annulus matrix) was simulated by changing their Young's moduli and Poisson's ratios, and the effect on cortical shell strain was investigated. Results show that the cortical shell strain is more sensitive to the ageing of the cortical shell and the cancellous bone than to the ageing of the nucleus pulposus, the annulus matrix, and the bony endplates and of the posterior elements. The results can help the clinicians focus on the aspects that mainly influence the vertebral cortex fracture risk factor.
Umemoto, Takeshi; Ueno, Ei; Matsumura, Takeshi; Yamakawa, Makoto; Bando, Hiroko; Mitake, Tsuyoshi; Shiina, Tsuyoshi
2014-08-01
The aim of this study was to reveal the background to the image variations in strain elastography (strain imaging [SI]) depending on the manner of manipulation (compression magnitude) during elasticity image (EI) acquisition. Thirty patients with 33 breast lesions who had undergone surgery followed by SI assessment in vivo were analyzed. An analytical approach to tissue elasticity based on the stress-elastic modulus (Young's modulus) relationship was adopted. Young's moduli were directly measured ex vivo in surgical specimens ranging from 2.60 kPa (fat) to 16.08 kPa (invasive carcinoma) under the weak-stress condition (<0.2-0.4 kPa, which corresponds to the appropriate "light touch" technique in SI investigation. The contrast (ratio) of lesion to fat in elasticity ex vivo gradually decreased as the stress applied increased (around 1.0 kPa) on the background of significant non-linearity of the breast tissue. Our results indicate that the differences in non-linearity in elasticity between the different tissues within the breast under minimal stress conditions are closely related to the variation in EI quality. The significance of the "pre-load compression" concept in tissue elasticity evaluation is recognized. Non-linearity of elasticity is an essential attribute of living subjects and could provide useful information having a considerable impact on clinical diagnosis in quantitative ultrasound elastography.
Finite Element Modelling of Large Plastic Strains in a Rolling Contact Metal Forming Process.
1987-08-01
developed by Pope [42] and Marcal (2] to solve the elastic- plastic problem . This method is essentially a piece- wise solution to the non-linear...problem. A summary of these early developments in numerical solution of elastic- plastic problems has been given by Marcal [431 and Yamada [44]. Yamada [45
Influence of elastic strains on the mask ratio in glassy polymer nanoimprint
NASA Astrophysics Data System (ADS)
Cross, Graham L. W.; O'Connell, Barry S.; Pethica, John B.
2005-02-01
During glassy polymer nanoimprint, a supported film is extruded from protruding (punch) to recessed (cavity) regions of a patterned stamp. The completeness of this extrusion determines the mask ratio for lithographic applications. We show that, for a given punch contact size, there is a residual layer of unextruded material with a mean thickness that is independent of initial film thickness, stamping time, or applied maximum load. Depth sensing indentation enables us to monitor deformation during the imprinting as well as after, and so understand the deformation process involved. It is found that both the geometry and mean thickness of the residual layer are influenced by the overall elastic properties of the stamping system.
Woiczinski, Matthias; Tollrian, Christopher; Schröder, Christian; Steinbrück, Arnd; Müller, Peter E; Jansson, Volkmar
2013-08-01
With the aging but still active population, research on total joint replacements relies increasingly on numerical methods, such as finite element analysis, to improve wear resistance of components. However, the validity of finite element models largely depends on the accuracy of their material behavior and geometrical representation. In particular, material properties are often based on manufacturer data or literature reports, but can alternatively be estimated by matching experimental measurements and structural predictions through modal analyses and identification of eigenfrequencies. The aim of the present study was to compare the accuracy of common setups used for estimating the eigenfrequencies of typical components often used in prosthetized joints. Eigenfrequencies of cobalt-chrome and ultra-high-molecular weight polyethylene components were therefore measured with four different setups, and used in modal analyses of corresponding finite element models for an iterative adjustment of their material properties. Results show that for the low-damped cobalt chromium endoprosthesis components, all common measuring setups provided accurate measurements. In the case of high-damped structures, measurements were only possible with setups including a continuously excitation system such as electrodynamic shakers. This study demonstrates that the iterative back-calculation of eigenfrequencies can be a reliable method to estimate the elastic properties for finite element models.
NASA Technical Reports Server (NTRS)
Salpekar, S. A.; Raju, I. S.; Obrien, T. K.
1987-01-01
Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtural crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finite-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.
Strain-rate Dependence of Elastic Modulus Reveals Silver Nanoparticle Induced Cytotoxicity.
Caporizzo, Matthew Alexander; Roco, Charles M; Ferrer, Maria Carme Coll; Grady, Martha E; Parrish, Emmabeth; Eckmann, David M; Composto, Russell John
Force-displacement measurements are taken at different rates with an atomic force microscope to assess the correlation between cell health and cell viscoelasticity in THP-1 cells that have been treated with a novel drug carrier. A variable indentation-rate viscoelastic analysis, VIVA, is employed to identify the relaxation time of the cells that are known to exhibit a frequency dependent stiffness. The VIVA agrees with a fluorescent viability assay. This indicates that dextran-lysozyme drug carriers are biocompatible and deliver concentrated toxic material (rhodamine or silver nanoparticles) to the cytoplasm of THP-1 cells. By modelling the frequency dependence of the elastic modulus, the VIVA provides three metrics of cytoplasmic viscoelasticity: a low frequency modulus, a high frequency modulus and viscosity. The signature of cytotoxicity by rhodamine or silver exposure is a frequency independent twofold increase in the elastic modulus and cytoplasmic viscosity, while the cytoskeletal relaxation time remains unchanged. This is consistent with the known toxic mechanism of silver nanoparticles, where metabolic stress causes an increase in the rigidity of the cytoplasm. A variable indentation-rate viscoelastic analysis is presented as a straightforward method to promote the self-consistent comparison between cells. This is paramount to the development of early diagnosis and treatment of disease.
Finite element solutions for crack-tip behavior in small-scale yielding
NASA Technical Reports Server (NTRS)
Tracey, D. M.
1976-01-01
The subject considered is the stress and deformation fields in a cracked elastic-plastic power law hardening material under plane strain tensile loading. An incremental plasticity finite element formulation is developed for accurate analysis of the complete field problem including the extensively deformed near tip region, the elastic-plastic region, and the remote elastic region. The formulation has general applicability and was used to solve the small scale yielding problem for a set of material hardening exponents. Distributions of stress, strain, and crack opening displacement at the crack tip and through the elastic-plastic zone are presented as a function of the elastic stress intensity factor and material properties.
Development of an elastic cell culture substrate for a novel uniaxial tensile strain bioreactor
Moles, Matthew D; Scotchford, Colin A; Ritchie, Alastair Campbell
2014-01-01
Bioreactors can be used for mechanical conditioning and to investigate the mechanobiology of cells in vitro. In this study a polyurethane (PU), Chronoflex AL, was evaluated for use as a flexible cell culture substrate in a novel bioreactor capable of imparting cyclic uniaxial tensile strain to cells. PU membranes were plasma etched, across a range of operating parameters, in oxygen. Contact angle analysis and X-ray photoelectron spectroscopy showed increases in wettability and surface oxygen were related to both etching power and duration. Atomic force microscopy demonstrated that surface roughness decreased after etching at 20 W but was increased at higher powers. The etching parameters, 20 W 40 s, produced membranes with high surface oxygen content (21%), a contact angle of 66° ± 7° and reduced topographical features. Etching and protein conditioning membranes facilitated attachment, and growth to confluence within 3 days, of MG-63 osteoblasts. After 2 days with uniaxial strain (1%, 30 cycles/min, 1500 cycles/day), cellular alignment was observed perpendicular to the principal strain axis, and found to increase after 24 h. The results indicate that the membrane supports culture and strain transmission to adhered cells. © 2013 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 102A: 2356–2364, 2014. PMID:23946144
NASA Astrophysics Data System (ADS)
Frigeri, Sergio; Stefanelli, Ulisse
2012-01-01
We prove the global existence of solutions for a shape-memory alloys constitutive model at finite strains. The model has been presented in Evangelista et al. (Int J Numer Methods Eng 81(6):761-785, 2010) and corresponds to a suitable finite-strain version of the celebrated Souza-Auricchio model for SMAs (Auricchio and Petrini in Int J Numer Methods Eng 55:1255-1284, 2002; Souza et al. in J Mech A Solids 17:789-806, 1998). We reformulate the model in purely variational fashion under the form of a rate-independent process. Existence of suitably weak (energetic) solutions to the model is obtained by passing to the limit within a constructive time-discretization procedure.
Puisys, Algirdas; Kuoppala, Ritva; Raustia, Aune; Juodzbalys, Gintaras
2016-01-01
ABSTRACT Objectives To systematically review risks of mechanical impact on peri-implant strain and prosthetic influence on stability across finite element studies. Material and Methods An online literature search was performed on MEDLINE and EMBASE databases published between 2011 and 2016. Following keywords tiered screening and selection of the title, abstract and full-text were performed. Studies of finite element analysis (FEA) were considered for inclusion that were written in English and revealed stress concentrations or strain at peri-implant bone level. Results There were included 20 FEA studies in total. Data were organized according to the following topics: bone layers, type of bone, osseointegration level, bone level, design of implant, diameter and length of implant, implant-abutment connection, type of supra-construction, loading axis, measurement units. The stress or strain at implant-bone contact was measured over all studies and numerical values estimated. Risks of overloading were accented as non-axial loading, misfits, cantilevers and the stability of peri-implant bone was related with the usage of platform switch connection of abutment. Conclusions Peri-implant area could be affected by non-axial loading, cantilever prosthetic elements, crown/implant ratio, type of implant-abutment connection, misfits, properties of restoration materials and antagonistic tooth. The heterogeneity of finite element analysis studies limits systematization of data. Results of these studies are comparable with other findings of in vitro, in vivo, prospective and retrospective studies. PMID:27833729
NASA Astrophysics Data System (ADS)
Chakraborty, Bidisha; Heyde, Brecht; Alessandrini, Martino; D'hooge, Jan
2016-04-01
Image registration techniques using free-form deformation models have shown promising results for 3D myocardial strain estimation from ultrasound. However, the use of this technique has mostly been limited to research institutes due to the high computational demand, which is primarily due to the computational load of the regularization term ensuring spatially smooth cardiac strain estimates. Indeed, this term typically requires evaluating derivatives of the transformation field numerically in each voxel of the image during every iteration of the optimization process. In this paper, we replace this time-consuming step with a closed-form solution directly associated with the transformation field resulting in a speed up factor of ~10-60,000, for a typical 3D B-mode image of 2503 and 5003 voxels, depending upon the size and the parametrization of the transformation field. The performance of the numeric and the analytic solutions was contrasted by computing tracking and strain accuracy on two realistic synthetic 3D cardiac ultrasound sequences, mimicking two ischemic motion patterns. Mean and standard deviation of the displacement errors over the cardiac cycle for the numeric and analytic solutions were 0.68+/-0.40 mm and 0.75+/-0.43 mm respectively. Correlations for the radial, longitudinal and circumferential strain components at end-systole were 0.89, 0.83 and 0.95 versus 0.90, 0.88 and 0.92 for the numeric and analytic regularization respectively. The analytic solution matched the performance of the numeric solution as no statistically significant differences (p>0.05) were found when expressed in terms of bias or limits-of-agreement.
Diffraction Profiles of Elasticity Bent Single Crystals with Constant Strain Gradients
Yan,H.; Kalenci, O.; Noyan, I.
2007-01-01
This work presents a set of equations that can be used to predict the dynamical diffraction profile from a non-transparent single crystal with a constant strain gradient examined in Bragg reflection geometry with a spherical incident X-ray beam. In agreement with previous work, the present analysis predicts two peaks: a primary diffraction peak, which would have still been observed in the absence of the strain gradient and which exits the specimen surface at the intersection point of the incident beam with the sample surface, and a secondary (mirage) peak, caused by the deflection of the wavefield within the material, which exits the specimen surface further from this intersection point. The integrated intensity of the mirage peak increases with increasing strain gradient, while its separation from the primary reflection peak decreases. The directions of the rays forming the mirage peak are parallel to those forming the primary diffraction peak. However, their spatial displacement might cause (fictitious) angular shifts in diffractometers equipped with area detectors or slit optics. The analysis results are compared with experimental data from an Si single-crystal strip bent in cantilever configuration, and the implications of the mirage peak for Laue analysis and high-precision diffraction measurements are discussed.
1980-05-31
data that several phenomena which should be modelled by the constitutive theory are: (1) the Bauschinger effect for reverse loading, (2) the nonunique ...evidence of its importance. Although significant work has been done to obtain working constitutive models, in many cases the theory has not been cast...nonlinear visco- elasticity theory for applicability to the conservation of momentum. Based on physical accuracy as well as computational efficiency the
Analysis of a theory of elasticity for masonry solids
NASA Astrophysics Data System (ADS)
Steigmann, D. J.
A N ANALYSIS of a theory of plane elasticity for materials with negligible tensile strength is presented. We show that, when viewed in the context of finite elasticity, this theory furnishes equilibrium deformations that are unstable according to the energy criterion. The equations of equilibrium are shown to be hyperbolic in certain sectors of the principal strain plane. These conclusions contradict predictions based on the existing infinitesimal displacement theory.
NASA Technical Reports Server (NTRS)
Salpekar, S. A.; Raju, I. S.; O'Brien, T. K.
1988-01-01
Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtual crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finte-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.
NASA Astrophysics Data System (ADS)
Rae, Philip J.; Trujillo, Carl P.; Lovato, Manuel L.
2009-12-01
The assumption that Young's modulus is strain-rate invariant is tested for 6061-T6 aluminium alloy and 1018 steel over 10 decades of strain-rate. For the same billets of material, 3 quasi-static strain-rates are investigated with foil strain gauges at room temperature. The ultrasonic sound speeds are measured and used to calculate the moduli at approximately 104 s-1. Finally, 1D plate impact is used to generate an elastic pre-cursor in the alloys at a strain-rate of approximately 106 s1 from which the longitudinal sound speed may be obtained. It is found that indeed the Young's modulus is strain-rate independent within the experimental accuracy.
Rae, Philip J; Trujillo, Carl; Lovato, Manuel
2009-01-01
The assumption that Young's modulus is strain-rate invariant is tested for 6061-T6 aluminium alloy and 1018 steel over 10 decades of strain-rate. For the same billets of material, 3 quasi-static strain-rates are investigated with foil strain gauges at room temperature. The ultrasonic sound speeds are measured and used to calculate the moduli at approximately 10{sup 4} s{sup -1}. Finally, ID plate impact is used to generate an elastic pre-cursor in the alloys at a strain-rate of approximately 10{sup 6} s{sup -1} from which the longitudinal sound speed may be obtained. It is found that indeed the Young's modulus is strain-rate independent within the experimental accuracy.
StrainModeler: A MATHEMATICA™-based program for 3D analysis of finite and progressive strain
NASA Astrophysics Data System (ADS)
Bobillo-Ares, Nilo C.; Aller, Jesús; Bastida, Fernando; Menéndez, Omar; Lisle, Richard J.
2015-05-01
StrainModeler is a program constructed in the MATHEMATICA™ environment that performs 3D progressive strain calculations for lines and planes undergoing any sequence of homogeneous deformations. The main inputs to the system define the initial line or plane to be deformed and the deformation sequence to be applied, including combinations of simple shear, pure shear and volume change. For the deformation of lines, the output of the program is the change of attitude of the initial line, which can be represented by graphics or plotted in an equal-area projection. For the deformation of planes, the program has several outputs: (i) change of attitude of the initial plane; (ii) magnitudes and ratio of the semi-axes of the strain ellipse on the deformed plane; (iii) orientation of the major and minor axes of the strain ellipse on the deformed plane; (iv) orientations of the axial planes of the folds formed on the deformed plane, and (v) area change on the deformed plane. The variation of any of these parameters can be shown against a linear parameter only linked to the number of steps involved in the deformation, as a kind of "time" line, or it can be shown against the variation of a parameter of the strain ellipsoid (e. g.: major axis/minor axis ratio). A sequence of directions can be also visualized as a curve in an equal-area plot. Three applications of the program are presented. In the first, the deformation by simple shear of a plane with any orientation is analyzed. In the second, we explore the formation of recumbent folds in layers with different initial orientations for simple shear and pure shear deformations. In the third, we use StrainModeler to analyze the deformation of a set of folds located in a ductile shear zone in the Variscan Belt of NW Spain.
Strain Rate Tensor Estimation in Cine Cardiac MRI Based on Elastic Image Registration
NASA Astrophysics Data System (ADS)
Sánchez-Ferrero, Gonzalo Vegas; Vega, Antonio Tristán; Grande, Lucilio Cordero; de La Higuera, Pablo Casaseca; Fernández, Santiago Aja; Fernández, Marcos Martín; López, Carlos Alberola
In this work we propose an alternative method to estimate and visualize the Strain Rate Tensor (SRT) in Magnetic Resonance Images (MRI) when Phase Contrast MRI (PCMRI) and Tagged MRI (TMRI) are not available. This alternative is based on image processing techniques. Concretely, image registration algorithms are used to estimate the movement of the myocardium at each point. Additionally, a consistency checking method is presented to validate the accuracy of the estimates when no golden standard is available. Results prove that the consistency checking method provides an upper bound of the mean squared error of the estimate. Our experiments with real data show that the registration algorithm provides a useful deformation field to estimate the SRT fields. A classification between regional normal and dysfunctional contraction patterns, as compared with experts diagnosis, points out that the parameters extracted from the estimated SRT can represent these patterns. Additionally, a scheme for visualizing and analyzing the local behavior of the SRT field is presented.
K.R. Arpin; T.F. Trimble
2003-04-01
This testing was undertaken to develop material true stress-true strain curves for elastic-plastic material behavior for use in performing transient analysis. Based on the conclusions of this test, the true stress-true strain curves derived herein are valid for use in elastic-plastic finite element analysis for structures fabricated from these materials. In addition, for the materials tested herein, the ultimate strain values are greater than those values cited as the limits for the elastic-plastic strain acceptance criteria for transient analysis.
Becker, D.F.; Hoskins, E.R.; Russell, J.E.
1983-03-01
Two-dimensional, finite-difference elastic modeling aids in planning an optimum seismic-acquisition scheme to define the extent of subsurface cavities resulting from in situ gasification. To understand the seismic effects of a cavity, two models are compared and contrasted. Model A consists of a low-velocity layer (LVL) in a half space; Model B contains a rectangular water-filled cavity in the LVL. Amplitude differences are the dominant effect on the surface records for each model. Cavity resonance and diffraction effects are more definitive in vertical seismic profiles (VSP's) and in a ''snapshot'' of the wave field. Interpretation and subtraction of corresponding records for both models shows the need for preand post-gasification seismic recording. Also VSP data are more informative than surface records.
NASA Astrophysics Data System (ADS)
Fan, L. X.; Guo, D. L.; Ren, F.; Xiao, X. H.; Cai, G. X.; Fu, Q.; Jiang, C. Z.
2007-12-01
Elastic strain fields at the interface of the epilayer and buffer layer of the InGaAsP/InP heterostructure were characterized by electron backscatter diffraction (EBSD) technology based on scanning electron microscopy. The InGaAsP/InP heterostructure which contained lattice misfit was under a dislocation-free condition. Image quality (IQ) was used as the strain sensitive parameter. From the image quality map and image quality curve, we observed directly the distribution of the elastic strain fields at the interface along the direction perpendicular to the interface as well as the interface structure between the epilayer and buffer layer by transmission electron microscopy and high resolution transmission microscopy.
NASA Astrophysics Data System (ADS)
Yang, Lei; Yan, Hongyong; Liu, Hong
2017-03-01
Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.
Finite-element method analysis of freestanding microrings for thin-film tensile strain measurements
NASA Astrophysics Data System (ADS)
Boutry, M.; Bosseboeuf, A.; Grandchamp, J. P.; Coffignal, G.
1997-12-01
Freestanding microring structures intended for the measurement of tensile stress or strain in thin films are analysed by linear buckling FEM analysis with thermal loads. It is shown that varying the tie length is helpful for increasing the strain measurement range of narrow devices while limiting the sensitivity factor variation and the wafer surface consumption. This reduces the need for large-diameter microstructures to measure low strain values and allows strain measurements in films with different thicknesses with a lower variation of the relative accuracy.
An elastic-plastic finite-element analysis of the J-resistance curve using a CTOD criterion
NASA Technical Reports Server (NTRS)
Newman, J. C., Jr.; Booth, B. C.; Shivakumar, K. N.
1988-01-01
The fracture process in compact and bend specimens was simulated using a two-dimensional finite-element analysis of the J-resistance (J-R) curve and a CTOD criterion. The J-R curves were calculated from the numerical results for each specimen type using several different methods. In general, the J-R curves obtained for the bend specimens were found to be higher than those for the compact specimens, especially beyond maximum load. However, below the maximum load, the modified deformation theory of plasticity and the contour-integral J(r) method resulted in very similar J-R curves for both specimen types.
NASA Technical Reports Server (NTRS)
Hashemi-Kia, Mostafa; Kilroy, Kevin L.; Parker, G.
1990-01-01
A computational procedure is described which can be used efficiently in identifying modeling errors which may arise from development of a structural finite element model. The procedure, which is referred to as the multi-level strain energy check, is set up in the form of a set of NASTRAN DMAP alters which provide sufficient information about the modeling errors at G-Set, N-Set, and F-Set levels. This technique was applied to two NASTRAN models, namely, the AH-64A and AH-1G models. Two modeling errors were identified for the AH-1G, which were then corrected.
NASA Astrophysics Data System (ADS)
Kroon, M.
2011-11-01
Rubbers and soft biological tissues may undergo large deformations and are also viscoelastic. The formulation of constitutive models for these materials poses special challenges. In several applications, especially in biomechanics, these materials are also relatively thin, implying that in-plane stresses dominate and that plane stress may therefore be assumed. In the present paper, a constitutive model for viscoelastic materials in the finite strain regime and under the assumption of plane stress is proposed. It is assumed that the relaxation behaviour in the direction of plane stress can be treated separately, which makes it possible to formulate evolution laws for the plastic strains on explicit form at the same time as incompressibility is fulfilled. Experimental results from biomechanics (dynamic inflation of dog aorta) and rubber mechanics (biaxial stretching of rubber sheets) were used to assess the proposed model. The assessment clearly indicates that the model is fully able to predict the experimental outcome for these types of material.
1992-02-04
idealized material. Fig. 4.14 Comparison of predicted strain path with that measured from experiment on Hostun sand performed by Lanier and Zitouni (1988...shows the comparison of predicted strain path with that measured from experiments on Hostun sand performed by Lanier and Zitouni (1988).I 4.2.4 Direct...4.14 Comparison of predicted strain path with that measured from experiment on Hostun sand performed by Lanier and Zitouni (1988). I I 1 71 1 1.0 0.12
NASA Astrophysics Data System (ADS)
Denu, Garuma Abdisa; Liu, Zongchen; Fu, Jiao; Wang, Hongxing
2017-01-01
We report the effect of geometrical shape of diamond nanowire on its mechanical properties. Finite element modeling using COMSOL Multiphysics software is used to simulate various diamond nanowire with circular, square, rectangular, hexagonal and triangular cross-sections. A bending test under concentrated load applied at one of the free ends is simulated using FEM. The force response of the nanowire under different loading is studied for the various cross-sections. The dimensions of each cross-section is chosen so that material properties such as Young's modulus can be kept constant for comparison in all the cross-sections. It is found out that the bending capability of a triangular nanowire is higher compared to other cross-sections due to its lowest second moment. Circular and hexagonal cross-section show highest stiffness. The study of mechanical property of diamond nanowires is useful for optimal nanomechanical designs where the effect of cross-section has to be taken into account.
