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.
NASA Astrophysics Data System (ADS)
Cervera, M.; Lafontaine, N.; Rossi, R.; Chiumenti, M.
2016-09-01
This paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales. A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields ( P1 P1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr-Coulomb and Drucker-Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.
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.
A coupled BEM-FEM method for finite strain magneto-elastic boundary-value problems
NASA Astrophysics Data System (ADS)
Nedjar, B.
2017-05-01
The first objective of this contribution is the formulation of nonlinear problems in magneto-elasticity involving finite geometry of the surrounding free space. More specifically for the magnetic part of the problem, the surrounding free space is described by means of a boundary integral equation for which boundary elements are used that are appropriately coupled with the finite element discretization used inside the material. The second objective is to develop a numerical strategy to solve the strongly coupled magneto-mechanics problem at hand. Herein we provide a staggered scheme consisting of a magnetostatic resolution employing the above coupled BEM-FEM procedure at fixed deformation, followed by a mechanical resolution at fixed magnetic fields. This decoupled method renders the whole solution strategy very appealing since, among others, the first BEM-FEM resolution is linear for some prototype models, and the remaining mechanical resolution is analogous to nowadays classical nonlinear elastostatic problems in the finite strain range. Some nonlinear boundary-value problems are simulated to demonstrate the applicability of the proposed framework.
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.
NASA Astrophysics Data System (ADS)
Wang, Z.; Rudraraju, S.; Garikipati, K.
2016-09-01
We present a field formulation for defects that draws from the classical representation of the cores as force dipoles. We write these dipoles as singular distributions. Exploiting the key insight that the variational setting is the only appropriate one for the theory of distributions, we arrive at universally applicable weak forms for defects in nonlinear elasticity. Remarkably, the standard, Galerkin finite element method yields numerical solutions for the elastic fields of defects that, when parameterized suitably, match very well with classical, linearized elasticity solutions. The true potential of our approach, however, lies in its easy extension to generate solutions to elastic fields of defects in the regime of nonlinear elasticity, and even more notably for Toupin's theory of gradient elasticity at finite strains (Toupin Arch. Ration. Mech. Anal., 11 (1962) 385). In computing these solutions we adopt recent numerical work on an isogeometric analytic framework that enabled the first three-dimensional solutions to general boundary value problems of Toupin's theory (Rudraraju et al. Comput. Methods Appl. Mech. Eng., 278 (2014) 705). We first present exhaustive solutions to point defects, edge and screw dislocations, and a study on the energetics of interacting dislocations. Then, to demonstrate the generality and potential of our treatment, we apply it to other complex dislocation configurations, including loops and low-angle grain boundaries.
1980-07-01
certain properties of the solution to the analogous crack problem in the linearized theory. We then show that, at least for the Mooney - Rivlin material...an incompressible material con- forming to (1.18) is supplied by the Mooney - Rivlin material, with the complete plane-strain elastic potential (I) R... Mooney - Rivlin material, a solution with this parity cannot possibly exist. To this end suppose o0 !now that W is given by (1.19). Eliminating a between
NASA Astrophysics Data System (ADS)
Srinivasa, A. R.; Reddy, J. N.
2013-03-01
The aim of this paper is to develop the governing equations for a fully constrained finitely deforming hyperelastic Cosserat continuum where the directors are constrained to rotate with the body rotation. This is the generalization of small deformation couple stress theories and would be useful for developing mathematical models for an elastic material with embedded stiff short fibers or inclusions (e.g., materials with carbon nanotubes or nematic elastomers, cellular materials with oriented hard phases, open cell foams, and other similar materials), that account for certain longer range interactions. The theory is developed as a limiting case of a regular Cosserat elastic material where the directors are allowed to rotate freely by considering the case of a high "rotational mismatch energy". The theory is developed using the formalism of Lagrangian mechanics, with the static case being based on Castigliano's first theorem. By considering the stretch U and the rotation R as additional independent variables and using the polar decomposition theorem as an additional constraint equation, we obtain the governing and as well as the boundary conditions for finite deformations. The resulting equations are further specialized for plane strain and axisymmetric finite deformations, deformations of beams and plates with small strain and moderate rotation, and for small deformation theories. We also show that the boundary conditions for this theory involve "surface tension" like terms due to the higher gradients in the strain energy function. For beams and plates, the rotational gradient dependent strain energy does not require additional variables (unlike Cosserat theories) and additional differential equations; nor do they raise the order of the differential equations, thus allowing us to include a material length scale dependent response at no extra "computational cost" even for finite deformation beam/plate theories
A strain-consistent elastic plate model with surface elasticity
NASA Astrophysics Data System (ADS)
Ru, C. Q.
2016-03-01
A strain-consistent elastic plate model is formulated in which both initial surface tension and the induced residual stress are treated as finite values, and the exactly same strain expressions are consistently employed for both the surface and the bulk plate. Different than most of previous related models which follow the original Gurtin-Murdoch model and include some non-strain displacement gradient terms (which cannot be expressed in terms of the surface infinitesimal strains or the von Karman-type strains) in the surface stress-strain relations, the present model does not include any non-strain displacement gradient terms in the surface stress-strain relations. For a free elastic plate with in-plane movable edges, the present model predicts that initial surface tension exactly cancels out the induced residual compressive stress. On the other hand, if all edges are in-plane immovable, residual stress cannot develop in the plate and the initial surface tension causes a tensile net membrane force. In addition, the present model predicts that initial surface tension reduces the effective bending rigidity of the plate, while this reduction does not depend on Poisson ratio. In particular, self-buckling of a free elastic plate under tensile surface tension cannot occur unless the effective bending rigidity of plate vanishes or becomes negative.
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.
Contact problems for a finitely deformed incompressible elastic halfspace
NASA Astrophysics Data System (ADS)
Selvadurai, A. P. S.
2015-01-01
This paper examines the class of problems related to the interaction between a finitely deformed incompressible elastic halfspace and contacting elements that include smooth, flat rigid indenters with elliptical and circular shapes and a thick plate of infinite extent. The contact between the finitely deformed elastic halfspace and the contacting elements is assumed to be bilateral. The interaction between both the rigid circular indenter and the finitely deformed halfspace is induced by a Mindlin force that acts at the interior of the halfspace regions and by exterior loads. Similar considerations apply for the contact between the flexible plate of infinite extent and the finitely deformed elastic halfspace. The theory of small deformations superposed on large deformations proposed by Green et al. (Proc R Soc Ser A 211:128-155, 1952) is used as the basis for the formulation of the problem, and results of potential theory and integral transform techniques are used to develop the analytical results. In particular, explicit results are presented for the displacement of the rigid elliptical indenter and the maximum deflection of the flexible plate induced by the Mindlin forces, when the finitely deformed halfspace region has a strain energy function of the Mooney-Rivlin form.
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.
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.
A comparison between different finite elements for elastic and aero-elastic analyses.
Mahran, Mohamed; ELsabbagh, Adel; Negm, Hani
2017-11-01
In the present paper, a comparison between five different shell finite elements, including the Linear Triangular Element, Linear Quadrilateral Element, Linear Quadrilateral Element based on deformation modes, 8-node Quadrilateral Element, and 9-Node Quadrilateral Element was presented. The shape functions and the element equations related to each element were presented through a detailed mathematical formulation. Additionally, the Jacobian matrix for the second order derivatives was simplified and used to derive each element's strain-displacement matrix in bending. The elements were compared using carefully selected elastic and aero-elastic bench mark problems, regarding the number of elements needed to reach convergence, the resulting accuracy, and the needed computation time. The best suitable element for elastic free vibration analysis was found to be the Linear Quadrilateral Element with deformation-based shape functions, whereas the most suitable element for stress analysis was the 8-Node Quadrilateral Element, and the most suitable element for aero-elastic analysis was the 9-Node Quadrilateral Element. Although the linear triangular element was the last choice for modal and stress analyses, it establishes more accurate results in aero-elastic analyses, however, with much longer computation time. Additionally, the nine-node quadrilateral element was found to be the best choice for laminated composite plates analysis.
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.
Analysis of finite deformations of elastic solids by the finite element method.
NASA Technical Reports Server (NTRS)
Oden, J. T.; Key, J. E.
1971-01-01
Finite element applications, particularly to analyses of finite deformations in elastic solids, are reviewed, along with the difficulties encountered in the formulation of certain problems and in their numerical solution. Various approaches are discussed for overcoming these and other difficulties. A computer program designed for finite elasticity problems is described, and several numerical examples are presented.
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
Role of Higher-Order Elastic Moduli in Large Elastic Finite Deformation
NASA Astrophysics Data System (ADS)
Suzuki, Tetsuro; Osuka, Ken'ichi
1993-05-01
It is proposed here that the change in free energy of crystals associated with large elastic finite deformation can be estimated using higher-order elastic moduli up to a limited order. Numerical estimation of the change in free energy is performed for two examples of finite elastic deformation, with use of the data for higher-order elastic moduli of β-brass obtained by Swartz. One example is Bain deformation, which converts a bcc lattice into an fcc lattice or vice versa. The other is shear deformation along the (100) atomic plane.
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.
NASA Technical Reports Server (NTRS)
Bauld, N. R., Jr.; Goree, J. G.
1983-01-01
The accuracy of the finite difference method in the solution of linear elasticity problems that involve either a stress discontinuity or a stress singularity is considered. Solutions to three elasticity problems are discussed in detail: a semi-infinite plane subjected to a uniform load over a portion of its boundary; a bimetallic plate under uniform tensile stress; and a long, midplane symmetric, fiber reinforced laminate subjected to uniform axial strain. Finite difference solutions to the three problems are compared with finite element solutions to corresponding problems. For the first problem a comparison with the exact solution is also made. The finite difference formulations for the three problems are based on second order finite difference formulas that provide for variable spacings in two perpendicular directions. Forward and backward difference formulas are used near boundaries where their use eliminates the need for fictitious grid points.
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.
Numerical solution of acoustic scattering by finite perforated elastic plates.
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.
Numerical solution of acoustic scattering by finite perforated elastic plates
2016-01-01
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. PMID:27274685
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.
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.
Accuracy assessment of elastic strain measurement by EBSD.
Villert, S; Maurice, C; Wyon, C; Fortunier, R
2009-02-01
A detailed accuracy analysis of electron backscatter diffraction (EBSD) elastic strain measurement has been carried out using both simulated and experimental patterns. Strains are determined by measuring shifts between two EBSD patterns (one being the reference) over regions of interest (ROI) using an iterative cross-correlation algorithm. An original minimization procedure over 20 regions of interests gives a unique solution for the eight independent components of the deviatoric displacement gradient tensor. It is shown that this method leads to strain measurements on simulated patterns with an accuracy better than 10(-4). The influence of the projection parameters is also investigated. The accuracy assessment is illustrated by two worked examples: (i) four-point bending of a silicon single crystal and (ii) Si(1-x)Ge(x) layers on a Si substrate. Experimental results are compared with finite-element simulations.
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.
Hodge, S.C.; Minicucci, J.M.
1997-11-01
A test program was undertaken to demonstrate the ability of elastic-plastic finite element methods to predict dynamic inelastic response for simple structural members. Cantilever and fixed-beam specimens were tested to levels that produced plastic straining in the range of 2.0% and to 3.0% and permanent sets. Acceleration, strain, and displacement data were recorded for use in analytical correlation. Correlation analyses were performed using the ABAQUS finite element code. Results of the correlation show that current elastic-plastic analysis techniques accurately capture dynamic inelastic response (displacement, acceleration) due to rapidly applied dynamic loading. Peak elastic and inelastic surface strains are accurately predicted. To accurately capture inelastic straining near connections, a solid model, including fillet welds, is necessary. The hardening models currently available in the ABAQUS code (isotropic, kinematic) do not accurately capture inelastic strain reversals caused by specimen rebound. Analyses performed consistently underpredicted the peak strain level of the first inelastic reversal and the rebound deflection and overpredicted the permanent set of structures experiencing inelastic rebound. Based on these findings, an improved hardening model is being implemented in the ABAQUS code by the developers. The intent of this model upgrade is to improve the ability of the program to capture inelastic strain reversals and to predict permanent sets.
Hodge, S.C.; Minicucci, J.M.
1996-11-01
A test program was undertaken to demonstrate the ability of elastic-plastic finite element methods to predict dynamic inelastic response for simple structural members. Cantilever and fixed-beam specimens were tested to levels that produced plastic straining in the range of 2.0% to 3.0% and permanent sets. Acceleration, strain, and displacement data were recorded for use in analytical correlation. Correlation analyses were performed using the ABAQUS finite element code. Results of the correlation show that current elastic-plastic analysis techniques accurately capture dynamic inelastic response (displacement, acceleration) due to rapidly applied dynamic loading. Peak elastic and inelastic surface strains are accurately predicted. To accurately capture inelastic straining near connections, a solid model, including fillet welds, is necessary. The hardening models currently available in the ABAQUS code (isotropic, kinematic) do not accurately capture inelastic strain reversals caused by specimen rebound. Analyses performed consistently underpredicted the peak strain level of the first inelastic reversal and the rebound deflection and overpredicted the permanent set of structures experiencing inelastic rebound. Based on these findings, an improved hardening model is being implemented in the ABAQUS code by the developers. The intent of this model upgrade is to improve the ability of the program to capture inelastic strain reversals and to predict permanent sets.
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.
Continuum elasticity modeling of nanostructure evolution in strained film epitaxy
NASA Astrophysics Data System (ADS)
Gamage, Champika G.
The formation of surface nanostructures such as islands or quantum dots during strained film epitaxy has attracted great interest in recent years. The underlying mechanisms have been attributed to the occurrence of morphological instabilities of the strained films, for which the coupling between film-substrate material properties and growth conditions play a major role. Morphological properties of an epitaxially grown film and the self-organization process of coherent strained islands are analyzed via the development of a continuum elasticity model based on the 2nd order perturbation method. Effects of wetting stress due to film-substrate interactions have been incorporated in the resulting nonlinear dynamic equation governing the film morphological profile. We study the formation and evolution of surface strained islands or quantum dots for different film/substrate misfit strains, via analyzing the time-dependent behavior of the structure factor for surface heights, its various moments, and the surface roughness. Three regimes of island array evolution have been identified, including a film instability regime at early stage, a slow power-law-type coarsening at intermediate time, and the crossover to a saturated state, with detailed behavior dependent on misfit strains but not qualitatively on finite system sizes. It is found to be controlled by the strength of film-substrate wetting interaction which would constrain the valley-to-peak mass transport and hence the growth of island height, and also determined by the effect of elastic interaction between surface islands and the high-order strain energy of individual islands at late evolution stage. The results are compared to previous experimental and theoretical efforts on quantum dots coarsening and saturation. We also study the formation of these nanostructures on a nonplanar patterned substrate. The properties of islands formed are highly affected and controlled by the periodicity and amplitude of the pre
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.
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.
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 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.
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.
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.
In vivo measurements of human neck skin elasticity using MRI and finite element modeling.
An, Yunqiang; Ji, Changjin; Li, Yong; Wang, Jianxia; Zhang, Xinyue; Huang, Yaqi
2017-04-01
The assessment of mechanical properties of the human skin is very important in investigating the mechanism of obstructive sleep apnea, a common disorder characterized by repetitive collapse and obstruction of the upper airway during sleep. In this study, a unique method, combining magnetic resonance imaging (MRI) and finite element modeling (FEM), was developed to obtain the value of the in vivo elastic modulus of the neck skin. A total of 22 subjects, 16 males and six females, were recruited to participate in the MRI studies. The changes in the airway and the neck size resulting from fluid shift from the lower body to the neck were measured based on the MR images. A two-dimensional plane strain FE model was built to simulate such changes in the neck cross-section for each subject. Solving an inverse problem using FEM by matching the measured data, we obtained the in vivo elastic modulus of the neck skin to be 1.78 ± 1.73 MPa. Results showed that the elastic modulus tended to increase with age and body mass index for these subjects. A sensitivity analysis of the muscle and fat mechanical parameters was also performed to test their effects on the predicted skin elasticity. The unique method developed in this study for measuring the in vivo elastic modulus of the neck skin is quite effective, and the skin elasticity value obtained using this method is credible. © 2017 American Association of Physicists in Medicine.
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.
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)
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.
Coupling finite and boundary element methods for 2-D elasticity problems
NASA Technical Reports Server (NTRS)
Krishnamurthy, T.; Raju, I. S.; Sistla, R.
1993-01-01
A finite element-boundary element (FE-BE) coupling method for two-dimensional elasticity problems is developed based on a weighted residual variational method in which a portion of the domain of interest is modeled by FEs and the remainder of the region by BEs. The performance of the FE-BE coupling method is demonstrated via applications to a simple 'patch test' problem and three-crack problems. The method passed the patch tests for various modeling configurations and yielded accurate strain energy release rates for the crack problems studied.
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.
NASA Astrophysics Data System (ADS)
Daymond, Mark R.
2004-10-01
Stress measurement by neutron or synchrotron x-ray diffraction is a nondestructive technique that provides insights into strain and/or stress fields deep within engineering components and structures. The technique is seeing increased use for the validation of finite element process models, however, present FE models predict a continuum elastic strain rather than diffraction strains. An expression is therefore derived for a physically realistic weighting of strains obtained from multiple single peak diffraction measurements of internal elastic strain in order to determine a macroscopic equivalent elastic strain, and hence stress. A practical approach to the use of the expression is suggested. A similar expression is derived for the equivalent weighting used in Rietveld refinements, for both polychromatic and monochromatic sources, which is applicable to both neutron and x-ray diffraction. The use of these expressions is illustrated for both textured and untextured, cubic (steel) and hexagonal (titanium) symmetry polycrystals. The physically realistic weighting is different from that used in the Rietveld refinement however both provide good estimates of the macroscopic equivalent elastic strain.
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.
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.
A solid-shell Cosserat point element ( SSCPE) for elastic thin structures at finite deformation
NASA Astrophysics Data System (ADS)
Jabareen, Mahmood; Mtanes, Eli
2016-07-01
The objective of this study is to develop a new solid-shell element using the Cosserat point theory for modeling thin elastic structures at finite deformations. The point-wise Green-Lagrange strain tensor is additively decomposed into homogeneous and inhomogeneous parts. Only the latter part of the strain tensor is modified by the assumed natural strain ANS concept to avoid both curvature-thickness locking and transverse shear locking. To the authors' knowledge, such modification has not been applied yet in the literature, and here it is referred to as the assumed natural inhomogeneous strain ANIS concept. Moreover, a new methodology for determining the constitutive coefficients of the strain energy function, which controls the inhomogeneous deformations, is proposed. The resulting coefficients ensure both accuracy, robustness, and elimination of all locking pathologies in the solid-shell Cosserat point element ( SSCPE). The performance of the developed SSCPE is verified and tested via various benchmark problems and compared to other solid, shell, and solid-shell elements. These examples demonstrate that the SSCPE is accurate, robust, stable, free of locking, and can be used for modeling thin structures at both small and finite deformations.
Modeling elastic anisotropy in strained heteroepitaxy.
Dixit, Gopal Krishna; Ranganathan, Madhav
2017-09-20
Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the [Formula: see text] [Formula: see text] on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to [Formula: see text] facets on the surface.
Modeling elastic anisotropy in strained heteroepitaxy
NASA Astrophysics Data System (ADS)
Krishna Dixit, Gopal; Ranganathan, Madhav
2017-09-01
Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the Ge0.25 Si0.75 on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to < 1 0 5 > facets on the surface.
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.
Subject Specific Finite Elasticity Simulations of the Pelvic Floor
Noakes, Kimberley F.; Pullan, Andrew J.; Bissett, Ian P.; Cheng, Leo K.
2008-01-01
An anatomically realistic computational model of the pelvic floor and anal canal regions was used in this study to examine the mechanics of normal defecatory function within the female pelvic floor. This subject-specific, MRI-based model enabled mechanical simulations to be performed and quantitatively assessed against experimental data retrieved from the same volunteer. The levator ani muscle group mesh was used as the domain over which the governing equations of finite elasticity were solved using the finite element method with a Mooney-Rivlin material law. Deformation of the levator ani was simulated during a ‘bear down’ maneuver in order to visualize the way this muscle group functions in an asymptomatic subject. A pressure of 4 kPa was imposed on the mesh and the computed mesh displacements were compared to those obtained from dynamic MR images with an average, experimentally consistent, downwards displacement of 27.2 mm being achieved. The RMS error for this movement was 0.7 mm equating to a percentage error of 2.6% in the supero-inferior direction and 13.7 mm or 74.5% in the antero-posterior direction. PMID:18757058
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)
Vattré, A.
2017-08-01
A parametric energy-based framework is developed to describe the elastic strain relaxation of interface dislocations. By means of the Stroh sextic formalism with a Fourier series technique, the proposed approach couples the classical anisotropic elasticity theory with surface/interface stress and elasticity properties in heterogeneous interface-dominated materials. For any semicoherent interface of interest, the strain energy landscape is computed using the persistent elastic fields produced by infinitely periodic hexagonal-shaped dislocation configurations with planar three-fold nodes. A finite element based procedure combined with the conjugate gradient and nudged elastic band methods is applied to determine the minimum-energy paths for which the pre-computed energy landscapes yield to elastically favorable dislocation reactions. Several applications on the Au/Cu heterosystems are given. The simple and limiting case of a single set of infinitely periodic dislocations is introduced to determine exact closed-form expressions for stresses. The second limiting case of the pure (010) Au/Cu heterophase interfaces containing two crossing sets of straight dislocations investigates the effects due to the non-classical boundary conditions on the stress distributions, including separate and appropriate constitutive relations at semicoherent interfaces and free surfaces. Using the quantized Frank-Bilby equation, it is shown that the elastic strain landscape exhibits intrinsic dislocation configurations for which the junction formation is energetically unfavorable. On the other hand, the mismatched (111) Au/Cu system gives rise to the existence of a minimum-energy path where the fully strain-relaxed equilibrium and non-regular intrinsic hexagonal-shaped dislocation rearrangement is accompanied by a significant removal of the short-range elastic energy.
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…
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.
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.
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.
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.
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
Elastic buckling of stiffened plates by the finite element method
Sabir, A.B.; Djoudi, M.S.
1995-09-01
The finite element method is used to obtain the elastic buckling loads of stiffened plates. The plates are modeled by rectangular plate elements and the stiffeners which are rectangular in cross section are modeled by exact beam elements. Eccentrically located stiffeners as well as stiffeners having centroids coinciding with the middle surface of the plates are considered. The effect of the flexural rigidity of the stiffeners relative to that of the plates on the buckling load is investigated. Square plates simply supported along the four edges are considered when subjected to uniform uniaxial compressive loads. Further investigations are carried out to examine the effect of the number of stiffeners and their locations on the buckling load and the mode of buckling. Stiffeners positioned in the direction of the applied compressive load or in the transverse direction are also considered. The method used in the calculation of the buckling load is the subspace iteration technique. This method is shown to produce acceptable results for the eigenvalues and the associated eigenvectors of the transidental equations for the combined stiffness and geometric matrices for the stiffened plates. The buckling loads as well as the modes of buckling are determined and compared where possible with existing solutions.
Painter Street Overcrossing: Linear-elastic finite element dynamic analysis
Salveson, M.W.
1991-08-01
Painter Street Overcrossing is a two span continuous box girder bridge Highway 101 near Rio Del, California. It has been heavily instrumented with strong motion accelerometers by the California Department of Mines and Geology Strong Motion Instrumentation Program. On 11/21/86, the response of the bridge to a magnitude 5.1 earthquake (epicentral distance 32 km) was measured. This report considers the data generated at stations six, seven, and eight, during this earthquake. Station six recorded the vertical accelerations at the midpoint of the long span. Station seven recorded the transverse accelerations at the top of the bent. Station eight recorded the vertical accelerations at the midpoint of the short span. Typically, seismic analysis is done with the aid of a linear-elastic finite element code. Damping is assumed to be viscous. This report summarizes the results of such an analysis using the commercial P.C. based program SAP90. This analysis conforms as closely as possible to a typical'' seismic analysis. It is intended to be used as basis for comparison against a non-linear analysis to be done using NIKE3D. This report contains detailed information about the models used to represent the bridge. The results of each analysis and discussions of the results are included. 2 refs., 37 figs.
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.
Mangeri, John; Heinonen, Olle; Karpeyev, Dmitry; Nakhmanson, Serge
2015-07-07
Core-shell nanoparticle systems of Zn-ZnO and ZnO-TiO2 are studied computationally using finite element methods. The inclusion of a surface free energy and the elastic mismatch of the core and shell create an imprinting effect within the shell structure that produces a wide variation of strains. Due to this diversity of strains, the sharp direct band gap edges of the bulk semiconductor are observed to be broadened. We show that a variety of factors, such as particle size, core-to-shell volume ratio, applied hydrostatic pressure, shell microstructure, as well as the effect of elastic anisotropy, can influence the distribution of optical band gap values throughout the particle.
Mangeri, John; Heinonen, Olle; Karpeyev, Dmitry; Nakhmanson, Serge
2015-07-01
Core-shell nanoparticle systems of Zn-ZnO and ZnO-TiO2 are studied computationally using finite-element methods. The inclusion of a surface free energy and the elastic mismatch of the core and shell create an imprinting effect within the shell structure that produces a wide variation of strains. Due to this diversity of strains, the sharp, direct, band-gap edges of the bulk semiconductor are observed to be broadened. We show that a variety of factors, such as particle size, core-to-shell volume ratio, applied hydrostatic pressure, shell microstructure, as well as the effect of elastic anisotropy, can influence the distribution of optical band-gap values throughout the particle.
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
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.
NASA Astrophysics Data System (ADS)
Aldakheel, Fadi
2017-05-01
The coupled thermo-mechanical strain gradient plasticity theory that accounts for microstructure-based size effects is outlined within this work. It extends the recent work of Miehe et al. (Comput Methods Appl Mech Eng 268:704-734, 2014) to account for thermal effects at finite strains. From the computational viewpoint, the finite element design of the coupled problem is not straightforward and requires additional strategies due to the difficulties near the elastic-plastic boundaries. To simplify the finite element formulation, we extend it toward the micromorphic approach to gradient thermo-plasticity model in the logarithmic strain space. The key point is the introduction of dual local-global field variables via a penalty method, where only the global fields are restricted by boundary conditions. Hence, the problem of restricting the gradient variable to the plastic domain is relaxed, which makes the formulation very attractive for finite element implementation as discussed in Forest (J Eng Mech 135:117-131, 2009) and Miehe et al. (Philos Trans R Soc A Math Phys Eng Sci 374:20150170, 2016).