NASA Technical Reports Server (NTRS)
Xue, W.-M.; Atluri, S. N.
1985-01-01
In this paper, all possible forms of mixed-hybrid finite element methods that are based on multi-field variational principles are examined as to the conditions for existence, stability, and uniqueness of their solutions. The reasons as to why certain 'simplified hybrid-mixed methods' in general, and the so-called 'simplified hybrid-displacement method' in particular (based on the so-called simplified variational principles), become unstable, are discussed. A comprehensive discussion of the 'discrete' BB-conditions, and the rank conditions, of the matrices arising in mixed-hybrid methods, is given. Some recent studies aimed at the assurance of such rank conditions, and the related problem of the avoidance of spurious kinematic modes, are presented.
Brunt, Lucy H.; Norton, Joanna L.; Bright, Jen A.; Rayfield, Emily J.; Hammond, Chrissy L.
2015-01-01
Abnormal joint morphogenesis is linked to clinical conditions such as Developmental Dysplasia of the Hip (DDH) and to osteoarthritis (OA). Muscle activity is known to be important during the developmental process of joint morphogenesis. However, less is known about how this mechanical stimulus affects the behaviour of joint cells to generate altered morphology. Using zebrafish, in which we can image all joint musculoskeletal tissues at high resolution, we show that removal of muscle activity through anaesthetisation or genetic manipulation causes a change to the shape of the joint between the Meckel's cartilage and Palatoquadrate (the jaw joint), such that the joint develops asymmetrically leading to an overlap of the cartilage elements on the medial side which inhibits normal joint function. We identify the time during which muscle activity is critical to produce a normal joint. Using Finite Element Analysis (FEA), to model the strains exerted by muscle on the skeletal elements, we identify that minimum principal strains are located at the medial region of the joint and interzone during mouth opening. Then, by studying the cells immediately proximal to the joint, we demonstrate that biomechanical strain regulates cell orientation within the developing joint, such that when muscle-induced strain is removed, cells on the medial side of the joint notably change their orientation. Together, these data show that biomechanical forces are required to establish symmetry in the joint during development. PMID:26253758
Rayfield, Emily J
2011-01-01
Finite element (FE) analysis is becoming a frequently used tool for exploring the craniofacial biomechanics of extant and extinct vertebrates. Crucial to the application of the FE analysis is the knowledge of how well FE results replicate reality. Here I present a study investigating how accurately FE models can predict experimentally derived strain in the mandible of the ostrich Struthio camelus, when both the model and the jaw are subject to identical conditions in an in-vitro loading environment. Three isolated ostrich mandibles were loaded hydraulically at the beak tip with forces similar to those measured during force transducer pecking experiments. Strains were recorded at four gauge sites at the dorsal and ventral dentary, and medial and lateral surangular. Specimen-specific FE models were created from computed tomography scans of each ostrich and loaded in an identical fashion as in the in-vitro test. The results show that the strain magnitudes, orientation, patterns and maximum : minimum principal strain ratios are predicted very closely at the dentary gauge sites, even though the FE models have isotropic and homogeneous material properties and solid internal geometry. Although the strain magnitudes are predicted at the postdentary sites, the strain orientations and ratios are inaccurate. This mismatch between the dentary and postdentary predictions may be due to the presence of intramandibular sutures or the greater amount of cancellous bone present in the postdentary region of the mandible and requires further study. This study highlights the predictive potential of even simple FE models for studies in extant and extinct vertebrates, but also emphasizes the importance of geometry and sutures. It raises the question of whether different parameters are of lesser or greater importance to FE validation for different taxonomic groups. PMID:20846282
NASA Astrophysics Data System (ADS)
Hu, Jiafei; Pan, Mengchun; Xin, Jianguang; Chen, Dixiang
2008-12-01
The magnetostrictive transducer is the most important part of the optic-fiber magnetic field sensor, and the optic-fiber/giant magnetostrictive(GMS) film coupled structure is a novel coupling form of the magnetostrictive transducer. Always we analyze the coupled structure based on the entire coupled structure being sputtered GMS material without tail-fibers. In practical application, the coupled structure has tail-fibers without films at two ends. When the entire coupled structure is immersed in the detected magnetic field, the detected magnetic field causes the GMS film strain then causing optic-fiber strain. This strain transmission process is different from it in the coupled structure entirely with GMS films without tail-fibers. The strain transmission relationship can be calculated theoretically in the coupled structure without tail-fibers, but it's complicated to theoretically calculate the strain transmission relationship in the coupled structure with tail-fibers. After large numbers of calculations and analyses by ANSYS software, we figure out some relationships of the two strain transmission processes in the respective structures and the stress distribution in the tail-fibers. These results are helpful to the practical application of the optic-fiber/ GMS film coupled structure.
NASA Astrophysics Data System (ADS)
Ooi, B. L.; Gilbert, J. M.; Aziz, A. Rashid A.
2016-08-01
Owing to the increasing demand for harvesting energy from environmental vibration for use in self-powered electronic applications, cantilever-based vibration energy harvesting has attracted considerable interest from various parties and has become one of the most common approaches to converting redundant mechanical energy into electrical energy. As the output voltage produced from a piezoelectric material depends largely on the geometric shape and the size of the beam, there is a need to model and compare the performance of cantilever beams of differing geometries. This paper presents the study of strain distribution in various shapes of cantilever beams, including a convex and concave edge profile elliptical beam that have not yet been discussed in any prior literature. Both analytical and finite-element models are derived and the resultant strain distributions in the beam are computed based on a MATLAB solver and ANSYS finite-element analysis tools. An optimum geometry for a vibration-based energy harvesting system is verified. Finally, experimental results comparing the power density for triangular and rectangular piezoelectric beams are also presented to validate the findings of the study, and the claim, as suggested in the literature, is verified.
Le Floc'h, Simon; Cloutier, Guy; Saijo, Yoshifumi; Finet, Gérard; Yazdani, Saami K; Deleaval, Flavien; Rioufol, Gilles; Pettigrew, Roderic I; Ohayon, Jacques
2012-12-01
Plaque elasticity (i.e., modulogram) and morphology are good predictors of plaque vulnerability. Recently, our group developed an intravascular ultrasound (IVUS) elasticity reconstruction method which was successfully implemented in vitro using vessel phantoms. In vivo IVUS modulography, however, remains a major challenge as the motion of the heart prevents accurate strain field estimation. We therefore designed a technique to extract accurate strain fields and modulograms from recorded IVUS sequences. We identified a set of four criteria based on tissue overlapping, RF-correlation coefficient between two successive frames, performance of the elasticity reconstruction method to recover the measured radial strain, and reproducibility of the computed modulograms over the cardiac cycle. This four-criterion selection procedure (4-CSP) was successfully tested on IVUS sequences obtained in twelve patients referred for a directional coronary atherectomy intervention. This study demonstrates the potential of the IVUS modulography technique based on the proposed 4-CSP to detect vulnerable plaques in vivo.
NASA Astrophysics Data System (ADS)
Das, Sujit; Herklotz, Andreas; Jia Guo, Er; Dörr, Kathrin
2014-04-01
[La0.7Ca0.3MnO3(2.6 nm)/SrTiO3(6.3 nm)]15 superlattices (SLs) have been simultaneously grown by Pulsed Laser Deposition (PLD) on different oxide substrates in an attempt to obtain different residual strain states. The substrates are (100)-oriented SrTiO3 (STO), LaAlO3 (LAO), and piezoelectric 0.72Pb (Mg1.3 Nb2.3)3-0.28PbTiO3 (PMN-PT). The La0.7Ca0.3MnO3 layers show tensile strain of ɛ = 1% on LAO and stronger strain on STO and PMN-PT (ɛ = 1.7%). The magnetization has been measured and is found to be quite different for the three SLs. Reversible biaxial compression of Δɛ=-0.1% using the PMN-PT substrate helps one to estimate which part of the differences in magnetic order among the samples is induced by elastic strain. The influence of elastic strain is found to be substantial, but does not completely account for the different behavior of the samples.
Zhang, Bao; Arola, Dwayne D; Roys, Steve; Gullapalli, Rao P
2011-08-01
The use of magnetic resonance (MR) imaging in conjunction with an endorectal coil is currently the clinical standard for the diagnosis of prostate cancer because of the increased sensitivity and specificity of this approach. However, imaging in this manner provides images and spectra of the prostate in the deformed state because of the insertion of the endorectal coil. Such deformation may lead to uncertainties in the localization of prostate cancer during therapy. We propose a novel 3-D elastic registration procedure that is based on the minimization of a physically motivated strain energy function that requires the identification of similar features (points, curves, or surfaces) in the source and target images. The Gauss-Seidel method was used in the numerical implementation of the registration algorithm. The registration procedure was validated on synthetic digital images, MR images from prostate phantom, and MR images obtained on patients. The registration error, assessed by averaging the displacement of a fiducial landmark in the target to its corresponding point in the registered image, was 0.2 ± 0.1 pixels on synthetic images. On the prostate phantom and patient data, the registration errors were 1.0 ± 0.6 pixels (0.6 ± 0.4 mm) and 1.8 ± 0.7 pixels (1.1 ± 0.4 mm), respectively. Registration also improved image similarity (normalized cross-correlation) from 0.72 ± 0.10 to 0.96 ± 0.03 on patient data. Registration results on digital images, phantom, and prostate data in vivo demonstrate that the registration procedure can be used to significantly improve both the accuracy of localized therapies such as brachytherapy or external beam therapy and can be valuable in the longitudinal follow-up of patients after therapy.
NASA Astrophysics Data System (ADS)
Ihringer, J.; Abrahams, S. C.
1984-12-01
Group-theoretical normal-mode analysis of the antifluorite A2BX6 structure in space group P4mnc (D64h) identifies two effective modes with Eg symmetry. Either mode may condense independently of the other at the phase transition to space group P21n (C52h). One mode produces a displacement of the A+ ions, the other a rotation of the BX62- octahedra. Lattice distortion thereby results from the coupling between order parameter (Q) and elastic strain (e). Linear and quadratic symmetry invariant coupling in terms of free energy results in e13~Q and, independently, e22-e11 ~Q2. The linear coupling produces a discontinuous change in soft-mode frequency at Tc, whereas the change in specific heat is caused primarily by the quadratic coupling. Measurements on K2TeBr6 reveal that one Eg mode condenses at the second-order phase transition to P21n at 400 K and follows a Landau critical power law with e13 ~(400K-T)12, leaving e22-e11=0 for 359
Pettit, J. R.; Walker, A.; Lowe, M. J. S.
2014-02-18
Defects which posses rough surfaces greatly affect ultrasonic wave scattering behaviour, often reducing the magnitude of reflected signals. Ultrasonic inspections rely upon this response for detecting and sizing flaws. For safety critical components reliable characterisation is crucial. Therefore, providing an accurate means to predict reductions in signal amplitude is essential. An extension of Kirchhoff theory has formed the basis for the UK power industry inspection justifications. However, it is widely recognised that these predictions are pessimistic owing to analytical approximations. A numerical full field modelling approach does not fall victim to such limitations. Here, a Finite Element model is used to aid in setting a non-conservative reporting threshold during the inspection of a large pressure vessel forging that might contain embedded rough defects. The ultrasonic response from multiple rough surfaces defined by the same statistical class is calculated for normal incident compression waves. The approach is validated by comparing coherent scattering with predictions made by Kirchhoff theory. At lower levels of roughness excellent agreement is observed, whilst higher values confirm the pessimism of Kirchhoff theory. Furthermore, the mean amplitude in the specular direction is calculated. This represents the information obtained during an inspection, indicating that reductions due to increasing roughness are significantly less than the coherent component currently being used.
NASA Astrophysics Data System (ADS)
Wakefield, David
Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures. Founded upon their inTENS finite element analysis suite, these activities have broadened to encompass ‘lighter than air' structures such as aerostats, hybrid air-vehicles and stratospheric balloons. Since 2004 Tensys have acted as consultants to the NASA Ultra Long Duration Balloon (ULDB) Program. Early implementations of the super-pressure balloon design chosen for ULDB have shown problems of geometric instability, characterised by improper deployment and the potential for overall geometric instability once deployed. The latter has been reproduced numerically using inTENS, and the former are better understood following a series of large-scale hangar tests simulating launch and ascent. In both cases the solution lies in minimising the film lobing between the tendons. These tendons, which span between base and apex end fittings, cause the characteristic pumpkin shape of the balloons and also provide valuable constraint against excessive film deformation. There is also the requirement to generate a biaxial stress field in order to mobilise in-plane shear stiffness. A consequence of reduced lobing between tendons is the development of higher stresses in the balloon film under pressure. The different thermal characteristics between tendons and film lead to further significant meridional stress under low temperature flight conditions. The non-linear viscoelastic response of the envelope film acts positively to help dissipate excessive stress and local concentrations. However, creep over time may produce lobe geometry variations sufficient to compromise the geometric stability of the balloon. The design of a balloon requires an analysis approach that addresses the questions of stress and stability over the duration of a flight by time stepping analyses using an appropriate material model. This paper summarises the Dynamic Relaxation
NASA Astrophysics Data System (ADS)
Sun, Yongle; Li, Q. M.; Withers, P. J.
2015-09-01
Realistic simulations are increasingly demanded to clarify the dynamic behaviour of foam materials, because, on one hand, the significant variability (e.g. 20% scatter band) of foam properties and the lack of reliable dynamic test methods for foams bring particular difficulty to accurately evaluate the strain-rate sensitivity in experiments; while on the other hand numerical models based on idealised cell structures (e.g. Kelvin and Voronoi) may not be sufficiently representative to capture the actual structural effect. To overcome these limitations, the strain-rate sensitivity of the compressive and tensile properties of closed-cell aluminium Alporas foam is investigated in this study by means of meso-scale realistic finite element (FE) simulations. The FE modelling method based on X-ray computed tomography (CT) image is introduced first, as well as its applications to foam materials. Then the compression and tension of Alporas foam at a wide variety of applied nominal strain-rates are simulated using FE model constructed from the actual cell geometry obtained from the CT image. The stain-rate sensitivity of compressive strength (collapse stress) and tensile strength (0.2% offset yield point) are evaluated when considering different cell-wall material properties. The numerical results show that the rate dependence of cell-wall material is the main cause of the strain-rate hardening of the compressive and tensile strengths at low and intermediate strain-rates. When the strain-rate is sufficiently high, shock compression is initiated, which significantly enhances the stress at the loading end and has complicated effect on the stress at the supporting end. The plastic tensile wave effect is evident at high strain-rates, but shock tension cannot develop in Alporas foam due to the softening associated with single fracture process zone occurring in tensile response. In all cases the micro inertia of individual cell walls subjected to localised deformation is found to
Kheirollahi, Hossein; Luo, Yunhua
2015-01-01
Accurate assessment of hip fracture risk is very important to prevent hip fracture and to monitor the effect of a treatment. A subject-specific QCT-based finite element model was constructed to assess hip fracture risk at the critical locations of femur during the single-leg stance and the sideways fall. The aim of this study was to improve the prediction of hip fracture risk by introducing a novel failure criterion to more accurately describe bone failure mechanism. Hip fracture risk index was defined using cross-section strain energy, which is able to integrate information of stresses, strains, and material properties affecting bone failure. It was found that the femoral neck and the intertrochanteric region have higher fracture risk than other parts of the femur, probably owing to the larger content of cancellous bone in these regions. The study results also suggested that women are more prone to hip fracture than men. The findings in this study have a good agreement with those clinical observations reported in the literature. The proposed hip fracture risk index based on strain energy has the potential of more accurate assessment of hip fracture risk. However, experimental validation should be conducted before its clinical applications. PMID:26601105
Savage, P; O'Donnell, B P; McHugh, P E; Murphy, B P; Quinn, D F
2004-02-01
Cardiovascular stents are metal scaffolds that are used in the treatment of atherosclerosis. These devices are typically composed of very thin struts (< or = 100 microm thickness, for coronary applications). At this size-scale the question arises as to the suitability of using bulk material properties in stent design. This paper investigates the use of finite element analysis to predict the mechanical failure of stent struts, typical of the strut size used in coronary stents. 316 L stainless steel in uniaxial loading was considered. To accurately represent the constitutive behavior of the material at this size-scale, a computational micromechanics approach was taken involving an explicit representation of the grain structure in the steel struts, and the use of crystal plasticity theory to represent the constitutive behavior of the individual grains. The development of the finite element models is discussed and results are presented for the predictions of tensile mechanical behavior as a function of strut thickness. The results showed that using this modelling approach, a size effect, already seen experimentally, is produced. This has significant implications for stent design, especially in the context of the desire to produce smaller stents for small bore neurovascular and peripheral artery applications.
NASA Astrophysics Data System (ADS)
Ali, Nasir; Asghar, Zaheer
2014-09-01
We have investigated the peristaltic motion of a non-Newtonian fluid characterized by the finitely extendable nonlinear elastic-Peterlin (FENE-P) fluid model. A background for the development of the differential constitutive equation of this model has been provided. The flow analysis is carried out both for two-dimensional planar channel and axisymmetric tube. The governing equations have been simplified under the widely used assumptions of long wavelength and low Reynolds number in a frame of reference that moves with constant wave speed. An exact solution is obtained for the stream function and longitudinal pressure gradient with no slip condition. We have portrayed the effects of Deborah number and extensibility parameter on velocity profile, trapping phenomenon, and normal stress. It is observed that normal stress is an increasing function of Deborah number and extensibility parameter. As far as the velocity at the channel (tube) center is concerned, it decreases (increases) by increasing Deborah number (extensibility parameter). The non-Newtonian rheology also affect the size of trapped bolus in a sense that it decreases (increases) by increasing Deborah number (extensibility parameter). Further, it is observed through numerical integration that both Deborah number and extensibility parameter have opposite effects on pressure rise per wavelength and frictional forces at the wall. Moreover, it is shown that the results for the Newtonian model can be deduced as a special case of the FENE-P model
Stribeck, Norbert; Zeinolebadi, Ahmad; Fakirov, Stoyko; Bhattacharyya, Debes; Botta, Stephan
2013-01-01
Straining of PVA/PE and PVA/PP blends (70:30) is monitored by small-angle x-ray scattering (SAXS). Sheet-extruded films with different predraw ratio are investigated. The discrete SAXS of predrawn samples originates from polyolefin nanofibrils inside of polyolefin microfibrils immersed in a PVA matrix. PE nanofibrils deform less than the macroscopic strain without volume change. PP nanofibrils experience macroscopic strain. They lengthen but their diameter does not decrease. This is explained by strain-induced crystallization of PP from an amorphous depletion shell around the core of the nanofibril. The undrawn PVA/PE film exhibits isotropic semicrystalline nanostructure. Undrawn PVA/PP holds PP droplets containing oriented stacks of semicrystalline PP like neat precursors of hard-elastic thermoplasts. Respective predrawn films are softer than the undrawn material, indicating conversion into the hard-elastic state. Embedding of the polyolefin significantly retards neck formation. The polyolefin microfibrils can easily be extracted from the water-soluble matrix. PMID:27877579
Error localization of finite element updating model based on element strain energy
NASA Astrophysics Data System (ADS)
Huang, Zi; Zang, Chaoping; Wang, Xiaowei; Jiang, Yuying
2016-09-01
An error localization indicator based on modal strain energy changes is proposed and used for selecting design parameters to be updated in model updating process. Taking an aeroengine combustor casing structure as an example, the ‘supermodel’ of combustor casing was established and validated with the test data and the reduced model (also called the design model) was built with the simplification of modelling. By comparing the modal strain energy changes between ‘supermodel’ and design model of combustor casing, the error locations of the reduced combustor casing modelling was highlighted by the error localization indicator. Then, the updating parameters of the design model were selected as the areas with significant variations of modal strain energy changes based on the error localization indicator. Defining the updating object function with the minimum of natural frequency errors between the FE model prediction and the modal test data, model updating of the design combustor casing model based sensitivity analysis method was carried out using the experimental modal data. After model updating, the maximum frequency error of the first ten modes was decreased from 27.1% to 1.2%, compared with the test data. The result shows the effectiveness of the proposed method and certain significance in parameter selection for model updating.
NASA Technical Reports Server (NTRS)
Gayda, J.
1994-01-01
A specialized, microstructural lattice model, termed MCFET for combined Monte Carlo Finite Element Technique, has been developed to simulate microstructural evolution in material systems where modulated phases occur and the directionality of the modulation is influenced by internal and external stresses. Since many of the physical properties of materials are determined by microstructure, it is important to be able to predict and control microstructural development. MCFET uses a microstructural lattice model that can incorporate all relevant driving forces and kinetic considerations. Unlike molecular dynamics, this approach was developed specifically to predict macroscopic behavior, not atomistic behavior. In this approach, the microstructure is discretized into a fine lattice. Each element in the lattice is labeled in accordance with its microstructural identity. Diffusion of material at elevated temperatures is simulated by allowing exchanges of neighboring elements if the exchange lowers the total energy of the system. A Monte Carlo approach is used to select the exchange site while the change in energy associated with stress fields is computed using a finite element technique. The MCFET analysis has been validated by comparing this approach with a closed-form, analytical method for stress-assisted, shape changes of a single particle in an infinite matrix. Sample MCFET analyses for multiparticle problems have also been run and, in general, the resulting microstructural changes associated with the application of an external stress are similar to that observed in Ni-Al-Cr alloys at elevated temperatures. This program is written in FORTRAN for use on a 370 series IBM mainframe. It has been implemented on an IBM 370 running VM/SP and an IBM 3084 running MVS. It requires the IMSL math library and 220K of RAM for execution. The standard distribution medium for this program is a 9-track 1600 BPI magnetic tape in EBCDIC format.
Costanzo, Francesco; Brasseur, James G
2015-03-01
There are strong medical motivations to measure changes in material properties of tubular organs, in vivo and in vitro. The current approach estimates hoop stress from intraluminal pressure using the Laplace law and identifies 'elastic modulus' as the slope of a curve fitted hoop stress plotted against strain data. We show that this procedure is fundamentally flawed because muscle and other soft tissue are closely incompressible, so that the total stress includes a volume-preserving material-dependent hydrostatic response that invalidates the method. Furthermore, we show that the Laplace law incorrectly estimates total stress in biological vessels. However, the great need to estimate elastic modulus leads us to develop an alternative practical method, based on shear stress-strain, i.e. insensitive to nonelastic response from incompressibility, but that uses the same measurement data as the current (incorrect) method. The individual material parameters in the underlying (unknown) constitutive relation combine into an effective shear modulus that is a true measure of elastic response, unaffected by incompressibility and without reference to the Laplace law. Furthermore, our effective shear modulus is determined directly as a function of deformation, rather than as the slope of a fitted curve. We validate our method by comparing effective shear moduli against exact shear moduli for four theoretical materials with different degrees of nonlinearity and numbers of material parameters. To further demonstrate applicability, we reanalyse an in vivo study with our new method and show that it resolves an inconsistent change in modulus with the current method.