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.
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.
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.
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
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.
Elastic buckling of plates with reinforced circular holes by the finite element method
Sabir, A.B.; Chow, F.Y.
1995-09-01
The elastic buckling loads of square plates having central circular holes is obtained by the use of the finite element method. The circular holes are reinforced around their edges by rings having rectangular cross sections and the effects of the size of hole and the amount of reinforcement of the buckling loads are determined. The finite elements used for calculating the inplane stresses in the plate prior and the instance of buckling are based on strain assumptions and the rings are presented by exact circular beam elements. The plate elements for inplane stresses have an additional degree of freedom due to inplane rotation to make them suitable for combination with the ring elements where the corresponding rotation constitute an essential external degree of freedom. The buckling loads considered are due to uniaxial, biaxial and shearing forces applied to the edges of the plates and the amount of reinforcement necessary to restore the buckling loads to those for plates not having any holes are determined.
Rahman, S.
1996-12-01
A new probabilistic model was developed for predicting elastic-plastic fracture response of circumferentially cracked pipes with finite-length, constant-depth, internal surface flaws subject to remote bending loads. It involves engineering estimation of energy release rate, J-tearing theory for characterizing ductile fracture, and standard methods of structural reliability theory. The underlying J-estimation model is based on deformation theory of plasticity, constitutive law characterized by power law model for stress-strain curve, and an equivalence criterion incorporating reduced thickness analogy for simulating system compliance due to the presence of a crack. New equations were developed to predict J-integral and were evaluated by comparing with available finite-element results from the current literature. Both analytical and simulation methods were formulated to determine the probabilistic characteristics of J. The same methods were used later to predict the probability of crack initiation and net-section collapse as a function of the applied load. Numerical examples are provided to illustrate the proposed methodology.
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.
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
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.
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.
Finite-Difference Algorithm for 3D Orthorhombic Elastic Wave Propagation
NASA Astrophysics Data System (ADS)
Jensen, R.; Preston, L. A.; Aldridge, D. F.
2016-12-01
Many geophysicists concur that an orthorhombic elastic medium, characterized by three mutually orthogonal symmetry planes, constitutes a realistic representation of seismic anisotropy in shallow crustal rocks. This symmetry condition typically arises via a dense system of vertically-aligned microfractures superimposed on a finely-layered horizontal geology. Mathematically, the elastic stress-strain constitutive relations for an orthorhombic body contain nine independent moduli. In turn, these moduli can be determined by observing (or prescribing) nine independent P-wave and S-wave phase speeds along different propagation directions. We are developing an explicit time-domain finite-difference (FD) algorithm for simulating 3D elastic wave propagation in a heterogeneous orthorhombic medium. The components of the particle velocity vector and the stress tensor are governed by a set of nine, coupled, first-order, linear, partial differential equations (PDEs) called the velocity-stress system. All time and space derivatives are discretized with centered and staggered FD operators possessing second- and fourth-order numerical accuracy, respectively. Simplified FD updating formulae (with significantly reduced operation counts) for stress components are obtained by restricting the principle axes of the modulus tensor to be parallel to the global rectangular coordinate axes. Moreover, restriction to a piecewise homogeneous earth model reduces computational memory demand for storing the ten (including mass density) model parameters. These restrictions will be relaxed in the future. Novel perfectly matched layer (PML) absorbing boundary conditions, specifically designed for orthorhombic media, effectively suppress grid boundary reflections. Initial modeling results reveal the well-established anisotropic seismic phenomena of complex wavefront shapes, split (fast and slow) S-waves, and shear waves generated by a spherically-symmetric explosion in a homogeneous body.
NASA Astrophysics Data System (ADS)
Heuzé, Thomas
2017-10-01
We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.
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.
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.
Retaining Large and Adjustable Elastic Strains of Kilogram-Scale Nb Nanowires.
Hao, Shijie; Cui, Lishan; Wang, Hua; Jiang, Daqiang; Liu, Yinong; Yan, Jiaqiang; Ren, Yang; Han, Xiaodong; Brown, Dennis E; Li, Ju
2016-02-10
Individual metallic nanowires can sustain ultralarge elastic strains of 4-7%. However, achieving and retaining elastic strains of such magnitude in kilogram-scale nanowires are challenging. Here, we find that under active load, ∼ 5.6% elastic strain can be achieved in Nb nanowires embedded in a metallic matrix deforming by detwinning. Moreover, large tensile (2.8%) and compressive (-2.4%) elastic strains can be retained in kilogram-scale Nb nanowires when the external load was fully removed, and adjustable in magnitude by processing control. It is then demonstrated that the retained tensile elastic strains of Nb nanowires can increase their superconducting transition temperature and critical magnetic field, in comparison with the unstrained original material. This study opens new avenues for retaining large and tunable elastic strains in great quantities of nanowires and elastic-strain-engineering at industrial scale.
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
Finite-thickness effects on the Rayleigh-Taylor instability in accelerated elastic solids
NASA Astrophysics Data System (ADS)
Piriz, S. A.; Piriz, A. R.; Tahir, N. A.
2017-05-01
A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes into account the finite transit time of the elastic waves across the slab thickness. For Atwood number AT=1 , the asymptotic growth rate is found to be in excellent agreement with the exact solution [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998), 10.1007/s000330050121], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.
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-thickness effects on the Rayleigh-Taylor instability in accelerated elastic solids.
Piriz, S A; Piriz, A R; Tahir, N A
2017-05-01
A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes into account the finite transit time of the elastic waves across the slab thickness. For Atwood number A_{T}=1, the asymptotic growth rate is found to be in excellent agreement with the exact solution [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998)10.1007/s000330050121], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.
Chemically pre-strained dielectric elastomers finite element analysis
NASA Astrophysics Data System (ADS)
Newell, Brittany; Krutz, Gary; Stewart, Frank; Pascal, Kevin
2017-04-01
The applications and feasibility of utilizing dielectric elastomer electroactive polymers in the industrial and medical sectors has drastically increased in recent years due to significant improvements in actuation potential, manufacturing, the introduction of new materials and modeling capabilities. One such development is the introduction of chemical pre-strain as a method of providing enhanced actuation. The purpose of this study was to utilize finite element analysis to analyze the mechanical actuation of an industrial fluoropolymer with chemical induced pre-strain and validate the model with experiential results. Results generated from the finite element analysis showed similar trends to results produced experimentally.
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.
Elastic properties of Sierpinski-like carpets: finite-element-based simulation.
Oshmyan, V G; Patlazhan, S A; Timan, S A
2001-11-01
The elastic properties of two-dimensional continuous composites of fractal structures are studied with the set of Sierpinski-like carpets filled by voids or rigid inclusions. The effective elastic moduli of these carpets are calculated numerically using the finite-element and position-space renormalization group techniques. The fixed-point problem is analyzed by flow diagrams in the plane of the current Poisson ratios and coefficients of anisotropy of the composites. It is found that in the general case the effective elastic moduli asymptotically approach a power-law behavior. Moreover, the common exponent characterizes the scaling behavior of each component of the elastic modulus tensor of a definite carpet. The values of the scaling exponents and positions of the fixed points are shown to be independent of the elastic properties of the host and depend significantly on the fractal dimension of the composite.
Elastic properties of Sierpinski-like carpets: Finite-element-based simulation
NASA Astrophysics Data System (ADS)
Oshmyan, V. G.; Patlazhan, S. A.; Timan, S. A.
2001-11-01
The elastic properties of two-dimensional continuous composites of fractal structures are studied with the set of Sierpinski-like carpets filled by voids or rigid inclusions. The effective elastic moduli of these carpets are calculated numerically using the finite-element and position-space renormalization group techniques. The fixed-point problem is analyzed by flow diagrams in the plane of the current Poisson ratios and coefficients of anisotropy of the composites. It is found that in the general case the effective elastic moduli asymptotically approach a power-law behavior. Moreover, the common exponent characterizes the scaling behavior of each component of the elastic modulus tensor of a definite carpet. The values of the scaling exponents and positions of the fixed points are shown to be independent of the elastic properties of the host and depend significantly on the fractal dimension of the composite.
NASA Astrophysics Data System (ADS)
Fanget, A.; Trumel, H.; Dragon, A.
1998-07-01
The dynamic behaviour of a propellant like material is modelized with viscoelastic-viscoplastic behaviour in the lagrangian finite strain frame work. Employment of logarithmic strain allows elastic-plastic decomposidon. The viscoelastic part is performed in differential form and is integrated by an explicit method. The plastic deformation is split into volumetric and distorsional parts which constitute two distinct state variables for compaction and yielding. This model has been implemented in a finite element 2D code. The algorithm of the implementation is presented and numerical and experimental results are shown.
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
Finite Element Modeling of Elastic-Plastic Crack Growth.
1982-07-01
material structures. 4) Environmental effects should be further researched by conducting fatigue and creep crack growth tests in different...8217’ Int. 3. for Numerical Method in Eng., Vol. 8, pp. 821-845, 1974. 15. Fiher, B.C. and Sherratt, F., ’’A Fracture Mechanics Analysis of Fatigue Crack...Chang, T.B., editor, "Part-Through Crack Fatigue Life Prediction,’’ ASfl, STP 687, 1977. 22. Ahmad, 3. and Loo, F.T.C., "Finite Element Analysis of
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.
A FINITE ELEMENT METHOD FOR ELASTICITY INTERFACE PROBLEMS WITH LOCALLY MODIFIED TRIANGULATIONS
XIE, HUI; LI, ZHILIN; QIAO, ZHONGHUA
2013-01-01
A finite element method for elasticity systems with discontinuities in the coefficients and the flux across an arbitrary interface is proposed in this paper. The method is based on a Cartesian mesh with local modifications to the mesh. The total degrees of the freedom of the finite element method remains the same as that of the Cartesian mesh. The local modifications lead to a quasi-uniform body-fitted mesh from the original Cartesian mesh. The standard finite element theory and implementation are applicable. Numerical examples that involve discontinuous material coefficients and non-homogeneous jump in the flux across the interface demonstrate the efficiency of the proposed method. PMID:24058368
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.
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 (
The Influence of Elastic Strain on Catalytic Activity in the Hydrogen Evolution Reaction.
Yan, Kai; Maark, Tuhina Adit; Khorshidi, Alireza; Sethuraman, Vijay A; Peterson, Andrew A; Guduru, Pradeep R
2016-05-17
Understanding the role of elastic strain in modifying catalytic reaction rates is crucial for catalyst design, but experimentally, this effect is often coupled with a ligand effect. To isolate the strain effect, we have investigated the influence of externally applied elastic strain on the catalytic activity of metal films in the hydrogen evolution reaction (HER). We show that elastic strain tunes the catalytic activity in a controlled and predictable way. Both theory and experiment show strain controls reactivity in a controlled manner consistent with the qualitative predictions of the HER volcano plot and the d-band theory: Ni and Pt's activities were accelerated by compression, while Cu's activity was accelerated by tension. By isolating the elastic strain effect from the ligand effect, this study provides a greater insight into the role of elastic strain in controlling electrocatalytic activity. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Karoui, A.; Sahtout, F. K.; Vlahovic, B.
2017-01-01
The study of strain and stress distributions and relaxation mechanisms during epitaxial deposition of ultra-thin film heterostructures is of critical importance for nanoelectronic materials. It provides guidance for the control of structures at the nanometer scale and insights into the underlying physics. In this paper, we present a time-dependent nonlinear finite element model, which realistically simulates the evolution of elastic and plastic deformation in SiGe heterostructured nanomaterials during epitaxial deposition. Dynamic elements have been used to simulate the layer-by-layer deposition and growth rate as well as chemical-mechanical polishing (CMP) planarization. The thickness of add-on and etched-off layers was limited to few nanometers depending on the final epitaxial layer thickness and its growth rate. The material plastic behavior is described by the Von Mises yield criterion coupled with isotropic work hardening conditions and the Levy-Mises flow rule. The model has been successfully applied to the growth of ultra-thin (15 nm) strained-Si/ S i1 -xG ex /Si(001) heterostructures. Depth and time dependent elastic and plastic stress and strain in the growing layers are quantified and the relaxation mechanisms are deduced. From the calculated elastic and plastic strain fields, we derived the relaxation factor, plastic strain rate, dislocation glide velocity, misfit, and threading dislocation density as well as several structural properties such as lattice parameters and misfit dislocation spacing and length. These were found in close agreement with published experimental data. The simulation was able to show at which step of the growth process and how often yielding events occur. Plastic deformation and so the nucleation and multiplication of dislocations appeared to occur consistently during growth of the graded-layer. The simulation was also able to predict that CMP of the SiGe-cap followed by a regrowth step will indeed further relax the graded layer
NASA Astrophysics Data System (ADS)
Wang, Jun; Moumni, Ziad; Zhang, Weihong; Xu, Yingjie; Zaki, Wael
2017-06-01
The paper presents a finite-strain constitutive model for shape memory alloys (SMAs) that accounts for thermomechanical coupling and martensite reorientation. The finite-strain formulation is based on a two-tier, multiplicative decomposition of the deformation gradient into thermal, elastic, and inelastic parts, where the inelastic deformation is further split into phase transformation and martensite reorientation components. A time-discrete formulation of the constitutive equations is proposed and a numerical integration algorithm is presented featuring proper symmetrization of the tensor variables and explicit formulation of the material and spatial tangent operators involved. The algorithm is used for finite element analysis of SMA components subjected to various loading conditions, including uniaxial, non-proportional, isothermal and adiabatic loading cases. The analysis is carried out using the FEA software Abaqus by means of a user-defined material subroutine, which is then utilized to simulate a SMA archwire undergoing large strains and rotations.
Strain and Absorption Coefficient of Finite Ge Structures on Si
NASA Astrophysics Data System (ADS)
Park, Sungbong; Ishikawa, Yasuhiko; Wada, Kazumi; Tsusaka, Yoshiyuki; Matsui, Junji
2009-06-01
A finite structure of Ge under tensile stress was investigated theoretically and experimentally focusing on applications to near-infrared photodetectors on (001) Si. We calculated the direct band gap energy of strained Ge between the conduction band and the heavy/light-hole valence band via the k·p theory. Three types of in-plane stresses were considered, i.e., a biaxial stress and uniaxial stresses along the <100> and <110> directions. On the basis of the direct band gap change, absorption spectra due to the direct transitions were calculated. The calculated absorption spectra showed that the biaxial stress is more effective than the uniaxial stresses in terms of the absorption red-shift, which increases the detection wavelength range. Localized strain measurements revealed that a selectively grown Ge mesa on (001) Si maintains a biaxial strain caused by the thermal expansion mismatch when its width is larger than 1 µm. A uniaxial stress probably develops owing to the strain relaxation in a finite Ge structure smaller than 1 µm. The application of Ge finite structures to waveguide photodetectors is discussed.
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.
Thomases, Becca; Guy, Robert D
2014-08-29
A computational model of finite-length undulatory swimmers is used to examine the physical origin of the effect of elasticity on swimming speed. We explore two distinct target swimming strokes: one derived from the motion of Caenorhabditis elegans, with large head undulations, and a contrasting stroke with large tail undulations. We show that both favorable stroke asymmetry and swimmer elasticity contribute to a speed-up, but a substantial boost results only when these two effects work together. We reproduce conflicting results from the literature simply by changing relevant physical parameters.
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.
Incremental stress-strain relation from granular elasticity: comparison to experiments.
Jiang, Yimin; Liu, Mario
2008-02-01
Granular media are reversible and elastic if the stress increments are small enough. An elastic stress-strain relation, employed previously to determine static stress distributions, in this paper is compared to experiments by Kuwano and Jardine [Geotechnique 52, 727 (2002)] on incremental stress-strain relations, and shown to yield satisfactory agreement. In addition, the yield condition is given a firmer footing.
Wu, Fu-Fa; Chan, K C; Jiang, Song-Shan; Chen, Shun-Hua; Wang, Gang
2014-06-16
Bulk metallic glasses exhibit high strength and large elastic strain limit but have no tensile ductility. However, bulk metallic glass composites reinforced by in-situ dendrites possess significantly improved toughness but at the expense of high strength and large elastic strain limit. Here, we report a bulk metallic glass composite with strong strain-hardening capability and large elastic strain limit. It was found that, by plastic predeformation, the bulk metallic glass composite can exhibit both a large elastic strain limit and high strength under tension. These unique elastic mechanical properties are attributed to the reversible B2↔B19' phase transformation and the plastic-predeformation-induced complicated stress state in the metallic glass matrix and the second phase. These findings are significant for the design and application of bulk metallic glass composites with excellent mechanical properties.
Wu, Fu-Fa; Chan, K. C.; Jiang, Song-Shan; Chen, Shun-Hua; Wang, Gang
2014-01-01
Bulk metallic glasses exhibit high strength and large elastic strain limit but have no tensile ductility. However, bulk metallic glass composites reinforced by in-situ dendrites possess significantly improved toughness but at the expense of high strength and large elastic strain limit. Here, we report a bulk metallic glass composite with strong strain-hardening capability and large elastic strain limit. It was found that, by plastic predeformation, the bulk metallic glass composite can exhibit both a large elastic strain limit and high strength under tension. These unique elastic mechanical properties are attributed to the reversible B2↔B19′ phase transformation and the plastic-predeformation-induced complicated stress state in the metallic glass matrix and the second phase. These findings are significant for the design and application of bulk metallic glass composites with excellent mechanical properties. PMID:24931632
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.
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)
Rubin, M. B.; Cardiff, P.
2017-06-01
Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.
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.
Simple structures test for elastic-plastic strain acceptance criterion validation
Trimble, T.F.; Krech, G.R.
1997-11-01
A Simple Structures Test Program was performed where several cantilevered beam and fixed-end beam test specimens (fabricated from HY-80 steel) were subjected to a series of analytically predetermined rapidly applied transient dynamic input loads. The primary objective of the test program was to obtain dynamic nonlinear response for simple structures subjected to these load inputs. Data derived from these tests was subsequently used to correlate to analysis predictions to assess the capability to analytically predict elastic-plastic nonlinear material behavior in structures using typical time-dependent (transient) design methods and the ABAQUS finite element analysis code. The installation of a significant amount of instrumentation on these specimens and post-test measurements enabled the monitoring and recording of strain levels, displacements, accelerations, and permanent set. An assessment of modeling parameters such as the element type and mesh refinement was made using these test results. In addition, currently available material models and the incremental time step procedure used in the transient analyses were evaluated. Comparison of test data to analysis results shows that displacements, accelerations, and peak strain can be predicted with a reasonable level of accuracy using detailed solid models of the tested specimens. Permanent set is overpredicted by a factor of approximately two. However, the accuracy of the prediction of permanent set is being enhanced by updating material modeling in the ABAQUS code to account for effects of strain reversal in oscillatory behavior of dynamically loaded specimens.
Simple structures tests for elastic-plastic strain acceptance criterion validation
Trimble, T.F.; Krech, G.R.
1996-11-01
A Simple Structures Test Program was performed where several cantilevered beam and fixed-end beam test specimens were subjected to a series of analytically predetermined rapidly applied transient dynamic input loads. The primary objective of the test program was to obtain dynamic nonlinear response for simple structures subjected to these load inputs. Data derived from these tests was subsequently used to correlate to analysis predictions to assess the capability to analytically predict elastic-plastic nonlinear material behavior in structures using typical time-dependent (transient) design methods and the ABAQUS finite element analysis code. The installation of a significant amount of instrumentation on these specimens and post-test measurements enabled the monitoring and recording of strain levels, displacements, accelerations, and permanent set. An assessment of modeling parameters such as the element type and mesh refinement was made using these test results. In addition, currently available material models and the incremental time step procedure used in the transient analyses were evaluated. Comparison of test data to analysis results shows that displacements, accelerations, and peak strain can be predicted with a reasonable level of accuracy using detailed solid models of the tested specimens. Permanent set is overpredicted by a factor of approximately two. However, the accuracy of the prediction of permanent set is being enhanced by updating material modeling in the ABAQUS code to account for effects of strain reversal in oscillatory behavior of dynamically loaded specimens.
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
Importance of elastic finite-size effects: Neutral defects in ionic compounds
Burr, P. A.; Cooper, M. W. D.
2017-09-15
Small system sizes are a well known source of error in DFT calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite size effects have been well characterised, but self-interaction of charge neutral defects is often discounted or assumed to follow an asymptotic behaviour and thus easily corrected with linear elastic theory. Here we show that elastic effect are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequatly small supercells are used; moreover,more » the spurious self-interaction does not follow the behaviour predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground state structure of (charge neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768 and 1500 atoms), and careful analysis determines that elastic effects, not electrostatic, are responsible. The spurious self-interaction was also observed in non-oxide ionic compounds and irrespective of the computational method used, thereby resolving long standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects are a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g. hybrid functionals) or when modelling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studies oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells | greater than 96 atoms.« less
Importance of elastic finite-size effects: Neutral defects in ionic compounds
NASA Astrophysics Data System (ADS)
Burr, P. A.; Cooper, M. W. D.
2017-09-01
Small system sizes are a well-known source of error in density functional theory (DFT) calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite-size effects have been well characterized, but self-interaction of charge-neutral defects is often discounted or assumed to follow an asymptotic behavior and thus easily corrected with linear elastic theory. Here we show that elastic effects are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequately small supercells are used; moreover, the spurious self-interaction does not follow the behavior predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground-state structure of (charge-neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768, and 1500 atoms), and careful analysis determines that elastic, not electrostatic, effects are responsible. The spurious self-interaction was also observed in nonoxide ionic compounds irrespective of the computational method used, thereby resolving long-standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects is a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g., hybrid functionals) or when modeling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studied oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells: greater than 96 atoms.
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.
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.
Band gap engineering in nano structured graphane by applying elastic strain
NASA Astrophysics Data System (ADS)
Kumar, Naveen; Sharma, Jyoti Dhar; Kumar, Ashok; Ahluwalia, P. K.
2013-02-01
The first principle calculations have been performed to investigate the influence of elastic strain namely: uniaxial compression (-a), symmetrical biaxial compression (-a-b) and asymmetric biaxial (-a+b) stain, on the electronic structure of graphane in chair conformation. It is found that the band gap can be tuned by elastic strain and depends on the type of applied strain. The nature of the graphane has been found to change from wide band gap semiconductor to metal at three types of strain i. e. 19% uniaxial compression, 16% biaxial compression and 16.5% asymmetric biaxial strain. Tunable band gap of graphane with elastic strain can make it suitable for the applications of electromechanical devices and for the fabrication of strain sensors.
1982-10-26
a >(2Er/rcf) (6.1) where a is the critical stress causing stable fracture, E is Young’s modulus, r is the crack surface energy and cf is the flaw...Continue on reverse side if necessary and identify by block number) A detailed analysis of the deformation and stress fields produced in an elastic...the elastic deformation and stress fields with finite element results being compared to the closed-form solutions obtained by Sneddon, the elastic
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
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
Spatial Parallelism of a 3D Finite Difference, Velocity-Stress Elastic Wave Propagation Code
MINKOFF,SUSAN E.
1999-12-09
Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately. finite difference simulations for 3D elastic wave propagation are expensive. We model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MP1 library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speed up. Because i/o is handled largely outside of the time-step loop (the most expensive part of the simulation) we have opted for straight-forward broadcast and reduce operations to handle i/o. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ''ghost cells''. When this communication is balanced against computation by allocating subdomains of reasonable size, we observe excellent scaled speed up. Allocating subdomains of size 25 x 25 x 25 on each node, we achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.
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.
A stabilized finite element method for finite-strain three-field poroelasticity
NASA Astrophysics Data System (ADS)
Berger, Lorenz; Bordas, Rafel; Kay, David; Tavener, Simon
2017-07-01
We construct a stabilized finite-element method to compute flow and finite-strain deformations in an incompressible poroelastic medium. We employ a three-field mixed formulation to calculate displacement, fluid flux and pressure directly and introduce a Lagrange multiplier to enforce flux boundary conditions. We use a low order approximation, namely, continuous piecewise-linear approximation for the displacements and fluid flux, and piecewise-constant approximation for the pressure. This results in a simple matrix structure with low bandwidth. The method is stable in both the limiting cases of small and large permeability. Moreover, the discontinuous pressure space enables efficient approximation of steep gradients such as those occurring due to rapidly changing material coefficients or boundary conditions, both of which are commonly seen in physical and biological applications.
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.
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.
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.
Microscale Rock mechanics: Determination with finite strain analyses
NASA Astrophysics Data System (ADS)
Förster, A.; Lempp, Ch.
2012-04-01
Analysis of the mechanics of rocks and rock masses play a fundamental role in the crucial risk assessment with respect to destruction of e.g. installations, tunnels, bridge constructions geothermal boreholes and cables. To constrain the mechanics of the rocks and rock masses under compressive and extensional stress regimes, finite strain analysis techniques are used to quantitatively estimate the amount of deformation. This method is an uncommon but powerful tool for strain determination even if marker particles are rarely in mechanical contrast to the matrix. The deformation of such markers is related to shearing, rotation and flattening during compaction, extension or reloading of the rocks. The deformation and rotation of the corresponding strain ellipse (R-value: ratio sigma1/sigma3) indicates the degree of the rock alteration during compaction, erosion or other deformation processes. Information about the orientation of the long axis of the strain ellipse relative to bedding direction or core axis could be given (phi-values). We present first results of laboratory compression tests on core samples of limestone, sandstone and conglomerate according to different matrix types and with varying grain sizes. Under varying applied pressures (from 5 MN/m2 to 52 MN/m2) strain analyses were used to estimate the amount of deformation. Limestone samples show an increase of deformation grades with an increase of the applied pressure (e.g. R=1.26-1.35), while in the sandstone and conglomerate samples the degree of deformation decrease with increasing applied pressures (e.g. Sandstone: R=1.43-1.38, Conglomerate: R=1.09-1.07). In addition, the conglomerate samples are characterised by a strong variability high phi-values (78° to 110°), while the phi-values of the limestone and the sandstone samples are constant around at 87° to 90°. Both high phi-values strain may indicate a high rotation of sigma1 related to one-dimensional compression.