NASA Technical Reports Server (NTRS)
Arya, V. K.
1990-01-01
The viability of advanced viscoplastic models for nonlinear finite element analyses of structural components is investigated. Several uniaxial and a multiaxial problem are analyzed using the finite element implementation of Freed's viscoplastic model. Good agreement between the experimental and calculated uniaxial results validates the finite element implementation and gives confidence to apply it to more complex multiaxial problems. A comparison of results for a sample structural component (the cowl lip of a hypersonic engine inlet) with the earlier elastic, elastic-plastic, and elastic-plastic-creep analyses available in the literature shows that the elastic-viscoplastic analyses yield more reasonable stress and strain distributions. Finally, the versatility of the finite-element-based solution technology presented herein is demonstrated by applying it to another viscoplastic model.
NASA Astrophysics Data System (ADS)
Reinoso, J.; Paggi, M.; Linder, C.
2017-02-01
Fracture of technological thin-walled components can notably limit the performance of their corresponding engineering systems. With the aim of achieving reliable fracture predictions of thin structures, this work presents a new phase field model of brittle fracture for large deformation analysis of shells relying on a mixed enhanced assumed strain (EAS) formulation. The kinematic description of the shell body is constructed according to the solid shell concept. This enables the use of fully three-dimensional constitutive models for the material. The proposed phase field formulation integrates the use of the (EAS) method to alleviate locking pathologies, especially Poisson thickness and volumetric locking. This technique is further combined with the assumed natural strain method to efficiently derive a locking-free solid shell element. On the computational side, a fully coupled monolithic framework is consistently formulated. Specific details regarding the corresponding finite element formulation and the main aspects associated with its implementation in the general purpose packages FEAP and ABAQUS are addressed. Finally, the applicability of the current strategy is demonstrated through several numerical examples involving different loading conditions, and including linear and nonlinear hyperelastic constitutive models.
NASA Astrophysics Data System (ADS)
Jain, Rahul; Pal, Surjya Kanta; Singh, Shiv Brat
2017-02-01
Friction Stir Welding (FSW) is a solid state joining process and is handy for welding aluminum alloys. Finite Element Method (FEM) is an important tool to predict state variables of the process but numerical simulation of FSW is highly complex due to non-linear contact interactions between tool and work piece and interdependency of displacement and temperature. In the present work, a three dimensional coupled thermo-mechanical method based on Lagrangian implicit method is proposed to study the thermal history, strain distribution and thermo-mechanical process in butt welding of Aluminum alloy 2024 using DEFORM-3D software. Workpiece is defined as rigid-visco plastic material and sticking condition between tool and work piece is defined. Adaptive re-meshing is used to tackle high mesh distortion. Effect of tool rotational and welding speed on plastic strain is studied and insight is given on asymmetric nature of FSW process. Temperature distribution on the workpiece and tool is predicted and maximum temperature is found in workpiece top surface.
NASA Astrophysics Data System (ADS)
Kenna, A.; Basu, B.
2015-07-01
Wind turbine support towers at heights in excess of 90m are nowadays being formed in steel, concrete and hybrid concrete and steel structures. As is the case for all towers of this height, the towers will be assembled using a number of segments, which will be connected in some way. These local connections are to be viewed as areas of potential local weakness in the overall tower assembly and require care in terms of design and construction. This work concentrates on identifying local damage which can occur at an interface connection by either material or bolt/tendon failure. Spatial strain patterns will be used to try to identify local damage areas around a 3 dimensional tower shell. A Finite Element (FE) model will be assembled which will describe a hybrid tower as a continuum of four-noded, two-dimensional Reisser- Mindlin shell elements. In order to simulate local damage, an element around the circumference of the tower interface will be subjected to a reduced stiffness. Strain patterns will be observed both in the undamaged and damaged states and these signals will be processed using a Discrete Wavelet Transform (DWT) algorithm to investigate if the damaged element can be identified.
NASA Astrophysics Data System (ADS)
Jain, Rahul; Pal, Surjya Kanta; Singh, Shiv Brat
2016-06-01
Friction Stir Welding (FSW) is a solid state joining process and is handy for welding aluminum alloys. Finite Element Method (FEM) is an important tool to predict state variables of the process but numerical simulation of FSW is highly complex due to non-linear contact interactions between tool and work piece and interdependency of displacement and temperature. In the present work, a three dimensional coupled thermo-mechanical method based on Lagrangian implicit method is proposed to study the thermal history, strain distribution and thermo-mechanical process in butt welding of Aluminum alloy 2024 using DEFORM-3D software. Workpiece is defined as rigid-visco plastic material and sticking condition between tool and work piece is defined. Adaptive re-meshing is used to tackle high mesh distortion. Effect of tool rotational and welding speed on plastic strain is studied and insight is given on asymmetric nature of FSW process. Temperature distribution on the workpiece and tool is predicted and maximum temperature is found in workpiece top surface.
Finite Element Simulation of Sheet Metal Forming Using Anisotropic Strain-Rate Potentials
Rabahallah, Meziane; Balan, Tudor; Bouvier, Salima; Bacroix, Brigitte; Teodosiu, Cristian
2007-05-17
In continuum mechanics, plastic anisotropy is described using anisotropic stress potentials or, alternatively, strain-rate potentials. In this work, a stress update algorithm is developed for this later case. The implicit, backward Euler method is adopted. A specific numerical treatment is required to deal with the plasticity criterion, which is not defined explicitly. Also, a sub-stepping procedure is adopted in order to deal with the strong nonlinearity of the yield surfaces when applied to FCC materials. The resulting algorithm is implemented in the static implicit version of the Abaqus FE code. Several recent plastic potentials have been implemented in this framework and their parameters identified for a number of BCC and FCC materials. Numerical simulations of a cup drawing process are performed in order to address the robustness of the implementation and the ability of these potentials to predict e.g. earing for materials with different anisotropy.
On numerically accurate finite element
NASA Technical Reports Server (NTRS)
Nagtegaal, J. C.; Parks, D. M.; Rice, J. R.
1974-01-01
A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional element types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing finite element program, is presented. This allows accurate computations to be made even for element designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various element designs and of the new variational procedure are illustrated. Elastic-plastic computation at finite strain are discussed.
Schileo, Enrico; Taddei, Fulvia; Cristofolini, Luca; Viceconti, Marco
2008-01-01
No agreement on the choice of the failure criterion to adopt for the bone tissue can be found in the literature among the finite element studies aiming at predicting fracture risk of bones. The use of stress-based criteria seems to prevail on strain-based ones, while basic bone biomechanics suggest using strain parameters to describe failure. The aim of the present combined experimental-numerical study was to verify, using subject-specific finite element models able to accurately predict strains, if a strain-based failure criterion could identify the failure patterns of bones. Three cadaver femurs were CT-scanned and subsequently fractured in a clinically relevant single-stance loading scenario. Load-displacement curves and high-speed movies were acquired to define the failure load and the location of fracture onset, respectively. Subject-specific finite element models of the three femurs were built from CT data following a validated procedure. A maximum principal strain criterion was implemented in the finite element models, and two stress-based criteria selected for comparison. The failure loads measured were applied to the models, and the computed risks of fracture were compared to the results of the experimental tests. The proposed principal strain criterion managed to correctly identify the level of failure risk and the location of fracture onset in all the modelled specimens, while Von Mises or maximum principal stress criteria did not give significant information. A maximum principal strain criterion can thus be defined a suitable candidate for the in vivo risk factor assessment on long bones.
An inclusion in one of two joined isotropic elastic half-spaces
NASA Astrophysics Data System (ADS)
Walpole, L. J.
1997-10-01
Two dissimilar, homogeneous and istropic, elastic half-spaces are bonded together over thier infinite plane of contract. An arbitrarily shaped finite part of one of them (an inclusion) tends spontaneously to undergo a unifrom infinitesimal strain, but, as it remains attached to and restrained by the surrounding material, an equilibrated state of stress and strain is established everywhere instead. By adopting a convenient expression for the fundamental field of a point force, we transformed inclusion. For a general shape of the inclussion and for particular spherical and finite cylindrical shapes in detail, we consider the evaluation of the elastic strain energy, especially of the interaction term which depends on the location of the inclusion and both pairs of elastic moduli, and which is of great significance in physical applications.
NASA Astrophysics Data System (ADS)
Kurz, I.; Roy, M.
2014-12-01
While we are aware of the extent and distribution of strain at the surface near the Pacific-North America plate boundary at the San Andreas Fault (SAF) system in California, at depth, our understanding is poor. Recent seismic observations suggest a narrow shear zone throughout the lithosphere corresponding to the narrow plate boundary at the surface. Surrounding the SAF in California, measurements of seismic anisotropy demonstrate orientations which vary depending on the location relative to the fault. Specifically, in northern California, the orientations align along the fault in its proximity, and in the east-west direction elsewhere. We investigate how the finite-strain ellipsoid (FSE) evolves for tracers in a 3D model of the lithosphere and asthenosphere beneath the SAF. The top surface of the mesh has a right-lateral strike-slip velocity boundary condition, and the bottom, a uniform asthenospheric flow velocity condition perpendicular to the strike-slip fault. We calculate the orientations of the FSE for various ratios of strike-slip to asthenospheric velocity and viscosity stratification. The two classes of models which we investigate simulate an asthenospheric channel beneath a uniform-thickness lithosphere and a variable-depth lithosphere-asthenosphere boundary (LAB). In an isoviscous fluid beneath a uniform-thickness lithosphere, strain rates, and thus FSE orientations, are constant throughout the channel, dependent on the ratio of the velocities but not the viscosity. For a two-layered asthenospheric channel of a higher-viscosity layer overlying a lower-viscosity layer, FSE orientations align with the strike-slip boundary in the upper layer and the drag in the lower layer. When we emulate a lithosphere of variable thickness across the fault by increasing the viscosity of the upper layer, we observe asymmetric FSE orientations across the step in the LAB. The direction of lithospheric thickening across the strike-slip fault govern these orientations
NASA Astrophysics Data System (ADS)
Ma, ShengQian; Li, Feng; Geng, JiGuo
2017-04-01
Since efficient synthesis of C2N holey two-dimensional (h2D) crystal has been possible, bandgap modulation through use of analogous nanoribbon and nanotube structures has attracted strong interest. In this study, bandgap modulation of Si2N-h2D nanoribbons and nanotubes under elastic strain has been deeply researched using density functional theory calculations. The results indicate that the bandgap of Si2N-h2D nanoribbons and nanotubes in zigzag and armchair configurations can be tuned in both directions, namely by stretching or compressing, in the range of ɛ = ( d - d 0)/ d 0 from -10% to 10%. It is also found that the bandgap of Si2N-h2D nanoribbons and nanotubes varies with their width. Therefore, it is predicted that Si2N-h2D nanoribbons and nanotubes have great potential for application in nanoscale strain sensors and optoelectronics.
Liao, Sheng-hui; Zhu, Xing-hao; Xie, Jing; Sohodeb, Vikesh Kumar; Ding, Xi
2016-01-01
The objective of this investigation is to analyze the influence of trabecular microstructure modeling on the biomechanical distribution of the implant-bone interface. Two three-dimensional finite element mandible models, one with trabecular microstructure (a refined model) and one with macrostructure (a simplified model), were built. The values of equivalent stress at the implant-bone interface in the refined model increased compared with those of the simplified model and strain on the contrary. The distributions of stress and strain were more uniform in the refined model of trabecular microstructure, in which stress and strain were mainly concentrated in trabecular bone. It was concluded that simulation of trabecular bone microstructure had a significant effect on the distribution of stress and strain at the implant-bone interface. These results suggest that trabecular structures could disperse stress and strain and serve as load buffers. PMID:27403424
Hanson, David E; Barber, John L; Subramanian, Gopinath
2013-12-14
Molecular networks comprised of crosslinked cis-1,4 polyisoprene, often referred to as "natural rubber," are one of the most common systems for the study of rubber elasticity. Under moderate tensile or compressive strain, network chains begin to assume straighter paths, as local molecular kinks are removed. Isoprene units along the chain backbone are mechanically forced from their equilibrium distributions of 18 possible rotational states into a smaller subset of states, restricted to more linear conformations with the greatest end-to-end distances. There are two consequences to this change: both the configurational entropy and average internal energy decrease. We find that the change in entropy, and resulting change in free energy, gives rise to an elastic force. We derive an expression for a chain extension force constant that we have incorporated in an explicit, three-dimensional meso-scale network simulation code. Using this force model, our simulations predict a macroscopic stress-strain relationship that closely matches published experimental values. We also predict a slight increase in temperature resulting from the change in average internal energy in the affected isoprene units that is consistent with experiments.
NASA Astrophysics Data System (ADS)
Hanson, David E.; Barber, John L.; Subramanian, Gopinath
2013-12-01
Molecular networks comprised of crosslinked cis-1,4 polyisoprene, often referred to as "natural rubber," are one of the most common systems for the study of rubber elasticity. Under moderate tensile or compressive strain, network chains begin to assume straighter paths, as local molecular kinks are removed. Isoprene units along the chain backbone are mechanically forced from their equilibrium distributions of 18 possible rotational states into a smaller subset of states, restricted to more linear conformations with the greatest end-to-end distances. There are two consequences to this change: both the configurational entropy and average internal energy decrease. We find that the change in entropy, and resulting change in free energy, gives rise to an elastic force. We derive an expression for a chain extension force constant that we have incorporated in an explicit, three-dimensional meso-scale network simulation code. Using this force model, our simulations predict a macroscopic stress-strain relationship that closely matches published experimental values. We also predict a slight increase in temperature resulting from the change in average internal energy in the affected isoprene units that is consistent with experiments.
Erba, Alessandro
2016-05-18
Symmetry features of the internal-strain tensor of crystals (whose components are mixed second-energy derivatives with respect to atomic displacements and lattice strains) are formally presented, which originate from translational-invariance, atomic equivalences, and atomic invariances. A general computational scheme is devised, and implemented into the public Crystal program, for the quantum-mechanical evaluation of the internal-strain tensor of crystals belonging to any space-group, which takes full-advantage of the exploitation of these symmetry-features. The gain in computing time due to the full symmetry exploitation is documented to be rather significant not just for high-symmetry crystalline systems such as cubic, hexagonal or trigonal, but also for low-symmetry ones such as monoclinic and orthorhombic. The internal-strain tensor is used for the evaluation of the nuclear relaxation term of the fourth-rank elastic and third-rank piezoelectric tensors of crystals, where, apart from a reduction of the computing time, the exploitation of symmetry is documented to remarkably increase the numerical precision of computed coefficients.
NASA Astrophysics Data System (ADS)
Parker, C.; Meere, P.; Mulchrone, K.; Stevenson, C.
2009-04-01
Strain analysis is commonly based on the axial ratio measurements of populations of approximately ellipsoid objects (e.g. sedimentary clasts), based on the assumption that these ‘strain markers' act passively during deformation. However truly passive strain markers are rare due to competency contrasts which can lead to underestimates of strain where the strain markers are more rigid than the deforming host. (Meere et al., 2007). Therefore we have used a combination of traditional strain analysis of sedimentary clasts, field and microstructural observations and anisotropy of magnetic susceptibility (AMS) measurements to quantify and validate the finite strain patterns across the Irish Variscan cleavage front. This region lies at the northern boundary of the European Rhenohercynian. Deformation of a thick (7 km +) Upper Devonian continental clastic sequence and overlying Carboniferous marine carbonate/clast sequence at the end of the Carboniferous consisted of an initial phase of layer parallel shortening, followed by folding, ongoing cleavage development and late stage accommodation thrusting. AMS data can help to quantify weak or subtle fabrics by effectively measuring the preferred orientation of iron bearing minerals (in this case clay minerals). Preliminary AMS results indicate a gradient in deformation intensity within lithologies across the cleavage front from the south to the north. A microstructural comparison from across the cleavage front is used to characterise the strain regime either side of the boundary. Integrating these techniques will refine our current knowledge of spatial distributions of strain in the periphery of orogenic forelands.
Grassi, Lorenzo; Väänänen, Sami P; Ristinmaa, Matti; Jurvelin, Jukka S; Isaksson, Hanna
2016-03-21
Subject-specific finite element models have been proposed as a tool to improve fracture risk assessment in individuals. A thorough laboratory validation against experimental data is required before introducing such models in clinical practice. Results from digital image correlation can provide full-field strain distribution over the specimen surface during in vitro test, instead of at a few pre-defined locations as with strain gauges. The aim of this study was to validate finite element models of human femora against experimental data from three cadaver femora, both in terms of femoral strength and of the full-field strain distribution collected with digital image correlation. The results showed a high accuracy between predicted and measured principal strains (R(2)=0.93, RMSE=10%, 1600 validated data points per specimen). Femoral strength was predicted using a rate dependent material model with specific strain limit values for yield and failure. This provided an accurate prediction (<2% error) for two out of three specimens. In the third specimen, an accidental change in the boundary conditions occurred during the experiment, which compromised the femoral strength validation. The achieved strain accuracy was comparable to that obtained in state-of-the-art studies which validated their prediction accuracy against 10-16 strain gauge measurements. Fracture force was accurately predicted, with the predicted failure location being very close to the experimental fracture rim. Despite the low sample size and the single loading condition tested, the present combined numerical-experimental method showed that finite element models can predict femoral strength by providing a thorough description of the local bone mechanical response.
NASA Astrophysics Data System (ADS)
Sankaranarayanan, Subramanian K. R. S.; Bhethanabotla, Venkat R.; Joseph, Babu
2007-10-01
Molecular dynamics simulation is used to investigate the mechanical properties of infinitely long, cylindrical bimetallic Pd-Pt nanowires, with an approximate diameter of 1.4nm and two different compositions (25% and 50% Pt). The nanowires are subjected to uniaxial tensile strain along the [001] axis with varying strain rates of 0.05%ps-1 , and 5.0%ps-1 , at simulation temperatures of 50 and 300K , to study the effects of strain rates and thermal conditions on the deformation characteristics and mechanical properties of the nanowire. The deformation and rupture mechanism of these nanowires is explored in detail. Comparisons to the behavior exhibited by pure Pd and Pt nanowires of similar diameter are also made. The effect of lattice mismatch on the observed deformation modes in bimetallic nanowires is also discussed. Our simulations indicate that Pd-Pt alloy nanowires of various compositions, with little lattice mismatch between Pd and Pt atoms, undergo similar deformation and rupture upon uniaxial stretching. It is found that yielding and fracture mechanisms depend on the applied strain rate as well as atomic arrangement and temperature. At low temperature and strain rate, where crystal order and stability are highly preserved, the calculated stress-strain response of pure Pt and Pd as well as Pd-Pt alloy nanowires showed clear periodic, stepwise dislocation-relaxation behavior. Crystalline to amorphous transformation takes place at high strain rates (5%ps-1) , with amorphous melting detected at 300K . Deformation of nanowires at higher strain rates and low temperature, where the superplasticity characteristic is significantly enhanced, results in the development of a multishell helical structure. Mechanical properties of the alloy nanowires are significantly different from those of bulk phase and are dictated by the applied strain rate, temperature, alloy composition, as well as the structural rearrangement associated with nanowire elongation. We find that Young
Elastic response of filamentous networks with compliant crosslinks.
Sharma, A; Sheinman, M; Heidemann, K M; MacKintosh, F C
2013-11-01
Experiments have shown that elasticity of disordered filamentous networks with compliant crosslinks is very different from networks with rigid crosslinks. Here, we model and analyze filamentous networks as a collection of randomly oriented rigid filaments connected to each other by flexible crosslinks that are modeled as wormlike chains. For relatively large extensions we allow for enthalpic stretching of crosslink backbones. We show that for sufficiently high crosslink density, the network linear elastic response is affine on the scale of the filaments' length. The nonlinear regime can become highly nonaffine and is characterized by a divergence of the elastic modulus at finite strain. In contrast to the prior predictions, we do not find an asymptotic regime in which the differential elastic modulus scales linearly with the stress, although an approximate linear dependence can be seen in a transition from entropic to enthalpic regimes. We discuss our results in light of recent experiments.
Correlation of composite material test results with finite element analysis
NASA Astrophysics Data System (ADS)
Guƫu, M.
2016-08-01
In this paper are presented some aspects regarding the method of simulation of composite materials testing with finite element analysis software. There were simulated tensile and shear tests of specimens manufactured from glass fiber reinforced polyester. For specimens manufacturing two types of fabrics were used: unidirectional and bidirectional. Experimentally determined elastic properties of composite material were used as input data. Modeling of composite architecture of the specimens was performed with ANSYS Composite PrepPost software. Finite element analysis stresses and strains on strain gauges bonding area were considered and compared with the real values in a diagram. After results comparison, potential causes of deviations were identified.
NASA Astrophysics Data System (ADS)
Staisch, L.; Styron, R. H.; James, S.; Turner, H. L.; Ashlock, A.; Cavness, C. L.; Collier, X.; Fauria, K.; Feinstein, R.; Murphy, R.; Williams, B.; Mattioli, G. S.; Jansma, P. E.; Cothren, J.
2007-12-01
The Caribbean, North and South American plates are converging at a rate of 2 cm/yr in the central region of the Lesser Antilles arc. Here we report high-precision GPS data in concert with forward modeling of a simplified subduction zone geometry to assess strain accumulation for the Lesser Antilles trench. We are able to constrain both vertical and horizontal surface deformation from campaign and continuous GPS observations from 28 geodetic benchmarks located in Guadeloupe, Dominica and Aves Island. Precise station positions were estimated with GIPSY-OASIS II using an absolute point positioning strategy and final, precise orbits, clocks, earth orientation parameters, and x-files. All position estimates were updated to ITRF05 and a revised Caribbean Euler pole was used to place our observations in a CAR-fixed frame. Surface displacements for each site were estimated over 2-7 years. CAR-fixed velocities are projected onto a 500 kilometer transect from the LA trench to Aves Island and compared to calculated displacements for 88 different subduction models. Finite dislocations within an elastic half-space with variable parameters such as angle of the subducting slab, the downdip extent of the locked zone, and percentage of plate interface locking were investigated. Other parameters, such as trench length and slip remained constant. Using a chi-squared, best-fit statistical criterion, the GPS data constrain the subduction interface to a 75 kilometer downdip extent, a 10° dip angle, and near 50% locking. This implies that the subduction zone offshore Dominica is in an interseismic state, thus accumulating strain and causing small westward and upward displacement of the Lesser Antilles relative to the stable Caribbean interior.
Elastic-plastic analysis of the SS-3 tensile specimen
Majumdar, S.