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.
Finite element model for aero-elastically tailored residential wind turbine blade design
NASA Astrophysics Data System (ADS)
Robinson, Eric Alan
Advances in passive wind turbine control systems have allowed wind turbines to achieve higher efficiencies and operate in wider inflow conditions than ever before. Within recent years, the adoption of aero-elastically tailored (bend-twist coupled) composite blades have been a pursued strategy. Unfortunately, for this strategy to be applied, traditional means of modeling, designing and manufacturing are no longer adequate. New parameters regarding non-linearities in deflections, stiffness, and aerodynamic loadings must now be implemented. To aid in the development of passive wind turbine system design, a finite element based aero-elastic program capable of computationally predicting blade deflection and twist under loading was constructed. The program was built around the idea of iteratively solving a blade composite structure to reach a maximum aero-elastic twist configuration under elevated wind speeds. Adopting a pre-existing blade geometry, from a pitch controlled small scale (3.5kW) turbine design, the program was tested to discover the geometry bend-twist coupling potential. This research would be a contributing factor in designing a passive pitch control replacement system for the turbine. A study of various model loading configurations was first performed to insure model validity. Then, a final model was used to analyze composite layups for selected spar configurations. Results characterize the aero-elastic twist properties for the selected configurations.
Acoustic scattering from a contrast agent microbubble near an elastic wall of finite thickness
NASA Astrophysics Data System (ADS)
Doinikov, Alexander A.; Aired, Leila; Bouakaz, Ayache
2011-11-01
Interest in the problem under consideration in this study is motivated by targeted ultrasound imaging where one has to deal with microbubble contrast agents pulsating near blood vessel walls. A modified Rayleigh-Plesset equation is derived that describes the oscillation of a contrast agent microbubble near an elastic wall of finite thickness. It is assumed that the medium behind the wall is a fluid but it is shown that the equation obtained is easily transformable to the case that the medium behind the wall is an elastic solid. In contrast to the model of a rigid wall, which predicts decreasing natural frequency of a bubble near the wall, the elastic wall model reveals that the bubble natural frequency can both decrease and increase, and in cases of interest for medical applications, the bubble natural frequency usually increases. It is found that the influence of an elastic wall on the acoustic response of a bubble is determined by the ratio between a cumulative parameter, which integrally characterizes the mechanical properties of the wall and has the dimension of density, and the density of the liquid surrounding the bubble. It is shown that the acoustic influence of the arterial wall on the bubble is weak and apparently cannot be used to recognize the moment when the bubble approaches the wall. However, in experiments where the behavior of bubbles near various plastic walls is observed, changes in the bubble response, such as increasing natural frequency and decreasing oscillation amplitude, are detectable.
Glynne-Jones, Peter; Mishra, Puja P; Boltryk, Rosemary J; Hill, Martyn
2013-04-01
A finite element based method is presented for calculating the acoustic radiation force on arbitrarily shaped elastic and fluid particles. Importantly for future applications, this development will permit the modeling of acoustic forces on complex structures such as biological cells, and the interactions between them and other bodies. The model is based on a non-viscous approximation, allowing the results from an efficient, numerical, linear scattering model to provide the basis for the second-order forces. Simulation times are of the order of a few seconds for an axi-symmetric structure. The model is verified against a range of existing analytical solutions (typical accuracy better than 0.1%), including those for cylinders, elastic spheres that are of significant size compared to the acoustic wavelength, and spheroidal particles.
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.
NASA Astrophysics Data System (ADS)
Whiteley, J. P.
2017-06-01
Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.
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.
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)
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.
Bönisch, Matthias; Calin, Mariana; van Humbeeck, Jan; Skrotzki, Werner; Eckert, Jürgen
2015-03-01
While the current research focus in the search for biocompatible low-modulus alloys is set on β-type Ti-based materials, the potential of fully martensitic Ti-based alloys remains largely unexplored. In this work, the influence of composition and pre-straining on the elastic properties of martensitic binary Ti-Nb alloys was studied. Additionally, the phase formation was compared in the as-cast versus the quenched state. The elastic moduli and hardness of the studied martensitic alloys are at a minimum of 16wt.% Nb and peak between 23.5 and 28.5wt.% Nb. The uniaxial deformation behavior of the alloys used is characterized by the absence of distinct yield points. Monotonic and cyclic (hysteretic) loading-unloading experiments were used to study the influence of Nb-content and pre-straining on the elastic moduli. Such experiments were also utilized to assess the recoverable elastic and anelastic deformations as well as hysteretic energy losses. Particular attention has been paid to the separation of non-linear elastic from anelastic strains, which govern the stress and strain limits to which a material can be loaded without deforming it plastically. It is shown that slight pre-straining of martensitic Ti-Nb alloys can lead to considerable reductions in their elastic moduli as well as increases in their total reversible strains. Copyright © 2014 Elsevier B.V. All rights reserved.
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.
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.
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
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.
Finite-element study of strain field in strained-Si MOSFET.
Liu, H H; Duan, X F; Xu, Q X
2009-02-01
The strain field in the channel of a p-type metal-oxide-semiconductor field effect transistor fabricated by integrating Ge pre-amorphization implantation for source/drain regions is evaluated using a finite-element method combining with large angle convergent-beam electron diffraction (LACBED). The finite-element calculation shows that there is a very large compressive strain in the top layer of the channel region caused by a low dose of Ge ion implantation in the source and drain extension regions. Moreover, a transition region is formed in the bottom of the channel region and the top of the Si substrate. These calculation results are in good agreement with the LACBED experiments.
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
Finite difference elastic wave modeling with an irregular free surface using ADER scheme
NASA Astrophysics Data System (ADS)
Almuhaidib, Abdulaziz M.; Nafi Toksöz, M.
2015-06-01
In numerical modeling of seismic wave propagation in the earth, we encounter two important issues: the free surface and the topography of the surface (i.e. irregularities). In this study, we develop a 2D finite difference solver for the elastic wave equation that combines a 4th- order ADER scheme (Arbitrary high-order accuracy using DERivatives), which is widely used in aeroacoustics, with the characteristic variable method at the free surface boundary. The idea is to treat the free surface boundary explicitly by using ghost values of the solution for points beyond the free surface to impose the physical boundary condition. The method is based on the velocity-stress formulation. The ultimate goal is to develop a numerical solver for the elastic wave equation that is stable, accurate and computationally efficient. The solver treats smooth arbitrary-shaped boundaries as simple plane boundaries. The computational cost added by treating the topography is negligible compared to flat free surface because only a small number of grid points near the boundary need to be computed. In the presence of topography, using 10 grid points per shortest shear-wavelength, the solver yields accurate results. Benchmark numerical tests using several complex models that are solved by our method and other independent accurate methods show an excellent agreement, confirming the validity of the method for modeling elastic waves with an irregular free surface.
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.
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.
Atomistic Calculation of Elastic Moduli in Strained Silicon
2007-04-01
stiffness calculation The IV and III–V semiconductors, in their cubic structure , have three independent elastic stiffnesses C11, C12 and C44. It was...select a model system (a cubic structure ) consisting of N = 8 × 33 = 216 atoms under the periodic boundary condition, and we solve Newton’s equation of
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.
Determination of Modulus of Elasticity and Shear Modulus by the Measurement of Relative Strains
NASA Astrophysics Data System (ADS)
Labašová, Eva
2016-12-01
This contribution is focused on determining the material properties (Young modulus and shear modulus) of the testing samples. The theoretical basis for determining material properties are the knowledge of linear elasticity and strength. The starting points are dependencies among the modulus of elasticity, shear modulus, normal stress and relative strain. The relative strains of the testing samples were obtained by measuring predefined load conditions using a strain-gauge bridge and the universal measurement system Quantum X MX 840. The integration of these tasks into the teaching process enhances practical and intellectual skills of students at secondary level technical universities.
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
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.
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.
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.
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 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)
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.
Finite element modeling for soft tissue surgery based on linear and nonlinear elasticity behavior.
Tillier, Y; Paccini, A; Durand-Reville, M; Chenot, J-L
2006-03-01
New surgical techniques require fine control from the surgeon's point of view. Until recently, the necessary experience was only obtainable through traditional training protocols (using cadavers, animals, etc.). However, numerous training simulators have now been developed for use in this area. We present a new approach based on a three-dimensional finite element software and on different kinds of linear and nonlinear elastic constitutive equations that is able to predict realistic results. To classify these equations in terms of accuracy, we performed ex-vivo experimental measurements on lamb kidneys. The software has been applied to soft tissue deformation, namely lamb kidney and human uterus, and the numerical results have been compared to experimental ones.
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 Astrophysics Data System (ADS)
Zhang, Pengchong; Liu, Jun; Lin, Gao
2017-04-01
The scaled boundary finite element method (SBFEM) and the precise integration algorithm (PIA) are utilized to analyze the extended displacement field in clamped or simple-supported magneto-electro-elastic plates produced by external transverse loadings. There are no limitation on boundary conditions and types of external forces. Only the in-plane dimensions are divided into 2D elements. By introducing a set of scaled boundary local coordinates, 3D governing partial differential equations are converted into the second order ordinary differential matrix equation. By means of the internal nodal force, a first order ordinary differential equation is obtained and its general solution is a matrix exponential. The PIA is introduced to calculate the matrix exponential and any desired accuracy can be obtained. Finally, several numerical examples are provided to validate the versatility of the proposed technique.
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.
NASA Astrophysics Data System (ADS)
Nobile, Fabio; Pozzoli, Matteo; Vergara, Christian
2014-09-01
In this paper we consider the numerical solution of the three-dimensional fluid-structure interaction problem in haemodynamics, in the case of real geometries, physiological data and finite elasticity vessel deformations. We study some new inexact schemes, obtained from semi-implicit approximations, which treat exactly the physical interface conditions while performing just one or few iterations for the management of the interface position and of the fluid and structure non-linearities. We show that such schemes allow to improve the efficiency while preserving the accuracy of the related exact (implicit) scheme. To do this we consider both a simple analytical test case and two real cases of clinical interest in haemodynamics. We also provide an error analysis for a simple differential model problem when a BDF method is considered for the time discretization and only few Newton iterations are performed at each temporal instant.
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.
An elastic-plastic finite element analysis of crack initiation, stable crack growth, and instability
NASA Technical Reports Server (NTRS)
Newman, J. C., Jr.
1984-01-01
Studies have been conducted to develop efficient techniques to simulate crack extension and to examine various local and global fracture criteria. Of the considered criteria, the crack-tip-opening angle (CTOA) or displacement (CTOD) at a specified distance from the crack tip was shown to be most suited for modeling stable crack growth and instability during the fracture process. The results obtained in a number of studies show the necessity for studying different crack configurations when assessing the validity of any fracture criteria. One of the objectives of the present investigation is related to a critical evaluation of the CTOD growth criterion using an elastic-plastic finite element analysis under monotonic loading to failure. The analysis was found to predict three stages of crack growth behavior under monotonic loading to failure. Calculated CTOD values agreed well with experimental values for crack growth initiation.
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
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.
A discontinuous finite element approach to cracking in coupled poro-elastic fluid flow models
NASA Astrophysics Data System (ADS)
Wilson, C. R.; Spiegelman, M. W.; Evans, O.; Ulven, O. I.; Sun, W.
2016-12-01
Reaction-driven cracking is a coupled process whereby fluid-induced reactions drive large volume changes in the host rock which produce stresses leading to crack propagation and failure. This in turn generates new surface area and fluid-flow pathways for subsequent reaction in a potentially self-sustaining system. This mechanism has has been proposed for the pervasive serpentinization and carbonation of peridotite, as well as applications to mineral carbon sequestration and hydrocarbon extraction. The key computational issue in this problem is implementing algorithms that adequately model the formation of discrete fractures. Here we present models using a discontinuous finite element method for modeling fracture formation (Radovitsky et al., 2011). Cracks are introduced along facets of the mesh by the relaxation of penalty parameters once a failure criterion is met. It is fully described in the weak form of the equations, requiring no modification of the underlying mesh structure and allowing fluid properties to be easily adjusted along cracked facets. To develop and test the method, we start by implementing the algorithm for the simplified Biot equations for poro-elasticity using the finite element model assembler TerraFERMA. We consider hydro-fracking around a borehole (Grassl et al., 2015), where elevated fluid pressure in the poro-elastic solid causes it to fail radially in tension. We investigate the effects of varying the Biot coefficient and adjusting the fluid transport properties in the vicinity of the crack and compare our results to related dual-graph models (Ulven & Sun, submitted). We discuss issues arising from this method, including the formation of null spaces and appropriate preconditioning and solution strategies. Initial results suggest that this method provides a promising way to incorporate cracking into our reactive fluid flow models and future work aims to integrate the mechanical and chemical aspects of this process.
NASA Astrophysics Data System (ADS)
Szumski, Richard Gerard
1993-01-01
The equations of motion for the vibration study of a partially elastic and partially linearly viscoelastic structure are developed in the time domain. The unique feature of these equations is that they contain both differential and integral terms. The integral terms are convolution integrals whose convolution is made between the time derivative of the viscoelastic relaxation modulus and the displacement history. They account for viscoelastic damping of the structure. The equations are simplified through the solution of a real eigenvalue problem which is subsequently used to decouple all but the damping term. A numerical solution procedure is presented using the finite element method for the spatial domain and a Runge Kutta-Verner numerical integration routine for temporal domain of the problem. Partial decoupling of the equations of motion reduces computation time and saves storage space. The convolution integrals are evaluated at each time step using the trapezoidal rule. Two new viscoelastic constitutive laws are introduced that are shown to characterize material properties over a broad frequency spectrum with few material parameters. They are convenient to work with because they have simple rational forms in both the time and frequency domains and also unconditionally obey the second law of thermodynamics. To verify the theory, computer program, and new viscoelastic constitutive laws, a simple elastic-viscoelastic structure known as a constrained layer damper was constructed and tested. The displacement history of the constrained layer damper was measured as an initial static displacement was suddenly released. Good agreement was obtained between the measurements and the numerical simulation of the same event using the theory developed here with the new constitutive laws. The solution procedure is a viable method for solving for the vibratory response of viscoelastically damped structures and is suitable for large-scale finite element analysis through a modified
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.
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).
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.
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)
Pogosov, V. V.; Kurbatsky, V. P.
2001-02-01
The effect of external strain on surface properties of simple metals is considered within the modified stabilized jellium model. The equations for the stabilization energy of the deformed Wigner-Seitz cells are derived as a function of the bulk electron density and the given deformation. The results for surface stress and work function of aluminium calculated within the self-consistent Kohn-Sham method are also given. The problem of anisotropy of the work function of finite system is discussed. A clear explanation of independent experiments on stress-induced contact potential difference at metal surfaces is presented.
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
Improving the finite element forward model of the human head by warping using elastic deformation.
Tizzard, A; Bayford, R H
2007-07-01
As the use of realistic geometry in the forward model of electrical impedance tomography (EIT) of brain function appears to improve image reconstruction, the generation of patient-specific finite element meshes has been the subject of much recent work. This paper presents a more rapid method of generating more geometrically accurate finite element meshes of the human head by warping existing meshes such that the surface boundary beneath the electrodes closely matches that of the subject with minimal degradation to the quality of the mesh. Pre-existing meshes of spheres and adult head models incorporating key internal anatomical features are warped, using elastic deformation, to match a phantom latex tank incorporating a real skull. The algorithm is described and tests are carried out to optimize the key parameters to ensure minimal degradation of mesh quality and distortion of internal features. Results show that the algorithm operating with the optimum parameters produces meshes of sound quality and could represent an important step in the timely and productive creation of forward models in clinical applications.
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.
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)
Militello, Carmelo; Felippa, Carlos A.
1990-01-01
The assumed natural strain formulation of finite elements is interpreted from a variational standpoint. The approach is based on hybrid extensions of the Reissner-type functional which uses the strains and displacements as independent fields. Consideration is restricted to linear elasticity. The four-node C(0) plate-bending quadrilateral is used as a specific example to illustrate the application of the present interpretation. A key finding is that any change in the strain-displacement interpolation from the variationally consistent interpolation must be associated in some way to the addition of incompatible displacement modes.
NASA Astrophysics Data System (ADS)
Reza Barati, Mohammad
2017-09-01
For the first time, a vibrating porous double-nanoplate system under in-plane periodic loads is modeled via the generalized nonlocal strain gradient theory (NSGT). Based on the proposed theory, one can examine both stiffness-softening and stiffness-hardening effects for a more accurate analysis of nanoplates. Nanopores or nanovoids are incorporated to the model based on a modified rule of mixture. Modeling of porous double-layered nanoplate is conducted according to a refined four-variable plate theory with fewer field variables than first-order plate theory. The governing equations and related classical and nonclassical boundary conditions are derived based on Hamilton's principle. These equations are solved for hinged nanoplates via Galerkin's method. It is shown that porosities, nonlocal parameter, strain gradient parameter, material gradation, interlayer stiffness, elastic foundation, side-to-thickness and aspect ratios have a notable impact on the vibration behavior of nanoporous materials.
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.
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
An Elastic Stress-Strain Relationship for Porous Rock Under Anisotropic Stress Conditions
NASA Astrophysics Data System (ADS)
Zhao, Yu; Liu, Hui-Hai
2012-05-01
A stress-strain relationship within porous rock under anisotropic stress conditions is required for modeling coupled hydromechanical processes associated with a number of practical applications. In this study, a three-dimensional stress-strain relationship is proposed for porous rock under elastic and anisotropic stress conditions. This relationship is a macroscopic-scale approximation that uses a natural-strain-based Hooke's law to describe deformation within a fraction of pores and an engineering-strain-based Hooke's law to describe deformation within the other part. This new relationship is evaluated using data from a number of uniaxial and triaxial tests published in the literature. Based on this new stress-strain relationship, we also develop constitutive relationships among stress, strain, and related stress-dependent hydraulic/mechanical properties (such as compressibility, shear modulus, and porosity). These relationships are demonstrated to be consistent with experimental observations.
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.
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).
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.
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. Copyright © 2013 Elsevier Ltd. All rights reserved.
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.
Lee, Bryan; Popescu, Dan C; Ourselin, Sébastien
2010-12-01
Surgical simulators provide another tool for training and practising surgical procedures, usually restricted to the use of cadavers. Our surgical simulator utilises Finite Element (FE) models based on linear elasticity. It is driven by displacements, as opposed to forces, allowing for realistic simulation of both deformation and haptic response at real-time rates. To achieve demanding computational requirements, the stiffness matrix K, which encompasses the geometrical and physical properties of the object, is precomputed, along with K⁻¹. Common to many surgical procedures is the requirement of cutting tissue. Introducing topology modifications, such as cutting, into these precomputed schemes does however come as a challenge, as the precomputed data needs to be modified, to reflect the new topology. In particular, recomputing K⁻¹ is too costly to be performed during the simulation. Our topology modification method is based upon updating K⁻¹ rather than entirely recomputing the matrix. By integrating condensation, we improve efficiency to allow for interaction with larger models. We can further enhance this by redistributing computational load to improve the system's real-time response. We exemplify our techniques with results from our surgical simulation system. Crown Copyright © 2010. Published by Elsevier Ltd. All rights reserved.
A time-domain finite element boundary integral approach for elastic wave scattering
NASA Astrophysics Data System (ADS)
Shi, F.; Lowe, M. J. S.; Skelton, E. A.; Craster, R. V.
2017-08-01
The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.
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.
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.
Giant linear strain gradient with extremely low elastic energy in a perovskite nanostructure array
Tang, Y. L.; Zhu, Y. L.; Liu, Y.; Wang, Y. J.; Ma, X. L.
2017-01-01
Although elastic strains, particularly inhomogeneous strains, are able to tune, enhance or create novel properties of some nanoscale functional materials, potential devices dominated by inhomogeneous strains have not been achieved so far. Here we report a fabrication of inhomogeneous strains with a linear gradient as giant as 106 per metre, featuring an extremely lower elastic energy cost compared with a uniformly strained state. The present strain gradient, resulting from the disclinations in the BiFeO3 nanostructures array grown on LaAlO3 substrates via a high deposition flux, induces a polarization of several microcoulomb per square centimetre. It leads to a large built-in electric field of several megavoltage per metre, and gives rise to a large enhancement of solar absorption. Our results indicate that it is possible to build up large-scale strain-dominated nanostructures with exotic properties, which in turn could be useful in the development of novel devices for electromechanical and photoelectric applications. PMID:28665413
Giant linear strain gradient with extremely low elastic energy in a perovskite nanostructure array
NASA Astrophysics Data System (ADS)
Tang, Y. L.; Zhu, Y. L.; Liu, Y.; Wang, Y. J.; Ma, X. L.
2017-06-01
Although elastic strains, particularly inhomogeneous strains, are able to tune, enhance or create novel properties of some nanoscale functional materials, potential devices dominated by inhomogeneous strains have not been achieved so far. Here we report a fabrication of inhomogeneous strains with a linear gradient as giant as 106 per metre, featuring an extremely lower elastic energy cost compared with a uniformly strained state. The present strain gradient, resulting from the disclinations in the BiFeO3 nanostructures array grown on LaAlO3 substrates via a high deposition flux, induces a polarization of several microcoulomb per square centimetre. It leads to a large built-in electric field of several megavoltage per metre, and gives rise to a large enhancement of solar absorption. Our results indicate that it is possible to build up large-scale strain-dominated nanostructures with exotic properties, which in turn could be useful in the development of novel devices for electromechanical and photoelectric applications.
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.
Kakeshita, Tomoyuki; Xiao, Fei; Fukuda, Takashi
2016-08-13
A Fe-31.2Pd (at.%) alloy exhibits a weak first-order martensitic transformation from a cubic structure to a tetragonal structure near 230 K. This transformation is associated with significant softening of elastic constant C'. Because of the softening, the alloy shows a large elastic strain of more than 6% in the [001] direction. In addition, the alloy has a critical point and shows a high elastocaloric effect in a wide temperature range for both the parent and the martensite phases.This article is part of the themed issue 'Taking the temperature of phase transitions in cool materials'. © 2016 The Author(s).
Appelo, D; Petersson, N A
2007-12-17
The isotropic elastic wave equation governs the propagation of seismic waves caused by earthquakes and other seismic events. It also governs the propagation of waves in solid material structures and devices, such as gas pipes, wave guides, railroad rails and disc brakes. In the vast majority of wave propagation problems arising in seismology and solid mechanics there are free surfaces. These free surfaces have, in general, complicated shapes and are rarely flat. Another feature, characterizing problems arising in these areas, is the strong heterogeneity of the media, in which the problems are posed. For example, on the characteristic length scales of seismological problems, the geological structures of the earth can be considered piecewise constant, leading to models where the values of the elastic properties are also piecewise constant. Large spatial contrasts are also found in solid mechanics devices composed of different materials welded together. The presence of curved free surfaces, together with the typical strong material heterogeneity, makes the design of stable, efficient and accurate numerical methods for the elastic wave equation challenging. Today, many different classes of numerical methods are used for the simulation of elastic waves. Early on, most of the methods were based on finite difference approximations of space and time derivatives of the equations in second order differential form (displacement formulation), see for example [1, 2]. The main problem with these early discretizations were their inability to approximate free surface boundary conditions in a stable and fully explicit manner, see e.g. [10, 11, 18, 20]. The instabilities of these early methods were especially bad for problems with materials with high ratios between the P-wave (C{sub p}) and S-wave (C{sub s}) velocities. For rectangular domains, a stable and explicit discretization of the free surface boundary conditions is presented in the paper [17] by Nilsson et al. In summary
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.
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. © 2015 Wiley Periodicals, Inc.
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.
Effect of high-energy X-ray doses on bone elastic properties and residual strains.
Singhal, A; Deymier-Black, Alix C; Almer, J D; Dunand, D C
2011-11-01
Bone X-ray irradiation occurs during medical treatments, sterilization of allografts, space travel and in vitro studies. High doses are known to affect the post-yield properties of bone, but their effect on the bone elastic properties is unclear. The effect of such doses on the mineral-organic interface has also not been adequately addressed. Here, the evolution of elastic properties and residual strains with increasing synchrotron X-ray dose (5-3880 kGy) is examined on bovine cortical bone. It is found that these doses affect neither the degree of nanometer-level load transfer between the hydroxyapatite (HAP) platelets and the collagen up to stresses of -60 MPa nor the microscopic modulus of collagen fibrils (both measured by synchrotron X-ray scattering during repeated in situ loading and unloading). However, the residual elastic strains in the HAP phase decrease markedly with increased irradiation, indicating damage at the HAP-collagen interface. The HAP residual strain also decreases after repeated loading/unloading cycles. These observations can be explained by temporary de-bonding at the HAP/collagen interface (thus reducing the residual strain), followed by rapid re-bonding (so that load transfer capability is not affected). Copyright © 2011 Elsevier Ltd. All rights reserved.
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. Copyright © 2016. Published by Elsevier B.V.
Zauel, R; Yeni, Y N; Bay, B K; Dong, X N; Fyhrie, D P
2006-02-01
The mechanical properties of cancellous bone and the biological response of the tissue to mechanical loading are related to deformation and strain in the trabeculae during function. Due to the small size of trabeculae, their motion is difficult to measure. To avoid the need to measure trabecular motions during loading the finite element method has been used to estimate trabecular level mechanical deformation. This analytical approach has been empirically successful in that the analytical models are solvable and their results correlate with the macroscopically measured stiffness and strength of bones. The present work is a direct comparison of finite element predictions to measurements of the deformation and strain at near trabecular level. Using the method of digital volume correlation, we measured the deformation and calculated the strain at a resolution approaching the trabecular level for cancellous bone specimens loaded in uniaxial compression. Smoothed results from linearly elastic finite element models of the same mechanical tests were correlated to the empirical three-dimensional (3D) deformation in the direction of loading with a coefficient of determination as high as 97% and a slope of the prediction near one. However, real deformations in the directions perpendicular to the loading direction were not as well predicted by the analytical models. Our results show, that the finite element modeling of the internal deformation and strain in cancellous bone can be accurate in one direction but that this does not ensure accuracy for all deformations and strains.