1998-09-01
Tensile tests of most irradiated specimens of vanadium alloys are conducted using the miniature SS-3 specimen which is not ASTM approved. Detailed elastic-plastic finite element analysis of the specimen was conducted to show that, as long as the ultimate to yield strength ratio is less than or equal to 1.25 (which is satisfied by many irradiated materials), the stress-plastic strain curve obtained by using such a specimen is representative of the true material behavior.
A simplified method for elastic-plastic-creep structural analysis
NASA Technical Reports Server (NTRS)
Kaufman, A.
1984-01-01
A simplified inelastic analysis computer program (ANSYPM) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects are calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.
A simplified method for elastic-plastic-creep structural analysis
NASA Technical Reports Server (NTRS)
Kaufman, A.
1985-01-01
A simplified inelastic analysis computer program (ANSYPM) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects are calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.
NASA Astrophysics Data System (ADS)
Mosby, Matthew; Matouš, Karel
2015-12-01
Three-dimensional simulations capable of resolving the large range of spatial scales, from the failure-zone thickness up to the size of the representative unit cell, in damage mechanics problems of particle reinforced adhesives are presented. We show that resolving this wide range of scales in complex three-dimensional heterogeneous morphologies is essential in order to apprehend fracture characteristics, such as strength, fracture toughness and shape of the softening profile. Moreover, we show that computations that resolve essential physical length scales capture the particle size-effect in fracture toughness, for example. In the vein of image-based computational materials science, we construct statistically optimal unit cells containing hundreds to thousands of particles. We show that these statistically representative unit cells are capable of capturing the first- and second-order probability functions of a given data-source with better accuracy than traditional inclusion packing techniques. In order to accomplish these large computations, we use a parallel multiscale cohesive formulation and extend it to finite strains including damage mechanics. The high-performance parallel computational framework is executed on up to 1024 processing cores. A mesh convergence and a representative unit cell study are performed. Quantifying the complex damage patterns in simulations consisting of tens of millions of computational cells and millions of highly nonlinear equations requires data-mining the parallel simulations, and we propose two damage metrics to quantify the damage patterns. A detailed study of volume fraction and filler size on the macroscopic traction-separation response of heterogeneous adhesives is presented.
Giordano, Chiara; Zappalà, Stefano; Kleiven, Svein
2017-02-23
Computational models incorporating anisotropic features of brain tissue have become a valuable tool for studying the occurrence of traumatic brain injury. The tissue deformation in the direction of white matter tracts (axonal strain) was repeatedly shown to be an appropriate mechanical parameter to predict injury. However, when assessing the reliability of axonal strain to predict injury in a population, it is important to consider the predictor sensitivity to the biological inter-subject variability of the human brain. The present study investigated the axonal strain response of 485 white matter subject-specific anisotropic finite element models of the head subjected to the same loading conditions. It was observed that the biological variability affected the orientation of the preferential directions (coefficient of variation of 39.41% for the elevation angle-coefficient of variation of 29.31% for the azimuth angle) and the determination of the mechanical fiber alignment parameter in the model (gray matter volume 55.55-70.75%). The magnitude of the maximum axonal strain showed coefficients of variation of 11.91%. On the contrary, the localization of the maximum axonal strain was consistent: the peak of strain was typically located in a 2 cm(3) volume of the brain. For a sport concussive event, the predictor was capable of discerning between non-injurious and concussed populations in several areas of the brain. It was concluded that, despite its sensitivity to biological variability, axonal strain is an appropriate mechanical parameter to predict traumatic brain injury.
Prado, Felippe Bevilacqua; Freire, Alexandre Rodrigues; Cláudia Rossi, Ana; Ledogar, Justin A; Smith, Amanda L; Dechow, Paul C; Strait, David S; Voigt, Tilman; Ross, Callum F
2016-12-01
The craniofacial skeleton is often described in the clinical literature as being comprised of vertical bony pillars, which transmit forces from the toothrow to the neurocranium as axial compressive stresses, reinforced transversely by buttresses. Here, we review the literature on bony microarchitecture, in vivo bone strain, and finite-element modeling of the facial skeleton of humans and nonhuman primates to address questions regarding the structural and functional existence of facial pillars and buttresses. Available bone material properties data do not support the existence of pillars and buttresses in humans or Sapajus apella. Deformation regimes in the zygomatic complex emphasize bending and shear, therefore conceptualizing the zygomatic complex of humans or nonhuman primates as a pillar obscures its patterns of stress, strain, and deformation. Human fossil relatives and chimpanzees exhibit strain regimes corroborating the existence of a canine-frontal pillar, but the notion of a zygomatic pillar has no support. The emerging consensus on patterns of strain and deformation in finite element models (FEMs) of the human facial skeleton corroborates hypotheses in the clinical literature regarding zygomatic complex function, and provide new insights into patterns of failure of titanium and resorbable plates in experimental studies. It is suggested that the "pillar and buttress" model of human craniofacial skeleton function be replaced with FEMs that more accurately and precisely represent in vivo function, and which can serve as the basis for future research into implants used in restoration of occlusal function and fracture repair. Anat Rec, 299:1753-1778, 2016. © 2016 Wiley Periodicals, Inc.
NASA Astrophysics Data System (ADS)
Baqersad, Javad
Health monitoring of rotating structures such as wind turbines and helicopter rotors is generally performed using conventional sensors that provide a limited set of data at discrete locations near or on the hub. These sensors usually provide no data on the blades or interior locations where failures may occur. Within this work, an unique expansion algorithm was extended and combined with finite element (FE) modeling and an optical measurement technique to identify the dynamic strain in rotating structures. The merit of the approach is shown by using the approach to predict the dynamic strain on a small non-rotating and rotating wind turbine. A three-bladed wind turbine having 2.3-meter long blades was placed in a semi-built-in boundary condition using a hub, a machining chuck, and a steel block. A finite element model of the three wind turbine blades assembled to the hub was created and used to extract resonant frequencies and mode shapes. The FE model was validated and updated using experimental modal tests. For the non-rotating optical test, the turbine was excited using a sinusoidal excitation, a pluck test, arbitrary impacts on three blades, and random force excitations with a mechanical shaker. The response of the structure to the excitations was measured using three-dimensional point tracking. A pair of high-speed cameras was used to measure the displacement of optical targets on the structure when the blades were vibrating. The measured displacements at discrete locations were expanded and applied to the finite element model of the structure to extract the full-field dynamic strain. The results of the work show an excellent correlation between the strain predicted using the proposed approach and the strain measured with strain-gages for all of the three loading conditions. Similar to the non-rotating case, optical measurements were also preformed on a rotating wind turbine. The point tracking technique measured both rigid body displacement and flexible
NASA Technical Reports Server (NTRS)
Houseman, G.; England, P.
1986-01-01
The present investigation has the objective to perform numerical experiments on a rheologically simple continuum model for the continental lithosphere. It is attempted to obtain a better understanding of the dynamics of continental deformation. Calculations are presented of crustal thickness distributions, stress, strain, strain rate fields, latitudinal displacements, and finite rotations, taking into account as basis a model for continental collision which treats the litoshphere as a thin viscous layer subject to indenting boundary conditions. The results of this paper support the conclusions of England and McKenzie (1982) regarding the role of gravity in governing the deformation of a thin viscous layer subject to indenting boundary conditions. The results of the experiments are compared with observations of topography, stress and strain rate fields, and palaeomagnetic latitudinal displacements in Asia.
Béland, Laurent Karim; Machado-Charry, Eduardo; Pochet, Pascal; Mousseau, Normand
2014-10-06
Here we investigate Ge mixing at the Si(001) surface and characterize the 2 N Si(001) reconstruction by means of hybrid quantum and molecular mechanics calculations (QM/MM). Avoiding fake elastic dampening, this scheme allows to correctly take into account long range deformation induced by reconstructed and defective surfaces. We focus in particular on the dimer vacancy line (DVL) and its interaction with Ge adatoms. We first show that calculated formation energies for these defects are highly dependent on the choice of chemical potential and that the latter must be chosen carefully. Characterizing the effect of the DVL on the deformation field, we also find that the DVL favors Ge segregation in the fourth layer close to the DVL. Using the activation-relaxation technique (ART nouveau) and QM/MM, we show that a complex diffusion path permits the substitution of the Ge atom in the fourth layer, with barriers compatible with mixing observed at intermediate temperature. We also show that the use of QM/MM results in much more signi cant corrections at the saddle points (up to 0.5 eV) that at minima, demonstrating its importance for describing kinetics correctly.
Béland, Laurent Karim; Machado-Charry, Eduardo; Pochet, Pascal; ...
2014-10-06
Here we investigate Ge mixing at the Si(001) surface and characterize the 2 N Si(001) reconstruction by means of hybrid quantum and molecular mechanics calculations (QM/MM). Avoiding fake elastic dampening, this scheme allows to correctly take into account long range deformation induced by reconstructed and defective surfaces. We focus in particular on the dimer vacancy line (DVL) and its interaction with Ge adatoms. We first show that calculated formation energies for these defects are highly dependent on the choice of chemical potential and that the latter must be chosen carefully. Characterizing the effect of the DVL on the deformation field,more » we also find that the DVL favors Ge segregation in the fourth layer close to the DVL. Using the activation-relaxation technique (ART nouveau) and QM/MM, we show that a complex diffusion path permits the substitution of the Ge atom in the fourth layer, with barriers compatible with mixing observed at intermediate temperature. We also show that the use of QM/MM results in much more signi cant corrections at the saddle points (up to 0.5 eV) that at minima, demonstrating its importance for describing kinetics correctly.« less
NASA Astrophysics Data System (ADS)
Béland, Laurent Karim; Machado-Charry, Eduardo; Pochet, Pascal; Mousseau, Normand
2014-10-01
We investigate Ge mixing at the Si(001) surface and characterize the 2×N Si(001) reconstruction by means of hybrid quantum and molecular mechanics calculations (QM/MM). Avoiding fake elastic dampening, this scheme allows to correctly take into account long-range deformation induced by reconstructed and defective surfaces. We focus in particular on the dimer vacancy line (DVL) and its interaction with Ge adatoms. We first show that calculated formation energies for these defects are highly dependent on the choice of chemical potential and that the latter must be chosen carefully. Characterizing the effect of the DVL on the deformation field, we also find that the DVL favors Ge segregation in the fourth layer close to the DVL. Using the activation-relaxation technique (ART nouveau) and QM/MM, we show that a complex diffusion path permits the substitution of the Ge atom in the fourth layer, with barriers compatible with mixing observed at intermediate temperature. We also show that the use of QM/MM results in much more significant corrections at the saddle points (up to 0.5 eV) that at minima, demonstrating its importance for describing kinetics correctly.
Le Floc'h, Simon; Ohayon, Jacques; Tracqui, Philippe; Finet, Gérard; Gharib, Ahmed M; Maurice, Roch L; Cloutier, Guy; Pettigrew, Roderic I
2009-07-01
It is now recognized that prediction of the vulnerable coronary plaque rupture requires not only an accurate quantification of fibrous cap thickness and necrotic core morphology but also a precise knowledge of the mechanical properties of plaque components. Indeed, such knowledge would allow a precise evaluation of the peak cap-stress amplitude, which is known to be a good biomechanical predictor of plaque rupture. Several studies have been performed to reconstruct a Young's modulus map from strain elastograms. It seems that the main issue for improving such methods does not rely on the optimization algorithm itself, but rather on preconditioning requiring the best estimation of the plaque components' contours. The present theoretical study was therefore designed to develop: 1) a preconditioning model to extract the plaque morphology in order to initiate the optimization process, and 2) an approach combining a dynamic segmentation method with an optimization procedure to highlight the modulogram of the atherosclerotic plaque. This methodology, based on the continuum mechanics theory prescribing the strain field, was successfully applied to seven intravascular ultrasound coronary lesion morphologies. The reconstructed cap thickness, necrotic core area, calcium area, and the Young's moduli of the calcium, necrotic core, and fibrosis were obtained with mean relative errors of 12%, 4% and 1%, 43%, 32%, and 2%, respectively.
Sui, Tan; Lunt, Alexander J G; Baimpas, Nikolaos; Sandholzer, Michael A; Hu, Jianan; Dolbnya, Igor P; Landini, Gabriel; Korsunsky, Alexander M
2014-01-01
Human enamel is a typical hierarchical mineralized tissue with a two-level composite structure. To date, few studies have focused on how the mechanical behaviour of this tissue is affected by both the rod orientation at the microscale and the preferred orientation of mineral crystallites at the nanoscale. In this study, wide-angle X-ray scattering was used to determine the internal lattice strain response of human enamel samples (with differing rod directions) as a function of in situ uniaxial compressive loading. Quantitative stress distribution evaluation in the birefringent mounting epoxy was performed in parallel using photoelastic techniques. The resulting experimental data was analysed using an advanced multiscale Eshelby inclusion model that takes into account the two-level hierarchical structure of human enamel, and reflects the differing rod directions and orientation distributions of hydroxyapatite crystals. The achieved satisfactory agreement between the model and the experimental data, in terms of the values of multidirectional strain components under the action of differently orientated loads, suggests that the multiscale approach captures reasonably successfully the structure-property relationship between the hierarchical architecture of human enamel and its response to the applied forces. This novel and systematic approach can be used to improve the interpretation of the mechanical properties of enamel, as well as of the textured hierarchical biomaterials in general.
Le Floc’h, Simon; Tracqui, Philippe; Finet, Gérard; Gharib, Ahmed M.; Maurice, Roch L.; Cloutier, Guy; Pettigrew, Roderic I.
2016-01-01
It is now recognized that prediction of the vulnerable coronary plaque rupture requires not only an accurate quantification of fibrous cap thickness and necrotic core morphology but also a precise knowledge of the mechanical properties of plaque components. Indeed, such knowledge would allow a precise evaluation of the peak cap-stress amplitude, which is known to be a good biomechanical predictor of plaque rupture. Several studies have been performed to reconstruct a Young’s modulus map from strain elastograms. It seems that the main issue for improving such methods does not rely on the optimization algorithm itself, but rather on preconditioning requiring the best estimation of the plaque components’ contours. The present theoretical study was therefore designed to develop: 1) a preconditioning model to extract the plaque morphology in order to initiate the optimization process, and 2) an approach combining a dynamic segmentation method with an optimization procedure to highlight the modulogram of the atherosclerotic plaque. This methodology, based on the continuum mechanics theory prescribing the strain field, was successfully applied to seven intravascular ultrasound coronary lesion morphologies. The reconstructed cap thickness, necrotic core area, calcium area, and the Young’s moduli of the calcium, necrotic core, and fibrosis were obtained with mean relative errors of 12%, 4% and 1%, 43%, 32%, and 2%, respectively. PMID:19164080
Void growth in an elastic-plastic medium.
NASA Technical Reports Server (NTRS)
Needleman, A.
1972-01-01
The uniaxial deformation of an elastic-plastic medium containing a doubly periodic square array of circular cylindrical voids is studied under plane-strain conditions. Both the effects of geometrical nonlinearities resulting from large deformation and physical nonlinearities arising from plastic material behavior are included in formulating the problem. A variational principle is used as the basis for implementing a finite-element solution. Results are obtained for the change in void shape and size under increasing overall strain, the overall tensile behavior of the material with voids, and the development of the plastic zone about a void.
Elastic Face, An Anatomy-Based Biometrics Beyond Visible Cue
Tsap, L V; Zhang, Y; Kundu, S J; Goldgof, D B; Sarkar, S
2004-03-29
This paper describes a face recognition method that is designed based on the consideration of anatomical and biomechanical characteristics of facial tissues. Elastic strain pattern inferred from face expression can reveal an individual's biometric signature associated with the underlying anatomical structure, and thus has the potential for face recognition. A method based on the continuum mechanics in finite element formulation is employed to compute the strain pattern. Experiments show very promising results. The proposed method is quite different from other face recognition methods and both its advantages and limitations, as well as future research for improvement are discussed.
Indentation-derived elastic modulus of multilayer thin films: Effect of unloading induced plasticity
Jamison, Ryan Dale; Shen, Yu -Lin
2015-08-13
Nanoindentation is useful for evaluating the mechanical properties, such as elastic modulus, of multilayer thin film materials. A fundamental assumption in the derivation of the elastic modulus from nanoindentation is that the unloading process is purely elastic. In this work, the validity of elastic assumption as it applies to multilayer thin films is studied using the finite element method. The elastic modulus and hardness from the model system are compared to experimental results to show validity of the model. Plastic strain is shown to increase in the multilayer system during the unloading process. Additionally, the indentation-derived modulus of a monolayer material shows no dependence on unloading plasticity while the modulus of the multilayer system is dependent on unloading-induced plasticity. Lastly, the cyclic behavior of the multilayer thin film is studied in relation to the influence of unloading-induced plasticity. Furthermore, it is found that several cycles are required to minimize unloading-induced plasticity.
Mechanistic Constitutive Models for Rubber Elasticity and Viscoelasticity
Puso, M
2003-01-21
Physically based models which describe the finite strain behavior of vulcanized rubber are developed. Constitutive laws for elasticity and viscoelasticity are derived by integrating over orientation space the forces due to each individual polymer chain. A novel scheme is presented which effectively approximates these integrals in terms of strain and strain invariants. In addition, the details involving the implementation of such models into a quasi-static large strain finite element formulation are provided. In order to account for the finite extensibility of a molecular chain, Langevin statistics is used to model the chain response. The classical statistical model of rubber assumes that polymer chains interact only at the chemical crosslinks. It is shown that such model when fitted for uniaxial tension data cannot fit compression or equibiaxial data. A model which incorporates the entanglement interactions of surrounding chains, in addition to the finite extensibility of the chains, is shown to give better predictions than the classical model. The technique used for approximating the orientation space integral was applied to both the classical and entanglement models. A viscoelasticity model based on the force equilibration process as described by Doi and Edwards is developed. An assumed form for the transient force in the chain is postulated. The resulting stress tensor is composed of an elastic and a viscoelastic portion with the elastic stress given by the proposed entanglement model. In order to improve the simulation of experimental data, it was found necessary to include the effect of unattached or dangling polymer chains in the viscoelasticity model. The viscoelastic effect of such chains is the manifestation of a disengagement process. This disengagement model for unattached polymer chains motivated an empirical model which was very successful in simulating the experimental results considered.
Faster, Easier Finite-Element Modeling Of Weld Offsets
NASA Technical Reports Server (NTRS)
Hong, C. Chen; Lichwala, Bradley E.
1993-01-01
In faster, easier technique, material in weld zone fictitiously softened to negligibly low modulus of elasticity, and material considered deformed to specified offset. Displacements caused by deformation computed by analysis of static stresses and strains in fictitiously deformed material, using specified offset as displacement boundary condition. Resulting displacements added to coordinates of corresponding nodes of original (nonoffset) mathematical model of welded part. Technique used to modify large finite-element mathematical model to any desired weld offset configuration in short time.
Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; Rossi, Simone
2015-11-12
Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.
Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...
2015-11-12
Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less
Yamaguchi, Takashi; Fukuda, Takashi Kakeshita, Tomoyuki; Harjo, Stefanus; Nakamoto, Tatsushi
2014-06-09
An Fe{sub 3}Pt alloy with degree of order 0.75 exhibits a second-order-like martensitic transformation from a cubic structure to a tetragonal one at about 90 K; its tetragonality c/a changes nearly continuously from 1 to 0.945 on cooling from 90 K to 14 K. We have investigated the change in lattice parameters in a single crystal of the Fe{sub 3}Pt alloy at 93 K under compressive stresses, σ, applied in the [001] direction by neutron diffraction. The tetragonality c/a has decreased continuously from 1 to 0.907 with an increase in |σ| up to |σ| = 280 MPa; the corresponding lattice strain in the [001] direction, due to the continuous structure change, increases from 0% to 6.1%. When the stress of 300 MPa is reached, c/a has changed abruptly from 0.907 to 0.789 due to a first-order martensitic transformation.
Stability boundaries for wrinkling in highly stretched elastic sheets
NASA Astrophysics Data System (ADS)
Li, Qingdu; Healey, Timothy J.
2016-12-01
We determine stability boundaries for the wrinkling of highly unidirectionally stretched, finely thin, rectangular elastic sheets. For a given fine thickness and length, a stability boundary here is a curve in the parameter plane, aspect ratio vs. the macroscopic strain; the values on one side of the boundary are associated with stable unwrinkled (flat) states, while stable wrinkled configurations correspond to all values on the other. In our recent work we demonstrated the importance of finite elasticity in the membrane part of such a model in order to capture the correct phenomena. Here we present and compare results for four distinct models: (i) the popular Föppl-von Kármán plate model (FvK), (ii) a correction of the latter, used in our earlier work, in which the approximate 2D Föppl strain tensor is replaced by the exact Green strain tensor, (iii) and (iv): effective 2D finite-elasticity membrane models based on 3D incompressible neo-Hookean and Mooney-Rivlin materials, respectively. In particular, (iii) and (iv) are superior models for elastomers. The 2D nonlinear, hyperelastic models (ii)-(iv) all incorporate the same quadratic bending energy used in FvK. Our results illuminate serious shortcomings of the latter in this problem, while also pointing to inaccuracies of model (ii) - in spite of yielding the correct qualitative phenomena in our earlier work. In each of these, the shortcoming is a due to a deficiency of the membrane part of the model.
An information-based machine learning approach to elasticity imaging.
Hoerig, Cameron; Ghaboussi, Jamshid; Insana, Michael F
2016-11-18
An information-based technique is described for applications in mechanical property imaging of soft biological media under quasi-static loads. We adapted the Autoprogressive method that was originally developed for civil engineering applications for this purpose. The Autoprogressive method is a computational technique that combines knowledge of object shape and a sparse distribution of force and displacement measurements with finite-element analyses and artificial neural networks to estimate a complete set of stress and strain vectors. Elasticity imaging parameters are then computed from estimated stresses and strains. We introduce the technique using ultrasonic pulse-echo measurements in simple gelatin imaging phantoms having linear-elastic properties so that conventional finite-element modeling can be used to validate results. The Autoprogressive algorithm does not require any assumptions about the material properties and can, in principle, be used to image media with arbitrary properties. We show that by selecting a few well-chosen force-displacement measurements that are appropriately applied during training and establish convergence, we can estimate all nontrivial stress and strain vectors throughout an object and accurately estimate an elastic modulus at high spatial resolution. This new method of modeling the mechanical properties of tissue-like materials introduces a unique method of solving the inverse problem and is the first technique for imaging stress without assuming the underlying constitutive model.
Vladimirov, I. N.; Tini, V.; Kiliclar, Y.; Reese, S.
2011-05-04
In this paper, we discuss the application of a newly developed coupled material model of finite anisotropic multiplicative plasticity and continuum damage to the numerical prediction of the forming limit diagram at fracture (FLDF). The model incorporates Hill-type plastic anisotropy, nonlinear Armstrong-Frederick kinematic hardening and nonlinear isotropic hardening. The numerical examples examine the simulation of forming limit diagrams at fracture by means of the so-called Nakajima stretching test. Comparisons with experimental data for aluminium sheets show a good agreement with the finite element results.