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.
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.
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.
Effects of elastic bed on hydrodynamic forces for a submerged sphere in an ocean of finite depth
NASA Astrophysics Data System (ADS)
Mohapatra, Smrutiranjan
2017-08-01
In this paper, we consider a hydroelastic model to examine the radiation of waves by a submerged sphere for both heave and sway motions in a single-layer fluid flowing over an infinitely extended elastic bottom surface in an ocean of finite depth. The elastic bottom is modeled as a thin elastic plate and is based on the Euler-Bernoulli beam equation. The effect of the presence of surface tension at the free-surface is neglected. In such situation, there exist two modes of time-harmonic waves: the one with a lower wavenumber (surface mode) propagates along the free-surface and the other with higher wavenumber (flexural mode) propagates along the elastic bottom surface. Based on the small amplitude wave theory and by using the multipole expansion method, we find the particular solution for the problem of wave radiation by a submerged sphere of finite depth. Furthermore, this method eliminates the need to use large and cumbersome numerical packages for the solution of such problem and leads to an infinite system of linear algebraic equations which are easily solved numerically by any standard technique. The added-mass and damping coefficients for both heave and sway motions are derived and plotted for different submersion depths of the sphere and flexural rigidity of the elastic bottom surface. It is observed that, whenever the sphere nearer to the elastic bed, the added-mass move toward to a constant value of 1, which is approximately twice of the value of added-mass of a moving sphere in a single-layer fluid flowing over a rigid and flat bottom surface.
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 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.
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
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
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.
Suzuki, Sara; Aoyama, Yusuke; Umezu, Mitsuo
2017-01-01
Background The mechanical interaction between blood vessels and medical devices can induce strains in these vessels. Measuring and understanding these strains is necessary to identify the causes of vascular complications. This study develops a method to measure the three-dimensional (3D) distribution of strain using tomographic particle image velocimetry (Tomo-PIV) and compares the measurement accuracy with the gauge strain in tensile tests. Methods and findings The test system for measuring 3D strain distribution consists of two cameras, a laser, a universal testing machine, an acrylic chamber with a glycerol water solution for adjusting the refractive index with the silicone, and dumbbell-shaped specimens mixed with fluorescent tracer particles. 3D images of the particles were reconstructed from 2D images using a multiplicative algebraic reconstruction technique (MART) and motion tracking enhancement. Distributions of the 3D displacements were calculated using a digital volume correlation. To evaluate the accuracy of the measurement method in terms of particle density and interrogation voxel size, the gauge strain and one of the two cameras for Tomo-PIV were used as a video-extensometer in the tensile test. The results show that the optimal particle density and interrogation voxel size are 0.014 particles per pixel and 40 × 40 × 40 voxels with a 75% overlap. The maximum measurement error was maintained at less than 2.5% in the 4-mm-wide region of the specimen. Conclusions We successfully developed a method to experimentally measure 3D strain distribution in an elastic silicone material using Tomo-PIV and fluorescent particles. To the best of our knowledge, this is the first report that applies Tomo-PIV to investigate 3D strain measurements in elastic materials with large deformation and validates the measurement accuracy. PMID:28910397
Takahashi, Azuma; Suzuki, Sara; Aoyama, Yusuke; Umezu, Mitsuo; Iwasaki, Kiyotaka
2017-01-01
The mechanical interaction between blood vessels and medical devices can induce strains in these vessels. Measuring and understanding these strains is necessary to identify the causes of vascular complications. This study develops a method to measure the three-dimensional (3D) distribution of strain using tomographic particle image velocimetry (Tomo-PIV) and compares the measurement accuracy with the gauge strain in tensile tests. The test system for measuring 3D strain distribution consists of two cameras, a laser, a universal testing machine, an acrylic chamber with a glycerol water solution for adjusting the refractive index with the silicone, and dumbbell-shaped specimens mixed with fluorescent tracer particles. 3D images of the particles were reconstructed from 2D images using a multiplicative algebraic reconstruction technique (MART) and motion tracking enhancement. Distributions of the 3D displacements were calculated using a digital volume correlation. To evaluate the accuracy of the measurement method in terms of particle density and interrogation voxel size, the gauge strain and one of the two cameras for Tomo-PIV were used as a video-extensometer in the tensile test. The results show that the optimal particle density and interrogation voxel size are 0.014 particles per pixel and 40 × 40 × 40 voxels with a 75% overlap. The maximum measurement error was maintained at less than 2.5% in the 4-mm-wide region of the specimen. We successfully developed a method to experimentally measure 3D strain distribution in an elastic silicone material using Tomo-PIV and fluorescent particles. To the best of our knowledge, this is the first report that applies Tomo-PIV to investigate 3D strain measurements in elastic materials with large deformation and validates the measurement accuracy.
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.
Ebner, C; Sarkar, R; Rajagopalan, J; Rentenberger, C
2016-06-01
A novel technique is used to measure the atomic-level elastic strain tensor of amorphous materials by tracking geometric changes of the first diffuse ring of selected area electron diffraction patterns (SAD). An automatic procedure, which includes locating the centre and fitting an ellipse to the diffuse ring with sub-pixel precision is developed for extracting the 2-dimensional strain tensor from the SAD patterns. Using this technique, atomic-level principal strains from micrometre-sized regions of freestanding amorphous Ti0.45Al0.55 thin films were measured during in-situ TEM tensile deformation. The thin films were deformed using MEMS based testing stages that allow simultaneous measurement of the macroscopic stress and strain. The calculated atomic-level principal strains show a linear dependence on the applied stress, and good correspondence with the measured macroscopic strains. The calculated Poisson's ratio of 0.23 is reasonable for brittle metallic glasses. The technique yields a strain accuracy of about 1×10(-4) and shows the potential to obtain localized strain profiles/maps of amorphous thin film samples. Copyright © 2016 Elsevier B.V. All rights reserved.
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.
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.
Vetter, A; Liu, Y; Witt, F; Manjubala, I; Sander, O; Epari, D R; Fratzl, P; Duda, G N; Weinkamer, R
2011-02-03
During secondary fracture healing, various tissue types including new bone are formed. The local mechanical strains play an important role in tissue proliferation and differentiation. To further our mechanobiological understanding of fracture healing, a precise assessment of local strains is mandatory. Until now, static analyses using Finite Elements (FE) have assumed homogenous material properties. With the recent quantification of both the spatial tissue patterns (Vetter et al., 2010) and the development of elastic modulus of newly formed bone during healing (Manjubala et al., 2009), it is now possible to incorporate this heterogeneity. Therefore, the aim of this study is to investigate the effect of this heterogeneity on the strain patterns at six successive healing stages. The input data of the present work stemmed from a comprehensive cross-sectional study of sheep with a tibial osteotomy (Epari et al., 2006). In our FE model, each element containing bone was described by a bulk elastic modulus, which depended on both the local area fraction and the local elastic modulus of the bone material. The obtained strains were compared with the results of hypothetical FE models assuming homogeneous material properties. The differences in the spatial distributions of the strains between the heterogeneous and homogeneous FE models were interpreted using a current mechanobiological theory (Isakson et al., 2006). This interpretation showed that considering the heterogeneity of the hard callus is most important at the intermediate stages of healing, when cartilage transforms to bone via endochondral ossification. Copyright © 2010 Elsevier Ltd. All rights reserved.
Tissue Doppler and strain imaging for evaluating tissue elasticity of breast lesions.
Thomas, Anke; Warm, Mathias; Hoopmann, Markus; Diekmann, Felix; Fischer, Thomas
2007-05-01
Sonoelastography depicts the intrinsic elastic properties of a tissue which are characterized by the strain applied to achieve tissue deformation and the velocity at which tissue deformation occurs. The present study served to investigate whether the specificity of B-mode ultrasound (US) can be improved by combining B-mode imaging with tissue Doppler imaging (TDI) and offline analysis of tissue strain imaging (TSI). Fifty women, 25 with malignant and 25 with benign focal breast lesions, were examined by US with a linear transducer (9 MHz, Aplio, Toshiba, Otawara, Japan). B-mode US views of the lesions were overlaid with color-coded TDI information and area quotients (AQ = area B-mode view/area TDI) were calculated. TSI views were reconstructed offline from the source data. This was done by placing a region of interest (ROI) in the target lesion and color-encoded display of the information. In addition, tissue elasticity was evaluated using a scale of 1-5 corresponding to the BI-RADS categories. Maximum strain (strain factor, SF) was determined in the ROI. All patients also underwent mammography. Sensitivities and specificities were calculated and statistical analysis was performed using Wilcoxon's test. Sensitivity/specificity was 96%/68% for B-mode US, 100%/40% for combined B-mode US and mammography, and 96%/80% for TSI. The AQ of benign and malignant lesions was significantly different (p = .00008) as was the difference in SF (p = .0004). The readers considered TSI a feasible technique. Evaluation of elasticity based on the quantification of strain factors improves characterization of focal breast lesions, especially the differentiation of BI-RADS 3 and 4 lesions. Surprisingly, significant results in characterizing breast lesions were obtained with the simple technique of TDI, showing a lower tissue displacement in malignant cases.
Butz, Kent D; Chan, Deva D; Nauman, Eric A; Neu, Corey P
2011-10-13
The noninvasive measurement of finite strains in biomaterials and tissues by magnetic resonance imaging (MRI) enables mathematical estimates of stress distributions and material properties. Such methods allow for non-contact and patient-specific modeling in a manner not possible with traditional mechanical testing or finite element techniques. Here, we employed three constitutive (i.e. linear Hookean, and nonlinear Neo-Hookean and Mooney-Rivlin) relations with known loading conditions and MRI-based finite strains to estimate stress patterns and material properties in the articular cartilage of tibiofemoral joints. Displacement-encoded MRI was used to determine two-dimensional finite strains in juvenile porcine joints, and an iterative technique estimated stress distributions and material properties with defined constitutive relations. Stress distributions were consistent across all relations, although the stress magnitudes varied. Material properties for femoral and tibial cartilage were found to be consistent with those reported in literature. Further, the stress estimates from Hookean and Neo-Hookean, but not Mooney-Rivlin, relations agreed with finite element-based simulations. A nonlinear Neo-Hookean relation provided the most appropriate model for the characterization of complex and spatially dependent stresses using two-dimensional MRI-based finite strain. These results demonstrate the feasibility of a new and computationally efficient technique incorporating MRI-based deformation with mathematical modeling to non-invasively evaluate the mechanical behavior of biological tissues and materials. Copyright © 2011 Elsevier Ltd. All rights reserved.
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.
Development of Ti-Nb-Zr alloys with high elastic admissible strain for temporary orthopedic devices.
Ozan, Sertan; Lin, Jixing; Li, Yuncang; Ipek, Rasim; Wen, Cuie
2015-07-01
A new series of beta Ti-Nb-Zr (TNZ) alloys with considerable plastic deformation ability during compression test, high elastic admissible strain, and excellent cytocompatibility have been developed for removable bone tissue implant applications. TNZ alloys with nominal compositions of Ti-34Nb-25Zr, Ti-30Nb-32Zr, Ti-28Nb-35.4Zr and Ti-24.8Nb-40.7Zr (wt.% hereafter) were fabricated using the cold-crucible levitation technique, and the effects of alloying element content on their microstructures, mechanical properties (tensile strength, yield strength, compressive yield strength, Young's modulus, elastic energy, toughness, and micro-hardness), and cytocompatibilities were investigated and compared. Microstructural examinations revealed that the TNZ alloys consisted of β phase. The alloy samples displayed excellent ductility with no cracking, or fracturing during compression tests. Their tensile strength, Young's modulus, elongation at rupture, and elastic admissible strain were measured in the ranges of 704-839 MPa, 62-65 GPa, 9.9-14.8% and 1.08-1.31%, respectively. The tensile strength, Young's modulus and elongation at rupture of the Ti-34Nb-25Zr alloy were measured as 839 ± 31.8 MPa, 62 ± 3.6 GPa, and 14.8 ± 1.6%, respectively; this alloy exhibited the elastic admissible strain of approximately 1.31%. Cytocompatibility tests indicated that the cell viability ratios (CVR) of the alloys are greater than those of the control group; thus the TNZ alloys possess excellent cytocompatibility. Copyright © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Showalter, Brent L.; DeLucca, John F.; Peloquin, John M.; Cortes, Daniel H.; Yoder, Jonathon H.; Jacobs, Nathan T.; Wright, Alexander C.; Gee, James C.; Vresilovic, Edward J.; Elliott, Dawn M.
2017-01-01
Tissue strain is an important indicator of mechanical function, but is difficult to noninvasively measure in the intervertebral disc. The objective of this study was to generate a disc strain template, a 3D average of disc strain, of a group of human L4–L5 discs loaded in axial compression. To do so, magnetic resonance images of uncompressed discs were used to create an average disc shape. Next, the strain tensors were calculated pixel-wise by using a previously developed registration algorithm. Individual disc strain tensor components were then transformed to the template space and averaged to create the disc strain template. The strain template reduced individual variability while highlighting group trends. For example, higher axial and circumferential strains were present in the lateral and posterolateral regions of the disc, which may lead to annular tears. This quantification of group-level trends in local 3D strain is a significant step forward in the study of disc biomechanics. These trends were compared to a finite element model that had been previously validated against the disc-level mechanical response. Depending on the strain component, 81–99% of the regions within the finite element model had calculated strains within one standard deviation of the template strain results. The template creation technique provides a new measurement technique useful for a wide range of studies, including more complex loading conditions, the effect of disc pathologies and degeneration, damage mechanisms, and design and evaluation of treatments. PMID:26694516
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.