Strain index: a new visualizing parameter for US elastography
NASA Astrophysics Data System (ADS)
Sosa-Cabrera, Dario; de Luis-García, R.; Tristán-Vega, A.; Alberola-López, Carlos; Ruiz-Alzola, Juan
2008-03-01
Elastography, an ultrasound modality based on the relation between tissue strain and its mechanical properties, has a strong potential in the diagnosis and prognosis of tumors. For instance, tissue affected by breast and prostate cancer undergoes a change in its elastic properties. These changes can be measured using ultrasound signals. The standard way to visualize the elastic properties of tissues in elastography is the representation of the axial strain. Other approaches investigate the information contained in shear strain elastograms, vorticity or the representation of the full strain tensor. In this paper, we propose to represent the elastic behaviour of tissues through the visualization of the Strain Index, related with the trace of the strain tensor. Based on the mathematical interpretation of the strain tensor, this novel parameter is equivalent to the sum of the eigenvalues of the strain tensor, and constitutes a measure of the total amount of strain of the soft tissue. In order to show the potential of this visualization approach, a tissue-mimicking phantom was modeled as a 10x10x5 cm region containing a centered 10mm cylindrical inclusion three times stiffer than the surrounding material, and its elastic behavior was simulated using finite elements software. Synthetic pre- and post-compression (1.25%) B-mode images were computer-generated with ultrasound simulator. Results show that the visualization of the tensor trace significantly improves the representation and detection of inclusions, and can help add insight in the detection of different types of tumors.
NASA Astrophysics Data System (ADS)
Ungár, Tamás; Harjo, Stefanus; Kawasaki, Takuro; Tomota, Yo; Ribárik, Gábor; Shi, Zengmin
2017-01-01
Based on high-resolution neutron diffraction experiments, we will show that in lath martensite steels, the initially homogeneous dislocation structure, i.e., homogeneous on the length scale of grain size, is disrupted by plastic deformation, which, in turn, produces a composite on the length scale of martensite lath packets. The diffraction patterns of plastically strained martensitic steel reveal characteristically asymmetric peak profiles in the same way as has been observed in materials with heterogeneous dislocation structures. The quasi homogeneous lath structure, formed by quenching, is disrupted by plastic deformation producing a composite structure. Lath packets oriented favorably or unfavorably for dislocation glide become soft or hard. Two lath packet types develop by work softening or work hardening in which the dislocation densities become smaller or larger compared to the initial average dislocation density. The decomposition into soft and hard lath packets is accompanied by load redistribution and the formation of long-range internal stresses between the two lath packet types. The composite behavior of plastically deformed lath martensite opens a new way to understand the elastic-plastic response in this class of materials.
NASA Astrophysics Data System (ADS)
Jamalpoor, A.; Ahmadi-Savadkoohi, A.; Hosseini-Hashemi, Sh
2016-10-01
This paper deals with the theoretical analysis of free vibration and biaxial buckling of magneto-electro-elastic (MEE) microplate resting on Kelvin-Voigt visco-Pasternak foundation and subjected to initial external electric and magnetic potentials, using modified strain gradient theory (MSGT). Kirchhoff plate model and Hamilton’s principle are employed to extract the governing equations of motion. Governing equations were analytically solved to obtain clear closed-form expression for complex natural frequencies and buckling loads using Navier’s approach. Numerical results are presented to reveal variations of natural frequency and buckling load ratio of MEE microplate against different amounts of the length scale parameter, initial external electric and magnetic potentials, aspect ratio, damping and transverse and shear stiffness parameters of the visco-Pasternak foundation, length to thickness ratio, microplate thickness and higher modes. Numerical results of this study illustrate that by increasing thickness-to-material length scale parameter ratio, both natural frequency and buckling load ratio predicted by MSGT and modified couple stress theory are reduced because the non-dimensional length scale parameter tends to decrease the stiffness of structures and make them more flexible. In addition, results show that initial external electric and initial external magnetic potentials have no considerable influence on the buckling load ratio and frequency of MEE microplate as the microplate thickness increases.
NASA Astrophysics Data System (ADS)
Garay-Reyes, C. G.; Hernández-Martínez, S. E.; Hernández-Rivera, J. L.; Cruz-Rivera, J. J.; Gutiérrez-Castañeda, E. J.; Dorantes-Rosales, H. J.; Aguilar-Santillan, J.; Martínez-Sánchez, R.
2017-02-01
According to Lifshitz, Slyozov, and Wagner (LSW) and Trans-Interface Diffusion-Controlled (TICD) theoretical models, this paper reports the microstructure and its coarsening behavior of γ' metastable-coherent precipitates in concentration gradient of Ni-13.75Ti (at%)/Ni generated by diffusion couple. The coarsening of precipitates was evaluated in two different Ti contents (R1-11.4Ti (at%) and R2-13Ti (at%)) generated along the concentration gradient and includes average size, size distributions and growth rate. The solvus and metastable-coherent bimodal lines as determined at 850 °C of 9.16 (at%) and 9.92Ti (at%) respectively by scanning electron microscopy. This paper suggests that elastic strains produced by the matrix/precipitate lattice mismatch caused significant deviations between the experimental results and those predicted by the LSW or TIDC theories. Activation energies for TIDC (Q i ) and LSW (Q r ) are Q r : 219.69 and 172.61 kJ mol-1 for R1 and R2 regions, respectively, and Q i : 218.46 and 164.56 kJmol-1 for R1 and R2 regions, respectively. A concentration gradient allows the study of various alloys with different concentration and volume-fraction in a single sample.
Daszkiewicz, Karol; Maquer, Ghislain; Zysset, Philippe K
2016-10-26
Boundary conditions (BCs) and sample size affect the measured elastic properties of cancellous bone. Samples too small to be representative appear stiffer under kinematic uniform BCs (KUBCs) than under periodicity-compatible mixed uniform BCs (PMUBCs). To avoid those effects, we propose to determine the effective properties of trabecular bone using an embedded configuration. Cubic samples of various sizes (2.63, 5.29, 7.96, 10.58 and 15.87 mm) were cropped from [Formula: see text] scans of femoral heads and vertebral bodies. They were converted into [Formula: see text] models and their stiffness tensor was established via six uniaxial and shear load cases. PMUBCs- and KUBCs-based tensors were determined for each sample. "In situ" stiffness tensors were also evaluated for the embedded configuration, i.e. when the loads were transmitted to the samples via a layer of trabecular bone. The Zysset-Curnier model accounting for bone volume fraction and fabric anisotropy was fitted to those stiffness tensors, and model parameters [Formula: see text] (Poisson's ratio) [Formula: see text] and [Formula: see text] (elastic and shear moduli) were compared between sizes. BCs and sample size had little impact on [Formula: see text]. However, KUBCs- and PMUBCs-based [Formula: see text] and [Formula: see text], respectively, decreased and increased with growing size, though convergence was not reached even for our largest samples. Both BCs produced upper and lower bounds for the in situ values that were almost constant across samples dimensions, thus appearing as an approximation of the effective properties. PMUBCs seem also appropriate for mimicking the trabecular core, but they still underestimate its elastic properties (especially in shear) even for nearly orthotropic samples.
NASA Astrophysics Data System (ADS)
Lidorikis, Elefterios; Bachlechner, Martina E.; Kalia, Rajiv K.; Nakano, Aiichiro; Vashishta, Priya
2005-09-01
A hybrid atomistic-continuum simulation approach has been implemented to study strain relaxation in lattice-mismatched Si/Si3N4 nanopixels on a Si(111) substrate. We couple the molecular-dynamics (MD) and finite-element simulation approaches to provide an atomistic description near the interface and a continuum description deep into the substrate, increasing the accessible length scales and greatly reducing the computational cost. The results of the hybrid simulation are validated against full multimillion-atom MD simulations. We find that strain relaxation in Si/Si3N4 nanopixels may occur through the formation of a network of interfacial domain boundaries reminiscent of interfacial misfit dislocations. They result from the nucleation of domains of different interfacial bonding at the free edges and corners of the nanopixel, and subsequent to their creation they propagate inwards. We follow the motion of the domain boundaries and estimate a propagation speed of about ˜2.5×103m/s . The effects of temperature, nanopixel architecture, and film structure on strain relaxation are also investigated. We find: (i) elevated temperature increases the interfacial domain nucleation rates; (ii) a thin compliant Si layer between the film and the substrate plays a beneficial role in partially suppressing strain relaxation; and (iii) additional control over the interface morphology may be achieved by varying the film structure.
Stresses in Copper Damascene Lines: In-situ Measurements and Finite Element Analysis
Gergaud, P.; Baldacci, A.; Thomas, O.; Rivero, C.; Sicardy, O.; Micha, J.-S.
2006-02-07
The mechanical properties of thin damascene Cu lines are investigated by in-situ x-ray diffraction, in-situ curvature measurements and finite element calculations. At variance with the behavior of blanket films, 0.3 {mu}m lines exhibit a thermo-elastic behavior which is well reproduced by finite element calculations. The curvature measurements confirm this pure elastic behavior. The triaxial stress state in the lines may explain the lack of plasticity at reduced temperatures because different stress tensor element make the resolved stress cancel out. Profile analysis of the X-ray peaks are compared to the strain distribution deduced from the finite element calculations. The good agreement confirms the large strain inhomogeneities in the lines due to interfacial effects.
2015-07-01
circular hole in an aluminium plate fitted with a titanium fastener that were computed using two-dimensional finite element contact analysis. By...used to validate the contact stress distributions associated with a circular hole in an aluminium plate fitted with a titanium fastener that were...fatigue life and aircraft structural integrity management of RAAF airframes. An aluminium coupon has been previously designed in support of the
Coupled Finite Element ? Potts Model Simulations of Grain Growth in Copper Interconnects
Radhakrishnan, Balasubramaniam; Gorti, Sarma B
2009-01-01
The paper addresses grain growth in copper interconnects in the presence of thermal expansion mismatch stresses. The evolution of grain structure and texture in copper in the simultaneous presence of two driving forces, curvature and elastic stored energy difference, is modeled by using a hybrid Potts model simulation approach. The elastic stored energy is calculated by using the commercial finite element code ABAQUS, where the effect of elastic anisotropy on the thermal mismatch stress and strain distribution within a polycrystalline grain structure is modeled through a user material (UMAT) interface. Parametric studies on the effect of trench width and the height of the overburden were carried out. The results show that the grain structure and texture evolution are significantly altered by the presence of elastic strain energy.
AUNMEUNGTONG, W.; KHONGKHUNTHIAN, P.; RUNGSIYAKULL, P.
2016-01-01
SUMMARY Finite Element Analysis (FEA) has been used for prediction of stress and strain between dental implant components and bone in the implant design process. Purpose Purpose of this study was to characterize and analyze stress and strain distribution occurring in bone and implants and to compare stress and strain of three different implant designs. Materials and methods Three different mini dental implant designs were included in this study: 1. a mini dental implant with an internal implant-abutment connection (MDIi); 2. a mini dental implant with an external implant-abutment connection (MDIe); 3. a single piece mini dental implant (MDIs). All implant designs were scanned using micro-CT scans. The imaging details of the implants were used to simulate models for FEA. An artificial bone volume of 9×9 mm in size was constructed and each implant was placed separately at the center of each bone model. All bone-implant models were simulatively loaded under an axial compressive force of 100 N and a 45-degree force of 100 N loading at the top of the implants using computer software to evaluate stress and strain distribution. Results There was no difference in stress or strain between the three implant designs. The stress and strain occurring in all three mini dental implant designs were mainly localized at the cortical bone around the bone-implant interface. Oblique 45° loading caused increased deformation, magnitude and distribution of stress and strain in all implant models. Conclusions Within the limits of this study, the average stress and strain in bone and implant models with MDIi were similar to those with MDIe and MDIs. The oblique 45° load played an important role in dramatically increased average stress and strain in all bone-implant models. Clinical implications Mini dental implants with external or internal connections have similar stress distribution to single piece mini dental implants. In clinical situations, the three types of mini dental implant
Hofmann, Felix; Song, Xu; Abbey, Brian; Jun, Tea-Sung; Korsunsky, Alexander M
2012-05-01
An understanding of the mechanical response of modern engineering alloys to complex loading conditions is essential for the design of load-bearing components in high-performance safety-critical aerospace applications. A detailed knowledge of how material behaviour is modified by fatigue and the ability to predict failure reliably are vital for enhanced component performance. Unlike macroscopic bulk properties (e.g. stiffness, yield stress, etc.) that depend on the average behaviour of many grains, material failure is governed by `weakest link'-type mechanisms. It is strongly dependent on the anisotropic single-crystal elastic-plastic behaviour, local morphology and microstructure, and grain-to-grain interactions. For the development and validation of models that capture these complex phenomena, the ability to probe deformation behaviour at the micro-scale is key. The diffraction of highly penetrating synchrotron X-rays is well suited to this purpose and micro-beam Laue diffraction is a particularly powerful tool that has emerged in recent years. Typically it uses photon energies of 5-25 keV, limiting penetration into the material, so that only thin samples or near-surface regions can be studied. In this paper the development of high-energy transmission Laue (HETL) micro-beam X-ray diffraction is described, extending the micro-beam Laue technique to significantly higher photon energies (50-150 keV). It allows the probing of thicker sample sections, with the potential for grain-level characterization of real engineering components. The new HETL technique is used to study the deformation behaviour of individual grains in a large-grained polycrystalline nickel sample during in situ tensile loading. Refinement of the Laue diffraction patterns yields lattice orientations and qualitative information about elastic strains. After deformation, bands of high lattice misorientation can be identified in the sample. Orientation spread within individual scattering volumes is
Agrawal, Neeraj J.; Weinstein, Joshua; Radhakrishnan, Ravi
2011-01-01
Using a recently developed multiscale simulation methodology, we describe the equilibrium behaviour of bilayer membranes under the influence of curvature-inducing proteins using a linearized elastic free energy model. In particular, we describe how the cooperativity associated with a multitude of protein–membrane interactions and protein diffusion on a membrane-mediated energy landscape elicits emergent behaviour in the membrane phase. Based on our model simulations, we predict that, depending on the density of membrane-bound proteins and the degree to which a single protein molecule can induce intrinsic mean curvature in the membrane, a range of membrane phase behaviour can be observed including two different modes of vesicle-bud nucleation and repressed membrane undulations. A state diagram as a function of experimentally tunable parameters to classify the underlying states is proposed. PMID:21243078
Strain hardening, avalanches, and strain softening in dense cross-linked actin networks
NASA Astrophysics Data System (ADS)
Åström, Jan A.; Kumar, P. B. Sunil; Vattulainen, Ilpo; Karttunen, Mikko
2008-05-01
Actin filament networks enable the cytoskeleton to adjust to internal and external forcing. These dynamic networks can adapt to changes by dynamically adjusting their cross-links. Here, we model actin filaments as cross-linked elastic fibers of finite dimensions, with the cross-links being approximately 1μm apart, and employ a full three-dimensional model to study their elastic properties by computer simulations. The results show compelling evidence that dense actin networks are characterized by (a) strain hardening without entropic elasticity, (b) avalanches of cross-link slippage leading to strain softening in the case of breakable cross-links, and (c) spontaneous formation of stress fibers in the case of dynamic cross-link formation and destruction.
Shinya, Akikazu; Ballo, Ahmed M; Lassila, Lippo V J; Shinya, Akiyoshi; Närhi, Timo O; Vallittu, Pekka K
2011-03-01
This study analyzed stress and strain mediated by 2 different implant materials, titanium (Ti) and experimental fiber-reinforced composite (FRC), on the implant and on the bone tissue surrounding the implant. Three-dimensional finite element models constructed from a mandibular bone and an implant were subjected to a load of 50 N in vertical and horizontal directions. Postprocessing files allowed the calculation of stress and strain within the implant materials and stresses at the bone-to-implant interface (stress path). Maximum stress concentrations were located around the implant on the rim of the cortical bone in both implant materials; Ti and overall stresses decreased toward the Ti implant apex. In the FRC implant, a stress value of 0.6 to 2.0 MPa was detected not only on the screw threads but also on the implant surface between the threads. Clear differences were observed in the strain distribution between the materials. Based on the results, the vertical load stress range of the FRC implant was close to the stress level for optimal bone growth. Furthermore, the stress at the bone around the FRC implant was more evenly distributed than that with Ti implant.
Using capillary forces to determine the elastic properties of mesoporous materials
NASA Astrophysics Data System (ADS)
Rolley, E.; Garroum, N.; Grosman, A.
2017-02-01
The capillary forces in mesoporous materials, when imbibed with liquid, are large enough to induce mechanical deformations. Using anisotropic porous silicon, we show that systematic measurements of strain as a function of the pore pressure can yield most of the elastic constants characterizing the porous matrix. The results of this poroelastic approach are in agreement with independent standard stress-strain measurements. The porosity dependence of Young's moduli as well as the values of Poisson's ratios are qualitatively consistent with porous silicon having a honeycomb structure. For a quantitative comparison, we performed finite element modeling of realistic pore geometries. The calculated elastic moduli are found to be much smaller than the measured ones. This is presumably due to both (i) finite-size effects, the Young's modulus of the 5-nm thick walls of the honeycomb could be notably smaller than the Young's modulus of bulk Si, and (ii) defects of the honeycomb structure along the pore axis.
Finite element model for brittle fracture and fragmentation
Li, Wei; Delaney, Tristan J.; Jiao, Xiangmin; ...
2016-06-01
A new computational model for brittle fracture and fragmentation has been developed based on finite element analysis of non-linear elasticity equations. The proposed model propagates the cracks by splitting the mesh nodes alongside the most over-strained edges based on the principal direction of strain tensor. To prevent elements from overlapping and folding under large deformations, robust geometrical constraints using the method of Lagrange multipliers have been incorporated. In conclusion, the model has been applied to 2D simulations of the formation and propagation of cracks in brittle materials, and the fracture and fragmentation of stretched and compressed materials.
ERIC Educational Resources Information Center
Girill, T. R.
1972-01-01
The Boyle-Mariotte gas law was formulated in terms of pneumatic springs," subsumed by Hooke under his own stress-strain relation, and generally regarded as a law of elasticity. The subsequent development of Boyle's principle and elasticity provide thought-provoking test cases for Kuhn's notations of paradigm and puzzle solving in physics.…
NASA Astrophysics Data System (ADS)
Yu, Betty; Kang, Soo-Young; Akthakul, Ariya; Ramadurai, Nithin; Pilkenton, Morgan; Patel, Alpesh; Nashat, Amir; Anderson, Daniel G.; Sakamoto, Fernanda H.; Gilchrest, Barbara A.; Anderson, R. Rox; Langer, Robert
2016-08-01
We report the synthesis and application of an elastic, wearable crosslinked polymer layer (XPL) that mimics the properties of normal, youthful skin. XPL is made of a tunable polysiloxane-based material that can be engineered with specific elasticity, contractility, adhesion, tensile strength and occlusivity. XPL can be topically applied, rapidly curing at the skin interface without the need for heat- or light-mediated activation. In a pilot human study, we examined the performance of a prototype XPL that has a tensile modulus matching normal skin responses at low strain (<40%), and that withstands elongations exceeding 250%, elastically recoiling with minimal strain-energy loss on repeated deformation. The application of XPL to the herniated lower eyelid fat pads of 12 subjects resulted in an average 2-grade decrease in herniation appearance in a 5-point severity scale. The XPL platform may offer advanced solutions to compromised skin barrier function, pharmaceutical delivery and wound dressings.
Implementation of a trapezoidal ring element in NASTRAN for elastic-plastic analysis
NASA Technical Reports Server (NTRS)
Chen, P. C. T.; Ohara, G. P.
1980-01-01
The explicit expressions for an elastic-plastic trapezoidal ring element are presented and implemented in NASTRAN computer program. The material is assumed to obey the von Mises' yield criterion, isotropic hardening rule and the Prandtl-Reuss flow relations. For the purpose of demonstration, two elastic-plastic problems are solved and compared with previous results. The first is a plane-strain tube under uniform internal pressure and the second, a finite-length tube loaded over part of its inner surface. A very good agreement was found in both test problems.
2011-09-01
vehicles, and for assessing real- time internal loads and structural integrity. INTRODUCTION Structural health management systems, which by...The key advantage of this revised variational formulation rests on the introduction of the weighting coefficients , ,e k gw w w in Eq. (8). This...reconstructed plate deflection distribution 3 max max( / 0.982). iMIN FEMw w (a) Strain rosettes at center of 3elementsiMIN
NASA Technical Reports Server (NTRS)
Hofmann, R.
1980-01-01
The STEALTH code system, which solves large strain, nonlinear continuum mechanics problems, was rigorously structured in both overall design and programming standards. The design is based on the theoretical elements of analysis while the programming standards attempt to establish a parallelism between physical theory, programming structure, and documentation. These features have made it easy to maintain, modify, and transport the codes. It has also guaranteed users a high level of quality control and quality assurance.
Elastic-plastic analysis using a triangular ring element in NASTRAN
NASA Technical Reports Server (NTRS)
Chen, P. C. T.
1980-01-01
An elastic plastic triangular ring element is implemented in NASTRAN computer program. The plane strain problem of partially plastic thick walled cylinder under internal pressure is solved and compared with the earlier finite difference solution. A very good agreement has been reached. In order to demonstrate its application to more general problems, an overloaded thread problem for the British Standard Buttress is examined. The maximum axial and principal stresses are located and their values are determined as functions of loadings.
NASA Astrophysics Data System (ADS)
Syzrantseva, K. V.; Syzrantsev, V. N.; Dvoynikov, M. V.
2017-02-01
Destruction of welds in metalwork is caused, in most cases, by low-cyclic fatigue. Among the wide spectrum of existing fatigue gauges, the Integral Strain Gauges are widely adopted in practice of experimental researches of different machine parts and carrying systems of vehicles. The paper proposes a new method based on finite element analysis of calibrating dependence establishment for ISG placed on the weld material by the use of few welded specimens of special geometrical shape providing the obtainment of several points of the calibrating curve in the tests process. Calibrating dependences allow determining the stress value σx in places of accumulated fatigue damages concentration which is used for serviceability estimation of welded joints by traditional techniques.
Weil, K. Scott; Koeppel, Brian J.
2008-05-15
One of the critical issues in designing and fabricating a high performance planar solid oxide fuel cell (pSOFC) stack is the development of the appropriate materials and techniques for hermetically sealing the metal and ceramic components. We are currently developing a foil-based approach that appears to offer good hermeticity and mechanical integrity, while minimizing the generation of interfacial stresses in either of the joint substrate materials, particulary the ceramic cell. Prior experimental work conducted on small-scale samples demonstrated the viability of the concept. Here we present recent results from computational analyses undertaken to investigate potential issues associated with scaling up the seal to full-scale pSOFC stack dimensions/geometry. Here we employ finite element modeling to assess the potential thermal cycling performance of this design, specifically as it pertains to sealing components with vastly different thermal expansion properties.
Probabilistic elastography: estimating lung elasticity.
Risholm, Petter; Ross, James; Washko, George R; Wells, William M
2011-01-01
We formulate registration-based elastography in a probabilistic framework and apply it to study lung elasticity in the presence of emphysematous and fibrotic tissue. The elasticity calculations are based on a Finite Element discretization of a linear elastic biomechanical model. We marginalize over the boundary conditions (deformation) of the biomechanical model to determine the posterior distribution over elasticity parameters. Image similarity is included in the likelihood, an elastic prior is included to constrain the boundary conditions, while a Markov model is used to spatially smooth the inhomogeneous elasticity. We use a Markov Chain Monte Carlo (MCMC) technique to characterize the posterior distribution over elasticity from which we extract the most probable elasticity as well as the uncertainty of this estimate. Even though registration-based lung elastography with inhomogeneous elasticity is challenging due the problem's highly underdetermined nature and the sparse image information available in lung CT, we show promising preliminary results on estimating lung elasticity contrast in the presence of emphysematous and fibrotic tissue.
A viscoelastic higher-order beam finite element
NASA Technical Reports Server (NTRS)
Johnson, Arthur R.; Tressler, Alexander
1996-01-01
A viscoelastic internal variable constitutive theory is applied to a higher-order elastic beam theory and finite element formulation. The behavior of the viscous material in the beam is approximately modeled as a Maxwell solid. The finite element formulation requires additional sets of nodal variables for each relaxation time constant needed by the Maxwell solid. Recent developments in modeling viscoelastic material behavior with strain variables that are conjugate to the elastic strain measures are combined with advances in modeling through-the-thickness stresses and strains in thick beams. The result is a viscous thick-beam finite element that possesses superior characteristics for transient analysis since its nodal viscous forces are not linearly dependent an the nodal velocities, which is the case when damping matrices are used. Instead, the nodal viscous forces are directly dependent on the material's relaxation spectrum and the history of the nodal variables through a differential form of the constitutive law for a Maxwell solid. The thick beam quasistatic analysis is explored herein as a first step towards developing more complex viscoelastic models for thick plates and shells, and for dynamic analyses. The internal variable constitutive theory is derived directly from the Boltzmann superposition theorem. The mechanical strains and the conjugate internal strains are shown to be related through a system of first-order, ordinary differential equations. The total time-dependent stress is the superposition of its elastic and viscous components. Equations of motion for the solid are derived from the virtual work principle using the total time-dependent stress. Numerical examples for the problems of relaxation, creep, and cyclic creep are carried out for a beam made from an orthotropic Maxwell solid.
Nonlinear Visco-Elastic Response of Composites via Micro-Mechanical Models
NASA Technical Reports Server (NTRS)
Gates, Thomas S.; Sridharan, Srinivasan
2005-01-01
Micro-mechanical models for a study of nonlinear visco-elastic response of composite laminae are developed and their performance compared. A single integral constitutive law proposed by Schapery and subsequently generalized to multi-axial states of stress is utilized in the study for the matrix material. This is used in conjunction with a computationally facile scheme in which hereditary strains are computed using a recursive relation suggested by Henriksen. Composite response is studied using two competing micro-models, viz. a simplified Square Cell Model (SSCM) and a Finite Element based self-consistent Cylindrical Model (FECM). The algorithm is developed assuming that the material response computations are carried out in a module attached to a general purpose finite element program used for composite structural analysis. It is shown that the SSCM as used in investigations of material nonlinearity can involve significant errors in the prediction of transverse Young's modulus and shear modulus. The errors in the elastic strains thus predicted are of the same order of magnitude as the creep strains accruing due to visco-elasticity. The FECM on the other hand does appear to perform better both in the prediction of elastic constants and the study of creep response.
Analysis of local strain in aluminum interconnects by convergent beam electron diffraction
NASA Astrophysics Data System (ADS)
Krämer, Stephan; Mayer, Joachim
1999-11-01
Energy filtered convergent beam electron diffraction (CBED) was used to investigate localized strain in aluminum interconnects. An analysis of the higher order Laue zone (HOLZ) line positions in CBED patterns makes it possible to measure the lattice strain with high accuracy (˜104) and high spatial resolution (10 to 100 nm). The strain development in a single grain was measured during thermal cycling between -170 °C and +100 °C. The grain showed reversible, elastic behavior over the whole temperature range building up large strains at low temperatures. By comparing with finite element simulations, a detailed understanding of the tri-axial strain state could be achieved.
The Degree of Nonlinearity and Anisotropy of Blood Vessel Elasticity
NASA Astrophysics Data System (ADS)
Zhou, J.; Fung, Y. C.
1997-12-01
Blood vessel elasticity is important to physiology and clinical problems involving surgery, angioplasty, tissue remodeling, and tissue engineering. Nonlinearity in blood vessel elasticity in vivo is important to the formation of solitons in arterial pulse waves. It is well known that the stress-strain relationship of the blood vessel is nonlinear in general, but a controversy exists on how nonlinear it is in the physiological range. Another controversy is whether the vessel wall is biaxially isotropic. New data on canine aorta were obtained from a biaxial testing machine over a large range of finite strains referred to the zero-stress state. A new pseudo strain energy function is used to examine these questions critically. The stress-strain relationship derived from this function represents the sum of a linear stress-strain relationship and a definitely nonlinear relationship. This relationship fits the experimental data very well. With this strain energy function, we can define a parameter called the degree of nonlinearity, which represents the fraction of the nonlinear strain energy in the total strain energy per unit volume. We found that for the canine aorta, the degree of nonlinearity varies from 5% to 30%, depending on the magnitude of the strains in the physiological range. In the case of canine pulmonary artery in the arch region, Debes and Fung [Debes, J. C. & Fung, Y. C.(1995) Am. J. Physiol. 269, H433-H442] have shown that the linear regime of the stress-strain relationship extends from the zero-stress state to the homeostatic state and beyond. Both vessels, however, are anisotropic in both the linear and nonlinear regimes.
Local elastic constants in thin films of an fcc crystal.
van Workum, Kevin; de Pablo, Juan J
2003-03-01
In this work we present a formalism for the calculation of the local elastic constants in inhomogeneous systems based on a method of planes. Unlike previous work, this formalism does not require the partitioning of the system into a set of finite volumes over which average elastic constants are calculated. Results for the calculation of the local elastic constants of a nearest-neighbor Lennard-Jones fcc crystal in the bulk and in a thin film are presented. The local constants are calculated at exact planes of the (001) face of the crystal. The average elastic constants of the bulk system are also computed and are consistent with the local constants. Additionally we present the local stress profiles in the thin film when a small uniaxial strain is applied. The resulting stress profile compares favorably with the stress profile predicted via the local elastic constants. The surface melting of a model for argon for which experimental and simulation data are available is also studied within the framework of this formalism.
Elastic-plastic models for multi-site damage
NASA Technical Reports Server (NTRS)
Actis, Ricardo L.; Szabo, Barna A.
1994-01-01
This paper presents recent developments in advanced analysis methods for the computation of stress site damage. The method of solution is based on the p-version of the finite element method. Its implementation was designed to permit extraction of linear stress intensity factors using a superconvergent extraction method (known as the contour integral method) and evaluation of the J-integral following an elastic-plastic analysis. Coarse meshes are adequate for obtaining accurate results supported by p-convergence data. The elastic-plastic analysis is based on the deformation theory of plasticity and the von Mises yield criterion. The model problem consists of an aluminum plate with six equally spaced holes and a crack emanating from each hole. The cracks are of different sizes. The panel is subjected to a remote tensile load. Experimental results are available for the panel. The plasticity analysis provided the same limit load as the experimentally determined load. The results of elastic-plastic analysis were compared with the results of linear elastic analysis in an effort to evaluate how plastic zone sizes influence the crack growth rates. The onset of net-section yielding was determined also. The results show that crack growth rate is accelerated by the presence of adjacent damage, and the critical crack size is shorter when the effects of plasticity are taken into consideration. This work also addresses the effects of alternative stress-strain laws: The elastic-ideally-plastic material model is compared against the Ramberg-Osgood model.
Jones, D.P.; Holliday, J.E.
1999-02-01
This paper provides a comparison between finite element analysis results and test data from the Pressure Vessel Research Council (PVRC) burst disk program. Testing sponsored by the PVRC over 20 years ago was done by pressurizing circular flat disks made from three different materials until failure by bursting. The purpose of this re-analysis is to investigate the use of finite element analysis (FEA) to assess the primary stress limits of the ASME Boiler and Pressure Vessel Code (1998) and to qualify the use of elastic-plastic (EP-FEA) for limit load calculations. The three materials tested represent the range of strength and ductility found in modern pressure vessel construction and include a low strength high ductility material, a medium strength medium ductility material, and a high strength low ductility low alloy material. Results of elastic and EP-FEA are compared to test data. Stresses from the elastic analyses are linearized for comparison of Code primary stress limits to test results. Elastic-plastic analyses are done using both best-estimate and elastic-perfectly plastic (EPP) stress-strain curves. Both large strain-large displacement (LSLD) and small strain-small displacement (SSSD) assumptions are used with the EP-FEA. Analysis results are compared to test results to evaluate the various analysis methods, models, and assumptions as applied to the bursting of thin disks.
A 3D Orthotropic Elastic Continuum Damage Material Model
English, Shawn Allen; Brown, Arthur A.
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.
NASA Astrophysics Data System (ADS)
Jiang, W. G.; Xiong, C. A.; Wu, X. G.
2013-11-01
The residual thermal stresses induced by the high-temperature sintering process in multilayer ceramic capacitors (MLCCs) are investigated by using a finite-element unit cell model, in which the strain gradient effect is considered. The numerical results show that the residual thermal stresses depend on the lateral margin length, the thickness ratio of the dielectrics layer to the electrode layer, and the MLCC size. At a given thickness ratio, as the MLCC size is scaled down, the peak shear stress reduces significantly and the normal stresses along the length and thickness directions change slightly with the decrease in the ceramic layer thickness t d as t d > 1 μm, but as t d < 1 μm, the normal stress components increase sharply with the increase in t d. Thus, the residual thermal stresses induced by the sintering process exhibit strong size effects and, therefore, the strain gradient effect should be taken into account in the design and evaluation of MLCC devices
Schrock, P; Lüpke, M; Seifert, H; Staszyk, C
2013-12-01
This study investigated the hypothetical contribution of biomechanical loading to the onset of equine odontoclastic tooth resorption and hypercementosis (EOTRH) and to elucidate the physiological age-related positional changes of the equine incisors. Based on high resolution micro-computed tomography (μCT) datasets, 3-dimensional models of entire incisor arcades and the canine teeth were constructed representing a young and an old incisor dentition. Special attention was paid to constructing an anatomically correct model of the periodontal ligament (PDL). Using previously determined Young's moduli for the equine incisor PDL, finite element (FE) analysis was performed. Resulting strains, stresses and strain energy densities (SEDs), as well as the resulting regions of tension and compression within the PDL and the surrounding bone were investigated during occlusion. The results showed a distinct distribution pattern of high stresses and corresponding SEDs in the PDL and bone. Due to the tooth movement, peaks of SEDs were obtained in the PDL as well as in the bone on the labial and palatal/lingual sides of the alveolar crest. At the root, highest SEDs were detected in the PDL on the palatal/lingual side slightly occlusal of the root tip. This distribution pattern of high SEDs within the PDL coincides with the position of initial resorptive lesions in EOTRH affected teeth. The position of high SEDs in the bone can explain the typical age-related alteration of shape and angulation of equine incisors.
NASA Astrophysics Data System (ADS)
Cowgill, E.; Gold, R. D.; Arrowsmith, R.; Friedrich, A. M.
2015-12-01
In elastic rebound theory, hazard increases as interseismic strain rebuilds after rupture. This model is challenged by the temporal variation in the pacing of major earthquakes that is both predicted by mechanical models and suggested by some long paleoseismic records (e.g., 1-3). However, the extent of such behavior remains unclear due to a lack of long (5-25 ky) records of fault slip. Using Monte Carlo analysis of 11 offset landforms, we determined a 16-ky record of fault slip for the active, left-lateral Altyn Tagh fault, which bounds the NW margin of the Tibetan Plateau. This history reveals a pulse of accelerated slip between 6.4 and 6.0 ka, during which the fault slipped 9 +14/-2 m at a rate of 23 +35/-5 mm/y, or ~3x the 16 ky average of 8.1 +1.2/-0.9mm/y. These two modes of earthquake behavior suggest temporal variation in the rates of stress storage and release. The simplest explanation for the pulse is a cluster of 2-8 Mw > 7.5 earthquakes. Such supercyclicity has been reported for the Sunda (4) and Cascadia (3) megathrusts, but contrasts with steady slip along the strike-slip Alpine fault (5), for example. A second possibility is that the pulse reflects a single, unusually large rupture. However, this Black Swan event is unlikely: empirical scaling relationships require a Mw 8.2 rupture of the entire 1200-km-long ATF to produce 7 m of average slip. Likewise, Coulomb stress change from rupture on the adjacent North Altyn fault is of modest magnitude and overlap with the ATF. Poor temporal correlation between precipitation and the slip pulse argues against climatically modulated changes in surface loading (lakes/ice) or pore-fluid pressure. "Paleoslip" studies such as this sacrifice the single-event resolution of paleoseismology in exchange for long records that quantify both the timing and magnitude of fault slip averaged over multiple ruptures, and are essential for documenting temporal variations in fault slip as we begin to use calibrated physical
Serra-Hsu, Frederick; Cheng, Jiqi; Lynch, Ted; Qin, Yi-Xian
2011-08-01
Ultrasound has been widely used to nondestructively evaluate various materials, including biological tissues. Quantitative ultrasound has been used to assess bone quality and fracture risk. A pulsed phase-locked loop (PPLL) method has been proven for very sensitive tracking of ultrasound time-of-flight (TOF) changes. The objective of this work was to determine if the PPLL TOF tracking is sensitive to bone deformation changes during loading. The ability to noninvasively detect bone deformations has many implications, including assessment of bone strength and more accurate osteoporosis diagnostics and fracture risk prediction using a measure of bone mechanical quality. Fresh sheep femur cortical bone shell samples were instrumented with three 3-element rosette strain gauges and then tested under mechanical compression with eight loading levels using an MTS machine. Samples were divided into two groups based on internal marrow cavity content: with original marrow, or replaced with water. During compressive loading ultrasound waves were measured through acoustic transmission across the mid-diaphysis of bone. Finite element analysis (FEA) was used to describe ultrasound propagation path length changes under loading based on µCT-determined bone geometry. The results indicated that PPLL output correlates well to measured axial strain, with R(2) values of 0.70 ± 0.27 and 0.62 ± 0.29 for the marrow and water groups, respectively. The PPLL output correlates better with the ultrasound path length changes extracted from FEA. For the two validated FEA tests, correlation was improved to R(2) = 0.993 and R(2) = 0.879 through cortical path, from 0.815 and 0.794 via marrow path, respectively. This study shows that PPLL readings are sensitive to displacement changes during external bone loading, which may have potential to noninvasively assess bone strain and tissue mechanical properties.
Hinterhofer, C; Haider, H; Apprich, V; Ferguson, J C; Collins, S N; Stanek, C
2009-03-01
Finite element modeling is a unique way of introducing technical and material research into medical science. A bovine distal hind limb was scanned using computed tomography for geometric image capture and the data were subsequently divided (segmented) into 4 tissue types: bone, bone marrow, soft tissue, and the horn capsule. Material data from previous studies were integrated into the model. Flexor tendons were assembled as longitudinal structures starting at their cross-sectional areas at the height of the metatarsophalangeal joint, proceeding in the plantaro-distal direction and meeting the distal phalanx at the tuberculum flexorium. Three different flooring situations (full support floor, bearing weight in the abaxial half of the lateral claw and in the dorsal halves of both claws, respectively) were created to evaluate the effects of loading. Full support resulted in von Mises stress levels between 3.5 and 1.5 MPa for the osseous structures and some regions of the segmented soft tissue; stress patterns in the bulb and sole of the claw capsule (1.5 MPa) and in the floor (0.5 MPa) were similar to pressure plate data in vivo and in vitro, with corresponding strain values of 2.4%. Reduced support resulted in higher stresses (up to approximately 8 MPa) in bones, claw capsules, and tendons; high strains ( approximately 11%) were found in the soft tissue, depending on how the floor was constructed. Although the models may still be anatomically improved, stress and strain calculations are possible with results comparable to related research, and the model shows interaction between the 2 digits. This possibly will help with further understanding of the biomechanical function of this 2-digit structure. With respect to clinical interpretation, reduced support to the bovine hind limb increases focal stress peaks in the different tissues, which may indicate a location of potential injury.
NASA Astrophysics Data System (ADS)
Watanabe, Ikumu; Terada, Kenjiro; Neto, Eduardo Alberto de Souza; Perić, Djordje
The objective of this contribution is to develop an elastic-plastic-damage constitutive model for crystal grain and to incorporate it with two-scale finite element analyses based on mathematical homogenization method, in order to characterize the macroscopic tensile strength of polycrystalline metals. More specifically, the constitutive model for single crystal is obtained by combining hyperelasticity, a rate-independent single crystal plasticity and a continuum damage model. The evolution equations, stress update algorithm and consistent tangent are derived within the framework of standard elastoplasticity at finite strain. By employing two-scale finite element analysis, the ductile behaviour of polycrystalline metals and corresponding tensile strength are evaluated. The importance of finite element formulation is examined by comparing performance of several finite elements and their convergence behaviour is assessed with mesh refinement. Finally, the grain size effect on yield and tensile strength is analysed in order to illustrate the versatility of the proposed two-scale model.
NASA Astrophysics Data System (ADS)
Wang, Ruey-Ven; McIntyre, Paul C.; Baniecki, John D.; Nomura, Kenji; Shioga, Takeshi; Kurihara, Kazuaki; Ishii, Masatoshi
2005-11-01
We demonstrate that large and simultaneous improvements in permittivity, tunability, and leakage current density of (Ba,Sr)TiO3 (BST)-based thin-film capacitors can be achieved by yttrium doping. We have found that, for a low deposition temperature (520 °C) sputtering process, Y-doped BST capacitors exhibit tenfold lower leakage current density (<10-9A/cm2 at 100KV/cm) and 70% higher permittivity than nominally undoped BST-based capacitors. Furthermore, this work suggests an intriguing correlation between dopant concentration-dependent elastic strain in the films and their enhanced dielectric properties.
A finite element model of ferroelectric/ferroelastic polycrystals
HWANG,STEPHEN C.; MCMEEKING,ROBERT M.
2000-02-17
A finite element model of polarization switching in a polycrystalline ferroelectric/ferroelastic ceramic is developed. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. Each crystallite is represented by a finite element with the possible dipole directions assigned randomly subject to crystallographic constraints. The model accounts for both electric field induced (i.e. ferroelectric) switching and stress induced (i.e. ferroelastic) switching with piezoelectric interactions. Experimentally measured elastic, dielectric, and piezoelectric constants are used consistently, but different effective critical energy barriers are selected phenomenologically. Electric displacement versus electric field, strain versus electric field, stress versus strain, and stress versus electric displacement loops of a ceramic lead lanthanum zirconate titanate (PLZT) are modeled well below the Curie temperature.
Op Den Buijs, Jorn; Dragomir-Daescu, Dan
2011-11-01
Two-dimensional finite element models of cadaveric femoral stiffness were developed to study their suitability as surrogates of bone stiffness and strength, using two-dimensional representations of femoral geometry and bone mineral density distributions. If successfully validated, such methods could be clinically applied to estimate patient bone stiffness and strength using simpler and less costly radiographs. Two-dimensional femur images were derived by projection of quantitative computed tomography scans of 22 human cadaveric femurs. The same femurs were fractured in a fall on the hip configuration. Femoral stiffness and fracture load were measured, and high speed video was recorded. Digital image correlation analysis was used to calculate the strain distribution from the high speed video recordings. Two-dimensional projection images were segmented and meshed with second-order triangular elements for finite element analysis. Elastic moduli of the finite elements were calculated based on the projected mineral density values inside the elements. The mapping of projection density values to elastic modulus was obtained using optimal parameter identification in a set of nine of the 22 specimens, and validated on the remaining 13 specimens. Finite element calculated proximal stiffness and strength correlated much better with experimental data than areal bone mineral density alone. In addition, finite element calculated strain distributions compared very well with strains obtained from digital image processing of the high speed video recordings, further validating the two-dimensional projected subject-specific finite element models.
NASA Technical Reports Server (NTRS)
Wu, R. W.; Witmer, E. A.
1972-01-01
A user-oriented FORTRAN 4 computer program, called JET 3, is presented. The JET 3 program, which employs the spatial finite-element and timewise finite-difference method, can be used to predict the large two-dimensional elastic-plastic transient Kirchhoff-type deformations of a complete or partial structural ring, with various support conditions and restraints, subjected to a variety of initial velocity distributions and externally-applied transient forcing functions. The geometric shapes of the structural ring can be circular or arbitrarily curved and with variable thickness. Strain-hardening and strain-rate effects of the material are taken into account.
NASA Technical Reports Server (NTRS)
Miller, Eric J.; Manalo, Russel; Tessler, Alexander
2016-01-01
A study was undertaken to investigate the measurement of wing deformation and internal loads using measured strain data. Future aerospace vehicle research depends on the ability to accurately measure the deformation and internal loads during ground testing and in flight. The approach uses the inverse Finite Element Method (iFEM). The iFEM is a robust, computationally efficient method that is well suited for real-time measurement of real-time structural deformation and loads. The method has been validated in previous work, but has yet to be applied to a large-scale test article. This work is in preparation for an upcoming loads test of a half-span test wing in the Flight Loads Laboratory at the National Aeronautics and Space Administration Armstrong Flight Research Center (Edwards, California). The method has been implemented into an efficient MATLAB® (The MathWorks, Inc., Natick, Massachusetts) code for testing different sensor configurations. This report discusses formulation and implementation along with the preliminary results from a representative aerospace structure. The end goal is to investigate the modeling and sensor placement approach so that the best practices can be applied to future aerospace projects.
Turner, Todd J.; Shade, Paul A; Bernier, Joel V.; Li, Shiu Fai; Schuren, Jay C.; Lind, Jonathan F.; Lienert, Ulrich; Kenesei, Peter; Suter, Robert; Blank, Basil; Almer, Jonathan
2016-01-01
We present both near-field HEDM data that maps out the grain morphology and intragranular crystallographic orientations and far-field HEDM data that provides the grain centroid, grain average crystallographic orientation, and grain average elastic strain tensor for each grain. Finally, we provide a finite element mesh that can be utilized to simulate deformation in the volume of this Ti-7Al specimen.
Finite deformation analysis of geomaterials
NASA Astrophysics Data System (ADS)
Jeremi, Boris; Runesson, Kenneth; Sture, Stein
2001-07-01
The mathematical structure and numerical analysis of classical small deformation elasto-plasticity is generally well established. However, development of large deformation elastic-plastic numerical formulation for dilatant, pressure sensitive material models is still a research area.In this paper we present development of the finite element formulation and implementation for large deformation, elastic-plastic analysis of geomaterials. Our developments are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A consistent linearization of the right deformation tensor together with the Newton method at the constitutive and global levels leads toward an efficient and robust numerical algorithm. The presented numerical formulation is capable of accurately modelling dilatant, pressure sensitive isotropic and anisotropic geomaterials subjected to large deformations. In particular, the formulation is capable of simulating the behaviour of geomaterials in which eigentriads of stress and strain do not coincide during the loading process.The algorithm is tested in conjunction with the novel hyperelasto-plastic model termed the B material model, which is a single surface (single yield surface, affine single ultimate surface and affine single potential surface) model for dilatant, pressure sensitive, hardening and softening geomaterials. It is specifically developed to model large deformation hyperelasto-plastic problems in geomechanics.We present an application of this formulation to numerical analysis of low confinement tests on cohesionless granular soil specimens recently performed in a SPACEHAB module aboard the Space Shuttle during the STS-89 mission. We compare numerical modelling with test results and show the significance of added confinement by the thin hyperelastic latex membrane undergoing large stretching.
NASA Astrophysics Data System (ADS)
Mohd Nor, M. K.; Ma'at, N.; Kamarudin, K. A.; Ismail, A. E.
2016-11-01
The constitutive models adopted to represent dynamic plastic behaviour are of great importance in the current design and analysis of forming processes. Many have studied this topic, leading to results in various technologies involving analytical, experimental and computational methods. Despite of this current status, it is generally agreed that there is still a need for improved constitutive models. There are still many issues relating to algorithm implementation of the proposed constitutive model in the selected code to represent the proposed formulation. Using this motivation, the implementation of a new constitutive model into the LLNL-DYNA3D code to predict the deformation behaviour of commercial aluminium alloys is discussed concisely in this paper. The paper initially explains the background and the basic structure of the LLNL-DYNA3D code. This is followed by a discussion on the constitutive models that have been chosen as the starting point for this work. The initial stage of this implementation work is then discussed in order to allow all the required material data and the deformation gradient tensor F to be read and initialised for the main analysis. Later, the key section of this implementation is discussed, which mainly relates to subroutine f3dm93 including equation of state (EOS) implementation. The implementation of the elastic-plastic part with isotropic plastic hardening, which establishes the relationship between stress and strain with respect to the isoclinic configuration Ω¯ i in the new deviatoric plane, is then presented before the implemented algorithm is validated against Plate Impact test data of the Aluminium Alloy 7010. A good agreement is obtained in each test.
Elasticity of Wadsleyite at 12 GPa1073K
W Liu; J Kung; B Li; N Nishiyama; Y Wang
2011-12-31
Elasticity of (Mg{sub 0.87}Fe{sub 0.13}){sub 2}SiO{sub 4} wadsleyite has been measured at simultaneous high pressure and high temperature to 12 GPa and 1073 K using ultrasonic interferometry in conjunction with synchrotron X-radiation. The elastic moduli and their pressure and temperature derivatives are precisely determined using pressure-standard-free third-order and fourth-order finite strain equations. Combined with previous thermoelastic data on olivine, the density, velocity and acoustic impedance contrasts between {alpha}- and {beta}-(Mg{sub 0.9}Fe{sub 0.1}){sub 2}SiO{sub 4} at 410-km depth are calculated along a 1673 K adiabatic geotherm. Both the third- and fourth-order finite strain equation fitting results give estimation of {approx}33-58% olivine content in the upper mantle to account for a seismic discontinuity of {approx}5% velocity jumps, and 8.5% (P wave) and 11.1% (S wave) impedance jumps at 410 km depth.
Kuryliuk, V. V. Korotchenkov, O. A.
2013-08-15
Within the elastic continuum model, with the use of the finite-element method, the stress-strain state of silicon-germanium heterostructures with semispherical germanium islands grown on an oxidized silicon surface is calculated. It is shown that as the density of islands is increased to limiting values, in the SiGe structure with open quantum dots the value and spatial distribution of the elastic-strain fields significantly change. The results of theoretical calculation allow the heterostructure portions with the maximum variation in the stress-strain state to be determined. The position of such a portions can be controlled by changing the density of islands.
Elastic proteins: biological roles and mechanical properties.
Gosline, John; Lillie, Margo; Carrington, Emily; Guerette, Paul; Ortlepp, Christine; Savage, Ken
2002-01-01
The term 'elastic protein' applies to many structural proteins with diverse functions and mechanical properties so there is room for confusion about its meaning. Elastic implies the property of elasticity, or the ability to deform reversibly without loss of energy; so elastic proteins should have high resilience. Another meaning for elastic is 'stretchy', or the ability to be deformed to large strains with little force. Thus, elastic proteins should have low stiffness. The combination of high resilience, large strains and low stiffness is characteristic of rubber-like proteins (e.g. resilin and elastin) that function in the storage of elastic-strain energy. Other elastic proteins play very different roles and have very different properties. Collagen fibres provide exceptional energy storage capacity but are not very stretchy. Mussel byssus threads and spider dragline silks are also elastic proteins because, in spite of their considerable strength and stiffness, they are remarkably stretchy. The combination of strength and extensibility, together with low resilience, gives these materials an impressive resistance to fracture (i.e. toughness), a property that allows mussels to survive crashing waves and spiders to build exquisite aerial filters. Given this range of properties and functions, it is probable that elastic proteins will provide a wealth of chemical structures and elastic mechanisms that can be exploited in novel structural materials through biotechnology. PMID:11911769
Study of the elastic behavior of synthetic lightweight aggregates (SLAs)
NASA Astrophysics Data System (ADS)
Jin, Na
Synthetic lightweight aggregates (SLAs), composed of coal fly ash and recycled plastics, represent a resilient construction material that could be a key aspect to future sustainable development. This research focuses on a prediction of the elastic modulus of SLA, assumed as a homogenous and isotropic composite of particulates of high carbon fly ash (HCFA) and a matrix of plastics (HDPE, LDPE, PS and mixture of plastics), with the emphasis on SLAs made of HCFA and PS. The elastic moduli of SLA with variable fly ash volume fractions are predicted based on finite element analyses (FEA) performed using the computer programs ABAQUS and PLAXIS. The effect of interface friction (roughness) between phases and other computation parameters; e.g., loading strain, stiffness of component, element type and boundary conditions, are included in these analyses. Analytical models and laboratory tests provide a baseline for comparison. Overall, results indicate ABAQUS generates elastic moduli closer to those predicted by well-established analytical models than moduli predicted from PLAXIS, especially for SLAs with lower fly ash content. In addition, an increase in roughness, loading strain indicated increase of SLAs stiffness, especially as fly ash content increases. The elastic moduli obtained from unconfined compression generally showed less elastic moduli than those obtained from analytical and ABAQUS 3D predictions. This may be caused by possible existence of pre-failure surface in specimen and the directly interaction between HCFA particles. Recommendations for the future work include laboratory measurements of SLAs moduli and FEM modeling that considers various sizes and random distribution of HCFA particles in SLAs.
A Method for Connecting Dissimilar Finite Element Meshes in Three Dimensions
Dohrmann, C.R.; Heinstein, M.W.; Key, S.W.
1998-11-12
A method is presented for connecting dissimilar finite element meshes in three dimensions. The method combines the concept of master and slave surfaces with the uniform strain approach for surface, corrections finite elements- By modifyhg the are made to element formulations boundaries of elements on the slave such that first-order patch tests are passed. The method can be used to connect meshes which use different element types. In addition, master and slave surfaces can be designated independently of relative mesh resolutions. Example problems in three-dimensional linear elasticity are presented.
Elastic waves in quasiperiodic structures
NASA Astrophysics Data System (ADS)
Velasco, V. R.; Zárate, J. E.
2001-08-01
We study the transverse and sagittal elastic waves in different quasiperiodic structures by means of the full transfer-matrix technique and surface Green-function matching method. The quasiperiodic structures follow Fibonacci, Thue-Morse and Rudin-Shapiro sequences, respectively. We consider finite structures having stress-free bounding surfaces and different generation orders, including up to more than 1000 interfaces. We obtain the dispersion relations for elastic waves and spatial localization of the different modes. The fragmentation of the spectrum for different sequences is evident for intermediate generation orders, in the case of transverse elastic waves, whereas, for sagittal elastic waves, higher generation orders are needed to show clearly the spectrum fragmentation. The results of Fibonacci and Thue-Morse sequences exhibit similarities not present in the results of Rudin-Shapiro sequences.
Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness.
Berger, J B; Wadley, H N G; McMeeking, R M
2017-02-20
A wide variety of high-performance applications require materials for which shape control is maintained under substantial stress, and that have minimal density. Bio-inspired hexagonal and square honeycomb structures and lattice materials based on repeating unit cells composed of webs or trusses, when made from materials of high elastic stiffness and low density, represent some of the lightest, stiffest and strongest materials available today. Recent advances in 3D printing and automated assembly have enabled such complicated material geometries to be fabricated at low (and declining) cost. These mechanical metamaterials have properties that are a function of their mesoscale geometry as well as their constituents, leading to combinations of properties that are unobtainable in solid materials; however, a material geometry that achieves the theoretical upper bounds for isotropic elasticity and strain energy storage (the Hashin-Shtrikman upper bounds) has yet to be identified. Here we evaluate the manner in which strain energy distributes under load in a representative selection of material geometries, to identify the morphological features associated with high elastic performance. Using finite-element models, supported by analytical methods, and a heuristic optimization scheme, we identify a material geometry that achieves the Hashin-Shtrikman upper bounds on isotropic elastic stiffness. Previous work has focused on truss networks and anisotropic honeycombs, neither of which can achieve this theoretical limit. We find that stiff but well distributed networks of plates are required to transfer loads efficiently between neighbouring members. The resulting low-density mechanical metamaterials have many advantageous properties: their mesoscale geometry can facilitate large crushing strains with high energy absorption, optical bandgaps and mechanically tunable acoustic bandgaps, high thermal insulation, buoyancy, and fluid storage and transport. Our relatively simple
Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness
NASA Astrophysics Data System (ADS)
Berger, J. B.; Wadley, H. N. G.; McMeeking, R. M.
2017-02-01
A wide variety of high-performance applications require materials for which shape control is maintained under substantial stress, and that have minimal density. Bio-inspired hexagonal and square honeycomb structures and lattice materials based on repeating unit cells composed of webs or trusses, when made from materials of high elastic stiffness and low density, represent some of the lightest, stiffest and strongest materials available today. Recent advances in 3D printing and automated assembly have enabled such complicated material geometries to be fabricated at low (and declining) cost. These mechanical metamaterials have properties that are a function of their mesoscale geometry as well as their constituents, leading to combinations of properties that are unobtainable in solid materials; however, a material geometry that achieves the theoretical upper bounds for isotropic elasticity and strain energy storage (the Hashin–Shtrikman upper bounds) has yet to be identified. Here we evaluate the manner in which strain energy distributes under load in a representative selection of material geometries, to identify the morphological features associated with high elastic performance. Using finite-element models, supported by analytical methods, and a heuristic optimization scheme, we identify a material geometry that achieves the Hashin–Shtrikman upper bounds on isotropic elastic stiffness. Previous work has focused on truss networks and anisotropic honeycombs, neither of which can achieve this theoretical limit. We find that stiff but well distributed networks of plates are required to transfer loads efficiently between neighbouring members. The resulting low-density mechanical metamaterials have many advantageous properties: their mesoscale geometry can facilitate large crushing strains with high energy absorption, optical bandgaps and mechanically tunable acoustic bandgaps, high thermal insulation, buoyancy, and fluid storage and transport. Our relatively simple
Two simplified procedures for predicting cyclic material response from a strain history
NASA Technical Reports Server (NTRS)
Kaufman, A.; Moreno, V.
1985-01-01
Simplified inelastic analysis procedures were developed at NASA Lewis and Pratt & Whitney Aircraft for predicting the stress-strain response at the critical location of a thermomechanically cycled structure. These procedures are intended primarily for use as economical structural analysis tools in the early design stages of aircraft engine hot section components where nonlinear finite-element analyses would be prohibitively expensive. Both simplified methods use as input the total strain history calculated from a linear elastic analysis. The elastic results are modified to approximate the characteristics of the inelastic cycle by incremental solution techniques. A von Mises yield criterion is used to determine the onset of active plasticity. The fundamental assumption of these methods is that the inelastic strain is local and constrained from redistribution by the surrounding elastic material.
Finite elements of nonlinear continua.
NASA Technical Reports Server (NTRS)
Oden, J. T.
1972-01-01
The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.
NASA Astrophysics Data System (ADS)
Gianola, Daniel; Strickland, Daniel; Huang, Yun-Ru; Derlet, Peter; Lee, Daeyeon
2015-03-01
We study the uniaxial compressive behavior of disordered colloidal free-standing micropillars composed of a mixture of 3 and 6 μm polystyrene particles. Mechanical annealing enables variation of the packing fraction across the phase space of colloidal glasses. The measured strengths and elastic moduli of the micropillars span almost three orders-of-magnitude despite similar plastic morphology governed by shear banding. We measure a robust correlation between strengths and elastic constants that is invariant to humidity, implying a critical strain of ~0.01 that is strikingly similar to that observed in metallic glasses and suggestive of a universal mode of cooperative plastic deformation. We estimate the characteristic strain of the underlying cooperative plastic event by considering the energy necessary to create an Eshelby-like ellipsoidal inclusion in an elastic matrix. We find that the characteristic strain is similar to that found in experiments and simulations of other disordered solids with distinct bonding and particle sizes, suggesting a universal criterion for the elastic to plastic transition in glassy materials with the capacity for finite plastic flow. In addition, we measure the statistics of load-drops for specimens at three packing fractions. At higher packing fractions, the load-drops scale as a power-law with an exponent close to mean field theory (MFT) predictions. However, the scaling at the lowest packing fraction deviates from MFT.
Strickland, Daniel J.; Huang, Yun-Ru; Lee, Daeyeon
2014-01-01
We study the uniaxial compressive behavior of disordered colloidal free-standing micropillars composed of a bidisperse mixture of 3- and 6-μm polystyrene particles. Mechanical annealing of confined pillars enables variation of the packing fraction across the phase space of colloidal glasses. The measured normalized strengths and elastic moduli of the annealed freestanding micropillars span almost three orders of magnitude despite similar plastic morphology governed by shear banding. We measure a robust correlation between ultimate strengths and elastic constants that is invariant to relative humidity, implying a critical strain of ∼0.01 that is strikingly similar to that observed in metallic glasses (MGs) [Johnson WL, Samwer K (2005) Phys Rev Lett 95:195501] and suggestive of a universal mode of cooperative plastic deformation. We estimate the characteristic strain of the underlying cooperative plastic event by considering the energy necessary to create an Eshelby-like ellipsoidal inclusion in an elastic matrix. We find that the characteristic strain is similar to that found in experiments and simulations of other disordered solids with distinct bonding and particle sizes, suggesting a universal criterion for the elastic to plastic transition in glassy materials with the capacity for finite plastic flow. PMID:25489098
Feng, Guo-Hua; Huang, Wei-Lun
2014-12-01
This paper presents a smart tuning-fork-shaped ionic polymer metal composite (IPMC) clamping actuator for biomedical applications. The two fingers of the actuator, which perform the clamping motion, can be electrically controlled through a unique electrode design on the IPMC material. The generated displacement or strain of the fingers can be sensed using an integrated soft strain-gage sensor. The IPMC actuator and associated soft strain gage were fabricated using a micromachining technique. A 13.5×4×2 mm(3) actuator was shaped from Nafion solution and a selectively grown metal electrode formed the active region. The strain gage consisted of patterned copper foil and polyethylene as a substrate. The relationship between the strain gage voltage output and the displacement at the front end of the actuator's fingers was characterized. The equivalent Young's modulus, 13.65 MPa, of the soft-strain-gage-integrated IPMC finger was analyzed. The produced clamping force exhibited a linear increasing rate of 1.07 mN/s, based on a dc driving voltage of 7 V. Using the developed actuator to clamp soft matter and simultaneously acquire its Young's modulus was achieved. This demonstrated the feasibility of the palpation function and the potential use of the actuator in minimally invasive surgery.
Inverted cones and their elastic creases
NASA Astrophysics Data System (ADS)
Seffen, Keith A.
2016-12-01
We study the elastic inversion of a right circular cone, in particular, the uniform shape of the narrow crease that divides its upright and inverted parts. Our methodology considers a cylindrical shell analogy for simplicity where the crease is the boundary layer deformation. Solution of its governing equation of deformation requires careful crafting of the underlying assumptions and boundary conditions in order to reveal an expression for the crease shape in closed form. We can then define the characteristic width of crease exactly, which is compared to a geometrically nonlinear, large displacement finite element analysis. This width is shown to be accurately predicted for shallow and steep cones, which imparts confidence to our original assumptions. Using the shape of crease, we compute the strain energy stored in the inverted cone, in order to derive an expression for the applied force of inversion by a simple energy method. Again, our predictions match finite element data very well. This study may complement other studies of creases traditionally formed in a less controlled manner, for example, during crumpling of lightweight sheets.
Quasi-Static Viscoelastic Finite Element Model of an Aircraft Tire
NASA Technical Reports Server (NTRS)
Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.
1999-01-01
An elastic large displacement thick-shell mixed finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at the element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses is included in the mixed variational functional. The nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the nonlinear elastic equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to computationally simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.
NASA Astrophysics Data System (ADS)
Hieber, Simone E.; Koumoutsakos, Petros
2008-11-01
We present a novel Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue. Linear solids are represented by the Lagrangian formulation of the stress-strain relationship that is extended to nonlinear solids by using the Lagrangian evolution of the deformation gradient described in a moving framework. The present method introduces a level set description, along with the particles, to capture the body deformations and to enforce the boundary conditions. Furthermore, the accuracy of the method in cases of large deformations is ensured by implementing a particle remeshing procedure. The method is validated in several benchmark problems, in two and three dimensions and the results compare well with the results of respective finite elements simulations. In simulations of large solid deformation under plane strain compression, the finite element solver exhibits spurious structures that are not present in the Lagrangian particle simulations. The particle simulations are compared with experimental results in an aspiration test of liver tissue.
A survey of mixed finite element methods
NASA Technical Reports Server (NTRS)
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
Elastic modulus of viral nanotubes
NASA Astrophysics Data System (ADS)
Zhao, Yue; Ge, Zhibin; Fang, Jiyu
2008-09-01
We report an experimental and theoretical study of the radial elasticity of tobacco mosaic virus (TMV) nanotubes. An atomic force microscope tip is used to apply small radial indentations to deform TMV nanotubes. The initial elastic response of TMV nanotubes can be described by finite-element analysis in 5nm indentation depths and Hertz theory in 1.5nm indentation depths. The derived radial Young’s modulus of TMV nanotubes is 0.92±0.15GPa from finite-element analysis and 1.0±0.2GPa from the Hertz model, which are comparable with the reported axial Young’s modulus of 1.1GPa [Falvo , Biophys. J. 72, 1396 (1997)].
Time-dependent strains and stresses in a pumpkin balloon
NASA Technical Reports Server (NTRS)
Gerngross, T.; Xu, Y.; Pellegrino, S.
2006-01-01
This paper presents a study of pumpkin-shaped superpressure balloons, consisting of gores made from a thin polymeric film attached to high stiffness, meridional tendons. This type of design is being used for the NASA ULDB balloons. The gore film shows considerable time-dependent stress relaxation, whereas the behaviour of the tendons is essentially time-independent. Upon inflation and pressurization, the "instantaneous", i.e. linear-elastic strain and stress distribution in the film show significantly higher values in the meridional direction. However, over time, and due to the biaxial visco-elastic stress relaxation of the the material, the hoop strains increase and the meridional stresses decrease, whereas the remaining strain and stress components remain substantially unchanged. These results are important for a correct assessment of the structural integrity of a pumpkin balloon in a long-duration mission, both in terms of the material performance and the overall stability of the shape of the balloon. An experimental investigation of the time dependence of the biaxial strain distribution in the film of a 4 m diameter, 48 gore pumpkin balloon is presented. The inflated shape of selected gores has been measured using photogrammetry and the time variation in strain components at some particular points of these gores has been measured under constant pressure and temperature. The results show good correlation with a numerical study, using the ABAQUS finite-element package, that includes a widely used model of the visco-elastic response of the gore material:
Significance of Strain in Formulation in Theory of Solid Mechanics
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.
2003-01-01
The basic theory of solid mechanics was deemed complete circa 1860 when St. Venant provided the strain formulation or the field compatibility condition. The strain formulation was incomplete. The missing portion has been formulated and identified as the boundary compatibility condition (BCC). The BCC, derived through a variational formulation, has been verified through integral theorem and solution of problems. The BCC, unlike the field counterpart, do not trivialize when expressed in displacements. Navier s method and the stiffness formulation have to account for the extra conditions especially at the inter-element boundaries in a finite element model. Completion of the strain formulation has led to the revival of the direct force calculation methods: the Integrated Force Method (IFM) and its dual (IFMD) for finite element analysis, and the completed Beltrami-Michell formulation (CBMF) in elasticity. The benefits from the new methods in elasticity, in finite element analysis, and in design optimization are discussed. Existing solutions and computer codes may have to be adjusted for the compliance of the new conditions. Complacency because the discipline is over a century old and computer codes have been developed for half a century can lead to stagnation of the discipline.
Dynamic response of visco-elastic plates
NASA Astrophysics Data System (ADS)
Kadıoǧlu, Fethi; Tekin, Gülçin
2016-12-01
In this study, a comprehensive analysis about the dynamic response characteristics of visco-elastic plates is given. To construct the functional in the Laplace-Carson domain for the analysis of visco-elastic plates based on the Kirchhoff hypothesis, functional analysis method is employed. By using this new energy functional in the Laplace-Carson domain, moment values that are important for engineers can be obtained directly with excellent accuracy and element equations can be written explicitly. Three-element model is considered for modelling the visco-elastic material behavior. The solutions obtained in the Laplace-Carson domain by utilizing mixed finite element formulation are transformed to the time domain using the Durbin's inverse Laplace transform technique. The proposed mixed finite element formulation is shown to be simple to implement and gives satisfactory results for dynamic response of visco-elastic plates.
Hay, Todd A.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.
2013-01-01
A model is developed for a pulsating and translating gas bubble immersed in liquid in a channel formed by two soft, thin elastic parallel layers having densities equal to that of the surrounding liquid and small, but finite, shear moduli. The bubble is nominally spherical but free to undergo small shape deformations. Shear strain in the elastic layers is estimated in a way which is valid for short, transient excitations of the system. Coupled nonlinear second-order differential equations are obtained for the shape and position of the bubble, and numerical integration of an expression for the liquid velocity at the layer interfaces yields an estimate of the elastic layer displacement. Numerical integration of the dynamical equations reveals behavior consistent with laboratory observations of acoustically excited bubbles in ex vivo vessels reported by Chen et al. [Phys. Rev. Lett. 106, 034301 (2011) and Ultrasound Med. Biol. 37, 2139–2148 (2011)]. PMID:23927185
NASA Astrophysics Data System (ADS)
Espada, M.; Lamas, L.
2017-03-01
This paper presents a back analysis procedure for identification of the elastic parameters of transversely isotropic rock cores, containing an overcoring triaxial strain probe, from the strains measured during a biaxial test. A three-dimensional finite element model was developed to simulate the biaxial test on the overcored rock specimen and to compute the strains at the location of the strain gauges. Different optimisation algorithms were tested and the most suitable one was selected. The back analysis procedure was tested for identification of the five elastic parameters and the two orientation angles that characterise a transversely isotropic rock core. Despite that, with the developed methodology, convergence was reached and all those parameters could be identified, sensitivity analyses demonstrated that the results obtained were not stable, and therefore, they were not reliable. By introducing constrains based on common practice and previous experience, a stable and robust methodology was achieved: the three elastic parameters, E 1, E 2 and ν 2, are reliably identified using the value of G 2 calculated with Saint-Venant expression and a fixed value of ν 1, while the orientation parameters are obtained from observation of overcored rock. Analysis of the results shows that application of this methodology represents an enormous step forward when compared with the traditional use of isotropy. Besides, the methodology is general and can also be used with other types of overcoring equipment. The five elastic parameters and the two orientation angles obtained can then be used, together with the overcoring strains, to compute the complete in situ state of stress.
Schichtel, N; Korte, C; Hesse, D; Janek, J
2009-05-07
Ionic transport in solids parallel to grain or phase boundaries is usually strongly enhanced compared to the bulk. Transport perpendicular to an interface (across an interface) is often much slower. Therefore in modern micro- and nanoscaled devices, a severe influence on the ionic/atomic transport properties can be expected due to the high density of interfaces.Transport processes in boundaries of ionic materials are still not understood on an atomic scale. In most of the studies on ionic materials the interfacial transport properties are explained by the influence of space charge regions. Here we discuss the influence of interfacial strain at semicoherent or coherent heterophase boundaries on ionic transport along these interfaces in ionic materials. A qualitative model is introduced for (untilted and untwisted) hetero phase boundaries. For experimental verification, the interfacial oxygen ionic conductivity of different multilayer systems consisting of cubic ZrO(2) stabilised by aliovalent dopands (YSZ, CSZ) and an insulating oxide is investigated as a function of structural mismatch. Recent results on extremely fast ionic conduction in YSZ/SrTiO(3) thin film systems ("colossal ionic concuctivity at interfaces") is discussed from the viewpoint of strain effects.
An experimental/analytical comparison of strains in encapsulated assemblies
Guess, T.R.; Burchett, S.N.
1991-11-01
A combined experimental and analytical study of strains developed in encapsulated assemblies during casting, curing and thermal excursions is described. The experimental setup, designed to measure in situ strains, consisted of thin, closed-end, Kovar tubes that were instrumented with strain gages and thermocouples before being over-cast with a polymeric encapsulant. Four bisphenol A (three diethanolamine cured and one anhydride cured) epoxy-based materials and one urethane elastomeric material were studied. After cure of the encapsulant, tube strains were measured over the temperature range of {minus}55{degrees}C to 90{degrees}C. The thermal excursion experiments were then numerically modeled using finite element analyses and the computed strains were compared to the experimental strains. The predicted strains were over estimated (conservative) when a linear, elastic, temperature-dependent material model was assumed for the encapsulant and the stress free temperature T{sub i} was assumed to correspond to the cure temperature {Tc} of the encapsulant. Very good agreement was obtained with linear elastic calculations provided that the stress free temperature corresponded to the onset of the glassy-to-rubbery transition range of the encapsulant. Finally, excellent agreement was obtained in one of the materials (828/DEA) when a viscoelastic material model was utilized and a stress free temperature corresponding to the cure temperature was assumed. 13 refs., 20 figs., 3 tabs.
Inelastic Strain Analysis of Solder Joint in NASA Fatigue Specimen
NASA Technical Reports Server (NTRS)
Dasgupta, Abhijit; Oyan, Chen
1991-01-01
The solder fatigue specimen designed by NASA-GSFC/UNISYS is analyzed in order to obtain the inelastic strain history during two different representative temperature cycles specified by UNISYS. In previous reports (dated July 25, 1990, and November 15, 1990), results were presented of the elastic-plastic and creep analysis for delta T = 31 C cycle, respectively. Subsequent results obtained during the current phase, from viscoplastic finite element analysis of the solder fatigue specimen for delta T = 113 C cycle are summarized. Some common information is repeated for self-completeness. Large-deformation continuum formulations in conjunction with a standard linear solid model is utilized for modeling the solder constitutive creep-plasticity behavior. Relevant material properties are obtained from the literature. Strain amplitudes, mean strains, and residual strains (as well as stresses) accumulated due to a representative complete temperature cycle are obtained as a result of this analysis. The partitioning between elastic strains, time-independent inelastic (plastic) strains, and time-dependent inelastic (creep) strains is also explicitly obtained for two representative cycles. Detailed plots are presented for two representative temperature cycles. This information forms an important input for fatigue damage models, when predicting the fatigue life of solder joints under thermal cycling
Indentation-derived elastic modulus of multilayer thin films: Effect of unloading induced plasticity
Jamison, Ryan Dale; Shen, Yu -Lin
2015-08-13
Nanoindentation is useful for evaluating the mechanical properties, such as elastic modulus, of multilayer thin film materials. A fundamental assumption in the derivation of the elastic modulus from nanoindentation is that the unloading process is purely elastic. In this work, the validity of elastic assumption as it applies to multilayer thin films is studied using the finite element method. The elastic modulus and hardness from the model system are compared to experimental results to show validity of the model. Plastic strain is shown to increase in the multilayer system during the unloading process. Additionally, the indentation-derived modulus of a monolayermore » material shows no dependence on unloading plasticity while the modulus of the multilayer system is dependent on unloading-induced plasticity. Lastly, the cyclic behavior of the multilayer thin film is studied in relation to the influence of unloading-induced plasticity. Furthermore, it is found that several cycles are required to minimize unloading-induced plasticity.« less
NASA Astrophysics Data System (ADS)
Shahzamanian, M. M.; Sahari, B. B.; Bayat, M.; Mustapha, F.; Ismarrubie, Z. N.
2013-01-01
In this paper, finite element contact analysis of a functionally graded (FG) brake disk in contact with a pad, subjected to rotation, contact pressure, and frictional heat, is presented. The material properties vary through the thickness according to a power-law characterized by a grading index, n. The contact surfaces are full-ceramic with full-metal free surface. The effects of n on the displacement, contact status, strain and stress are investigated. From the analysis, thermo-elastic and contact results are extremely dependent on n. Hence, n is an important criteria for the design of FG brake disks for automotive and aircraft applications.
Validation experiments on finite element models of an ostrich (Struthio camelus) cranium
Bright, Jen A.; Rayfield, Emily J.
2015-01-01
The first finite element (FE) validation of a complete avian cranium was performed on an extant palaeognath, the ostrich (Struthio camelus). Ex-vivo strains were collected from the cranial bone and rhamphotheca. These experimental strains were then compared to convergence tested, specimen-specific finite element (FE) models. The FE models contained segmented cortical and trabecular bone, sutures and the keratinous rhamphotheca as identified from micro-CT scan data. Each of these individual materials was assigned isotropic material properties either from the literature or from nanoindentation, and the FE models compared to the ex-vivo results. The FE models generally replicate the location of peak strains and reflect the correct mode of deformation in the rostral region. The models are too stiff in regions of experimentally recorded high strain and too elastic in regions of low experimentally recorded low strain. The mode of deformation in the low strain neurocranial region is not replicated by the FE models, and although the models replicate strain orientations to within 10° in some regions, in most regions the correlation is not strong. Cranial sutures, as has previously been found in other taxa, are important for modifying both strain magnitude and strain patterns across the entire skull, but especially between opposing the sutural junctions. Experimentally, we find that the strains on the surface of the rhamphotheca are much lower than those found on nearby bone. The FE models produce much higher principal strains despite similar strain ratios across the entirety of the rhamphotheca. This study emphasises the importance of attempting to validate FE models, modelling sutures and rhamphothecae in birds, and shows that whilst location of peak strain and patterns of deformation can be modelled, replicating experimental data in digital models of avian crania remains problematic. PMID:26500813
Elasticity limits structural superlubricity in large contacts
NASA Astrophysics Data System (ADS)
Sharp, Tristan A.; Pastewka, Lars; Robbins, Mark O.
2016-03-01
Geometrically imposed force cancellations lead to ultralow friction between rigid incommensurate crystalline asperities. Elastic deformations may avert this cancellation but are difficult to treat analytically in finite and three-dimensional systems. We use atomic-scale simulations to show that elasticity affects the friction only after the contact radius a exceeds a characteristic length set by the core width of interfacial dislocations bcore. As a increases past bcore, the frictional stress for both incommensurate and commensurate surfaces decreases to a constant value. This plateau corresponds to a Peierls stress that drops exponentially with increasing bcore but remains finite.
NASA Technical Reports Server (NTRS)
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.
Theory of epithelial elasticity
NASA Astrophysics Data System (ADS)
Krajnc, Matej; Ziherl, Primož
2015-11-01
We propose an elastic theory of epithelial monolayers based on a two-dimensional discrete model of dropletlike cells characterized by differential surface tensions of their apical, basal, and lateral sides. We show that the effective tissue bending modulus depends on the apicobasal differential tension and changes sign at the transition from the flat to the fold morphology. We discuss three mechanisms that stabilize the finite-wavelength fold structures: Physical constraint on cell geometry, hard-core interaction between non-neighboring cells, and bending elasticity of the basement membrane. We show that the thickness of the monolayer changes along the waveform and thus needs to be considered as a variable rather than a parameter. Next we show that the coupling between the curvature and the thickness is governed by the apicobasal polarity and that the amplitude of thickness modulation along the waveform is proportional to the apicobasal differential tension. This suggests that intracellular stresses can be measured indirectly by observing easily measurable morphometric parameters. We also study the mechanics of three-dimensional structures with cylindrical symmetry.
NASA Astrophysics Data System (ADS)
Renaud, Guillaume; Talmant, Maryline; Marrelec, Guillaume
2016-10-01
The nonlinear elasticity of solids at the microstrain level has been recently studied by applying dynamic acousto-elastic testing. It is the analog of conventional quasi-static acousto-elastic experiments but the strain-dependence (or stress-dependence) of ultrasonic wave-speed is measured with an applied strain ranging from 10-7 to 10-5 and produced by a stationary elastic wave. In conventional quasi-static acousto-elastic experiments, the strain is applied in a quasi-static manner; it exceeds 10-4 and can reach 10-2. In this work, we apply dynamic acousto-elastic testing to measure the third-order elastic constants of two isotropic materials: polymethyl methacrylate and dry Berea sandstone. The peak amplitude of the dynamic applied strain is 8 × 10-6. The method is shown to be particularly suitable for materials exhibiting large elastic nonlinearity like sandstones, since the measurement is performed in the domain of validity of the third-order hyperelastic model. In contrast, conventional quasi-static acousto-elastic experiments in such materials are often performed outside the domain of validity of the third-order hyperelastic model and the stress-dependence of the ultrasonic wave-speed must be extrapolated at zero stress, leading to approximate values of the third-order elastic constants. The uncertainty of the evaluation of the third-order elastic constants is assessed by repeating multiple times the measurements and with Monte-Carlo simulations. The obtained values of the Murnaghan third-order elastic constants are l = -73 GPa ± 9%, m = -34 GPa ± 9%, and n = -61 GPa ± 10% for polymethyl methacrylate, and l = -17 000 GPa ± 20%, m = -11 000 GPa ± 10%, and n = -30 000 GPa ± 20% for dry Berea sandstone.
Croft, M.; Shukla, V.; Akdogan, E. K.; Sadangi, R.; Ignatov, A.; Balarinni, L.; Tsakalakos, T.; Jisrawi, N.; Zhong, Z.; Horvath, K.
2009-05-01
Elastic and plastic strain evolution under four-point bending has been studied by synchrotron energy dispersive x-ray diffraction. Measured strain profiles across the specimen thickness showed an increasing linear elastic strain gradient under increasing four-point bending load up to approx2 kN. The bulk elastic modulus of Ti-6Al-4V was determined as 118 GPa. The onset of plastic deformation was found to set in at a total in-plane strain of approx0.008, both under tension and compression. Plastic deformation under bending is initiated in the vicinity of the surface and at a stress of 1100 MPa, and propagates inward, while a finite core region remains elastically deformed up to 3.67 kN loading. The onset of the plastic regime and the plastic regime itself has been verified by monitoring the line broadening of the (100) peak of alpha-Ti. The effective compression/tension stress-strain curve has been obtained from the scaling collapse of strain profile data taken at seven external load levels. A similar multiple load scaling collapse of the plastic strain variation has also been obtained. The level of precision in strain measurement reported herein was evaluated and found to be 1.5x10{sup -5} or better.
On the response of rubbers at high strain rates.
Niemczura, Johnathan Greenberg
2010-02-01
In this report, we examine the propagation of tensile waves of finite deformation in rubbers through experiments and analysis. Attention is focused on the propagation of one-dimensional dispersive and shock waves in strips of latex and nitrile rubber. Tensile wave propagation experiments were conducted at high strain-rates by holding one end fixed and displacing the other end at a constant velocity. A high-speed video camera was used to monitor the motion and to determine the evolution of strain and particle velocity in the rubber strips. Analysis of the response through the theory of finite waves and quantitative matching between the experimental observations and analytical predictions was used to determine an appropriate instantaneous elastic response for the rubbers. This analysis also yields the tensile shock adiabat for rubber. Dispersive waves as well as shock waves are also observed in free-retraction experiments; these are used to quantify hysteretic effects in rubber.
NASA Astrophysics Data System (ADS)
Kang, I. S.; Leal, L. G.
1987-07-01
A numerical technique for solving axisymmetric, unsteady free-boundary problems in fluid mechanics is presented. This finite-difference method is a generalization of the steady algorithm reported by Ryskin and Leal (1984). In this scheme, all boundary surfaces of the solution domain at any time coincide exactly with a coordinate line of a numerically generated orthogonal coordinate system. Thus, unreasonable grid deformation during calculation is not a problem. A transient algorithm for applying the orthogonal mapping technique to unsteady free-boundary problems is developed. The unsteady deformation of a bubble in a uniaxial extensional flow for Reynolds numbers between 0.1 and 100 is considered as an example.
Tissue elasticity measurement method using forward and inversion algorithms
NASA Astrophysics Data System (ADS)
Lee, Jong-Ha; Won, Chang-Hee; Park, Hee-Jun; Ku, Jeonghun; Heo, Yun Seok; Kim, Yoon-Nyun
2013-03-01
Elasticity is an important indicator of tissue health, with increased stiffness pointing to an increased risk of cancer. We investigated a tissue elasticity measurement method using forward and inversion algorithms for the application of early breast tumor identification. An optical based elasticity measurement system is developed to capture images of the embedded lesions using total internal reflection principle. From elasticity images, we developed a novel method to estimate the elasticity of the embedded lesion using 3-D finite-element-model-based forward algorithm, and neural-network-based inversion algorithm. The experimental results showed that the proposed characterization method can be diffierentiate the benign and malignant breast lesions.
Energy dissipation associated with crack extension in an elastic-plastic material
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Crews, J. H., Jr.
1987-01-01
Crack extension in elastic-plastic material involves energy dissipation through the creation of new crack surfaces and additional yielding around the crack front. An analytical procedure, using a two-dimensional elastic-plastic finite element method, was developed to calculate the energy dissipation components during a quasi-static crack extension. The fracture of an isotropic compact specimen was numerically simulated using the critical crack-tip-opening-displacement (CTOD) growth criterion. Two specimen sizes were analyzed for three values of critical CTOD. Results from the analyses showed that the total energy dissipation rate consisted of three components: the crack separation energy rate, the plastic energy dissipation rate, and the residual strain energy rate. All three energy dissipation components and the total energy dissipation rate initially increased with crack extension and finally reached constant values.
NASA Astrophysics Data System (ADS)
Nishi, H.
2004-08-01
Since the first wall and divertor components of fusion power plants are subjected to severe stresses caused by thermal expansion and electromagnetic forces, it is important to evaluate the fatigue strength of joints. In this study, elastic-plastic finite element analysis was performed for low cycle fatigue behavior of stainless steel/alumina dispersion-strengthened copper (DS Cu) joint in order to investigate the fatigue life and the fracture behavior of the joint. The results showed that a strain concentration occurred at the interface during low cycle fatigue, but as the strain range increased the strain concentration shifted away from the interface and into the DS Cu. The fatigue life and fracture location were evaluated taking into account of the strain concentration. Predictions of the fatigue life and fracture location were consistent with those measured by the low cycle fatigue test.
A nonaffine network model for elastomers undergoing finite deformations
NASA Astrophysics Data System (ADS)
Davidson, Jacob D.; Goulbourne, N. C.
2013-08-01
In this work, we construct a new physics-based model of rubber elasticity to capture the strain softening, strain hardening, and deformation-state dependent response of rubber materials undergoing finite deformations. This model is unique in its ability to capture large-stretch mechanical behavior with parameters that are connected to the polymer chemistry and can also be easily identified with the important characteristics of the macroscopic stress-stretch response. The microscopic picture consists of two components: a crosslinked network of Langevin chains and an entangled network with chains confined to a nonaffine tube. These represent, respectively, changes in entropy due to thermally averaged chain conformations and changes in entropy due to the magnitude of these conformational fluctuations. A simple analytical form for the strain energy density is obtained using Rubinstein and Panyukov's single-chain description of network behavior. The model only depends on three parameters that together define the initial modulus, extent of strain softening, and the onset of strain hardening. Fits to large stretch data for natural rubber, silicone rubber, VHB 4905 (polyacrylate rubber), and b186 rubber (a carbon black-filled rubber) are presented, and a comparison is made with other similar constitutive models of large-stretch rubber elasticity. We demonstrate that the proposed model provides a complete description of elastomers undergoing large deformations for different applied loading configurations. Moreover, since the strain energy is obtained using a clear set of physical assumptions, this model may be tested and used to interpret the results of computer simulation and experiments on polymers of known microscopic structure.
NASA Astrophysics Data System (ADS)
Paimushin, V. N.; Shishkin, V. M.
2015-11-01
A prismatic semiquadratic element with a nonclassical approximation of its displacements is suggested for modeling the composite and soft layers of a torsion bar and multilayered plate-rod structures. The stiffness, weight, damping, and geometric stiffness matrices of the above-mentioned element are obtained. Expressions for computing stresses in the finite element under the action of static loads and vibrations in the resonance zone are presented. Test examples confirming the validity of the element suggested are given. An example of finite element determination of the dynamic response of a multilayered torsion bar in the resonant mode is considered.
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Pai, Shantaram S.; Hopkins, Dale A.
2007-01-01
The strain formulation in elasticity and the compatibility condition in structural mechanics have neither been understood nor have they been utilized. This shortcoming prevented the formulation of a direct method to calculate stress. We have researched and understood the compatibility condition for linear problems in elasticity and in finite element analysis. This has lead to the completion of the method of force with stress (or stress resultant) as the primary unknown. The method in elasticity is referred to as the completed Beltrami-Michell formulation (CBMF), and it is the integrated force method (IFM) in structures. The dual integrated force method (IFMD) with displacement as the primary unknown has been formulated. IFM and IFMD produce identical responses. The variational derivation of the CBMF yielded the new boundary compatibility conditions. The CBMF can be used to solve stress, displacement, and mixed boundary value problems. The IFM in structures produced high-fidelity response even with a modest finite element model. The IFM has influenced structural design considerably. A fully utilized design method for strength and stiffness limitation has been developed. The singularity condition in optimization has been identified. The CBMF and IFM tensorial approaches are robust formulations because of simultaneous emphasis on the equilibrium equation and the compatibility condition.
On the determination of elastic moduli of cells by AFM based indentation
Ding, Yue; Xu, Guang-Kui; Wang, Gang-Feng
2017-01-01
The atomic force microscopy (AFM) has been widely used to measure the mechanical properties of biological cells through indentations. In most of existing studies, the cell is supposed to be linear elastic within the small strain regime when analyzing the AFM indentation data. However, in experimental situations, the roles of large deformation and surface tension of cells should be taken into consideration. Here, we use the neo-Hookean model to describe the hyperelastic behavior of cells and investigate the influence of surface tension through finite element simulations. At large deformation, a correction factor, depending on the geometric ratio of indenter radius to cell radius, is introduced to modify the force-indent depth relation of classical Hertzian model. Moreover, when the indent depth is comparable with an intrinsic length defined as the ratio of surface tension to elastic modulus, the surface tension evidently affects the indentation response, indicating an overestimation of elastic modulus by the Hertzian model. The dimensionless-analysis-based theoretical predictions, which include both large deformation and surface tension, are in good agreement with our finite element simulation data. This study provides a novel method to more accurately measure the mechanical properties of biological cells and soft materials in AFM indentation experiments. PMID:28368053
On the determination of elastic moduli of cells by AFM based indentation.
Ding, Yue; Xu, Guang-Kui; Wang, Gang-Feng
2017-04-03
The atomic force microscopy (AFM) has been widely used to measure the mechanical properties of biological cells through indentations. In most of existing studies, the cell is supposed to be linear elastic within the small strain regime when analyzing the AFM indentation data. However, in experimental situations, the roles of large deformation and surface tension of cells should be taken into consideration. Here, we use the neo-Hookean model to describe the hyperelastic behavior of cells and investigate the influence of surface tension through finite element simulations. At large deformation, a correction factor, depending on the geometric ratio of indenter radius to cell radius, is introduced to modify the force-indent depth relation of classical Hertzian model. Moreover, when the indent depth is comparable with an intrinsic length defined as the ratio of surface tension to elastic modulus, the surface tension evidently affects the indentation response, indicating an overestimation of elastic modulus by the Hertzian model. The dimensionless-analysis-based theoretical predictions, which include both large deformation and surface tension, are in good agreement with our finite element simulation data. This study provides a novel method to more accurately measure the mechanical properties of biological cells and soft materials in AFM indentation experiments.
NASA Astrophysics Data System (ADS)
Vattré, A.; Denoual, C.
2016-07-01
A thermodynamically consistent framework for combining nonlinear elastoplasticity and multivariant phase-field theory is formulated at large strains. In accordance with the Clausius-Duhem inequality, the Helmholtz free energy and time-dependent constitutive relations give rise to displacive driving forces for pressure-induced martensitic phase transitions in materials. Inelastic forces are obtained by using a representation of the energy landscape that involves the concept of reaction pathways with respect to the point group symmetry operations of crystal lattices. On the other hand, additional elastic forces are derived for the most general case of large strains and rotations, as well as nonlinear, anisotropic, and different elastic pressure-dependent properties of phases. The phase-field formalism coupled with finite elastoplastic deformations is implemented into a three-dimensional Lagrangian finite element approach and is applied to analyze the iron body-centered cubic (α-Fe) into hexagonal close-packed (ɛ-Fe) phase transitions under high hydrostatic compression. The simulations exhibit the major role played by the plastic deformation in the morphological and microstructure evolution processes. Due to the strong long-range elastic interactions between variants without plasticity, a forward α → ɛ transition is energetically unfavorable and remains incomplete. However, plastic dissipation releases considerably the stored strain energy, leading to the α ↔ ɛ ↔α‧ (forward and reverse) polymorphic phase transformations with an unexpected selection of variants.