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
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
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
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.}
Elastic modulus and stress-strain response of human enamel by nano-indentation.
He, Li Hong; Fujisawa, Naoki; Swain, Michael V
2006-08-01
Nano-indentation with a sharp (Berkovich) and two spherical indenters with nominal tip radii of 5 and 20 microm was used to determine the elastic modulus and stress-strain response of human enamel. Indentation tests were made over a wide range of peak loads from 1 to 450 mN in two orthogonal directions, i.e., parallel and perpendicular to enamel prisms. The elastic modulus and hardness (mean contact pressure) versus depth of penetration were determined for the three indenters. From the spherical indentation data, stress-strain curves (H-tantheta curve) of enamel were determined in the two orthogonal directions and were found to be different. The elastic modulus showed load dependence for both orientations of the enamel rod structure that depended on the indenter. However, these differences could be normalized upon considering the contact diameter. The indented sample was imaged with an SEM to investigate the near surface damage. In conclusion, prism-sheath structure played an important role in determining the mechanical properties as well as the localized fracture of enamel.
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
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)
Halford, G. R.; Saltsman, J. F.
1983-01-01
Procedures are presented for expressing the Strainrange Partitioning (SRP) method for creep fatigue life prediction in terms of total strain range. Inelastic and elastic strain-range - life relations are summed to give total strain-range - life relations. The life components due to inelastic strains are dealt with using conventional SRP procedures while the life components due to elastic strains are expressed as families of time-dependent terms for each type of SRP cycle. Cyclic constitutive material behavior plays an important role in establishing the elastic strain-range life relations as well as the partitioning of the inelastic strains. To apply the approach, however, it is not necessary to have to determine the magnitude of the inelastic strain range. The total strain SRP approach is evaluated and verified using two nickel base superalloys, AF2-1DA and Rene 95. Excellent agreement is demonstrated between observed and predicted cyclic lifetimes with 70 to 80 percent of the predicted lives falling within factors of two of the observed lives. The total strain-range SRP approach should be of considerable practical value to designers who are faced with creep-fatigue problems for which the inelastic strains cannot be calculated with sufficient accuracy to make reliable life predictions by the conventional inelastic strain range SRP approach.
Phase field modelling of strain induced crystal growth in an elastic matrix.
Laghmach, Rabia; Candau, Nicolas; Chazeau, Laurent; Munch, Etienne; Biben, Thierry
2015-06-28
When a crystal phase grows in an amorphous matrix, such as a crystallisable elastomer, containing cross-links and/or entanglements, these "topological constraints" need to be pushed away from the crystal phase to allow further crystallization. The accumulation of these topological constraints in the vicinity of the crystal interface may store elastic energy and affect the phase transition. To evaluate the consequences of such mechanism, we introduce a phase field model based on the Flory theory of entropic elasticity. We show that the growth process is indeed sensibly affected, in particular, an exponential increase of the surface energy with the displacement of the interface is induced. This explains the formation of stable nano-crystallites as it is observed in the Strain Induced Crystallization (SIC) of natural rubber. Although simple, the model developed here is able to account for many interesting features of SIC, for instance, the crystallite shapes and their sizes which depend on the applied deformation.
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.
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
(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.
Microscale elastic strain evolution following damage in Ti-SiC composites
NASA Astrophysics Data System (ADS)
Hanan, Jay C.; Swift, Geoffrey A.; Üstündag, Ersan; Beyerlein, Irene J.; Almer, Jonathan D.; Lienert, Ulrich; Haeffner, Dean R.
2002-12-01
Fiber fractures are crucial in initiating damage zones that ultimately determine the strength and lifetime of fiber-reinforced metal matrix composites. The evolution of damage in a metal matrix composite (MMC) comprised of a row of unidirectional SiC fibers (32 vol pct) surrounded by a Ti matrix was examined, for the first time, using X-ray microdiffraction. Multiple strain maps including both phases were collected in situ under applied tensile stress. The elastic axial strains were then compared to predictions from a modified shear-lag model, which, unlike other shear-lag models, considers the elastic response of both constituents. The strains showed good correlation with the model. The results confirmed, for the first time, both the need and validity of this new model specifically developed for large scale multifracture simulations of MMCs. The results also provided unprecedented insight for the model, revealing the necessity of incorporating such factors as plasticity of the matrix, residual stress in the composite, and selection of the load sharing parameter.
NASA Astrophysics Data System (ADS)
Menzel, Andreas M.
2016-08-01
One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)elastic substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we present a hydrodynamic description of (visco)elastic composite materials. For this purpose, additional strain variables reflect the state of the inclusions and their immediate environment. These additional strain variables in general are not set by a coarse-grained macroscopic displacement field. Apart from that, during our derivation, we also include the macroscopic variables of relative translations and relative rotations that were previously introduced in different contexts. As a central point, our approach reveals and classifies the importance of a macroscopic variable termed relative strains. We analyze two simplified minimal example geometries as an illustration.
Latifi, Neda; Miri, Amir K; Mongeau, Luc
2014-11-01
The aim of the present study was to quantify the effects of the specimen shape on the accuracy of mechanical properties determined from a shape-specific model generation strategy. Digital images of five rabbit vocal folds (VFs) in their initial undeformed conditions were used to build corresponding specific solid models. The displacement field of the VFs under uniaxial tensile test was then measured over the visible portion of the surface using digital image correlation. A three-dimensional finite element model was built, using ABAQUS, for each solid model, while imposing measured boundary conditions. An inverse-problem method was used, assuming a homogeneous isotropic linear elastic constitutive model. Unknown elastic properties were identified iteratively through an error minimization technique between simulated and measured force-time data. The longitudinal elastic moduli of the five rabbit VFs were calculated and compared to values from a simple analytical method and those obtained by approximating the cross-section as elliptical. The use of shape-specific models significantly reduced the standard deviation of the Young׳s moduli of the tested specimens. However, a non-parametric statistical analysis test, i.e., the Friedman test, yielded no statistically significant differences between the shape-specific method and the elliptic cylindrical finite element model. Considering the required procedures to reconstruct the shape-specific finite element model for each tissue specimen, it might be expedient to use the simpler method when large numbers of tissue specimens are to be compared regarding their Young׳s moduli. Copyright © 2014 Elsevier Ltd. All rights reserved.
Wu, Jian-Ying; Cervera, Miguel
2017-04-20
Damage-induced strain softening is of vital importance for the modeling of localized failure in frictional-cohesive materials. This paper addresses strain localization of damaging solids and the resulting consistent frictional-cohesive crack models. As a supplement to the framework recently established for stress-based continuum material models in rate form (Wu and Cervera 2015, 2016), several classical strain-based damage models, expressed usually in total and secant format, are considered. Upon strain localization of such damaging solids, Maxwell's kinematics of a strong (or regularized) discontinuity has to be reproduced by the inelastic damage strains, which are defined by a bounded characteristic tensor and an unbounded scalar related to the damage variable. This kinematic constraint yields a set of nonlinear equations from which the discontinuity orientation and damage-type localized cohesive relations can be derived. It is found that for the "Simó and Ju 1987" isotropic damage model, the localization angles and the resulting cohesive model heavily depend on lateral deformations usually ignored in classical crack models for quasi-brittle solids. To remedy this inconsistency, a modified damage model is proposed. Its strain localization analysis naturally results in a consistent frictional-cohesive crack model of damage type, which can be regularized as a classical smeared crack model. The analytical results are numerically verified by the recently-proposed mixed stabilized finite element method, regarding a singly-perforated plate under uniaxial tension. Remarkably, for all of the damage models discussed in this work, the numerically-obtained localization angles agree almost exactly with the closed-form results. This agreement, on the one hand, consolidates the strain localization analysis based on Maxwell's kinematics and, on the other hand, illustrates versatility of the mixed stabilized finite element method.
Wu, Jian-Ying; Cervera, Miguel
2017-01-01
Damage-induced strain softening is of vital importance for the modeling of localized failure in frictional-cohesive materials. This paper addresses strain localization of damaging solids and the resulting consistent frictional-cohesive crack models. As a supplement to the framework recently established for stress-based continuum material models in rate form (Wu and Cervera 2015, 2016), several classical strain-based damage models, expressed usually in total and secant format, are considered. Upon strain localization of such damaging solids, Maxwell’s kinematics of a strong (or regularized) discontinuity has to be reproduced by the inelastic damage strains, which are defined by a bounded characteristic tensor and an unbounded scalar related to the damage variable. This kinematic constraint yields a set of nonlinear equations from which the discontinuity orientation and damage-type localized cohesive relations can be derived. It is found that for the “Simó and Ju 1987” isotropic damage model, the localization angles and the resulting cohesive model heavily depend on lateral deformations usually ignored in classical crack models for quasi-brittle solids. To remedy this inconsistency, a modified damage model is proposed. Its strain localization analysis naturally results in a consistent frictional-cohesive crack model of damage type, which can be regularized as a classical smeared crack model. The analytical results are numerically verified by the recently-proposed mixed stabilized finite element method, regarding a singly-perforated plate under uniaxial tension. Remarkably, for all of the damage models discussed in this work, the numerically-obtained localization angles agree almost exactly with the closed-form results. This agreement, on the one hand, consolidates the strain localization analysis based on Maxwell’s kinematics and, on the other hand, illustrates versatility of the mixed stabilized finite element method. PMID:28772794
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
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.
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
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.
Rieger, R; Auregan, J C; Hoc, T
2017-09-08
The objective of the present study is to assess the mechanical behavior of trabecular bone based on microCT imaging and micro-finite-element analysis. In this way two methods are detailed: (i) direct determination of macroscopic elastic property of trabecular bone; (ii) inverse approach to assess mechanical properties of trabecular bone tissue. Thirty-five females and seven males (forty-two subjects) mean aged (±SD) 80±11.7 years from hospitals of Assistance publique-Hôpitaux de Paris (AP-HP) diagnosed with osteoporosis following a femoral neck fracture due to a fall from standing were included in this study. Fractured heads were collected during hip replacement surgery. Standardized bone cores were removed from the femoral head's equator by a trephine in a water bath. MicroCT images acquisition and analysis were performed with CTan(®) software and bone volume fraction was then determined. Micro-finite-element simulations were per-formed using Abaqus 6.9-2(®) software in order to determine the macroscopic mechanical behaviour of the trabecular bone. After microCT acquisition, a longitudinal compression test was performed and the experimental macroscopic Young's Modulus was extracted. An inverse approach based on the whole trabecular bone's mechanical response and micro-finite-element analysis was performed to determine microscopic mechanical properties of trabecular bone. In the present study, elasticity of the tissue was shown to be similar to that of healthy tissue but with a lower yield stress. Classical histomorphometric analysis form microCT imaging associated with an inverse micro-finite-element method allowed to assess microscopic mechanical trabecular bone parameters. Copyright © 2017 Elsevier Masson SAS. All rights reserved.
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.
Qian, Lihe; Todo, Mitsugu; Matsushita, Yasuyuki; Koyano, Kiyoshi
2009-01-01
To investigate the interactions of implant diameter, insertion depth, and loading angle on stress/strain fields in a three-dimensional finite element implant/jawbone system and to determine the influence of the loading angle on stress/strain fields while varying the implant diameter and insertion depth. Four finite element models were created, which corresponded to two implant diameters and two insertion depths. The jawbone was composed of cortical and cancellous bone and modeled as a linearly elastic medium; the implant had a detailed screw structure and was modeled as an elastic-plastic medium. Static loading was applied to the coronal surface of the implant with a maximum load of 200 N for all the models. Loading directions were varied, with buccolingually applied loading angles ranging from 0 to 85 degrees. Increases in the angle of force application caused not only increased maximum stress/strain values but worsened stress/strain distribution patterns in the bone and implant. The maximum stress in the bone always occurred at the upper edge of the cortical bone on the lingual side adjacent to the implant. The use of a larger-diameter implant or an increased insertion depth significantly reduced the maximum stress/strain values, improved the stress/strain distribution patterns and, in particular, decreased the stress/strain sensitivity to loading angle. A narrow-diameter implant, when inserted into jawbone with a shallow insertion depth and loaded with an oblique loading angle, is most unfavorable for stress distribution in both bone and implant. An optimized design of the neck region of an implant, in combination with a carefully controlled implant insertion depth that sets the threads of the implant neck well below the upper edge of the cortical bone, should be especially effective in improving the biomechanical environment for the maintenance of bone in implant/bone systems.
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.
Argani, L. P.; Bigoni, D.; Capuani, D.; Movchan, N. V.
2014-01-01
The infinite-body three-dimensional Green's function set (for incremental displacement and mean stress) is derived for the incremental deformation of a uniformly strained incompressible, nonlinear elastic body. Particular cases of the developed formulation are the Mooney–Rivlin elasticity and the J2-deformation theory of plasticity. These Green's functions are used to develop a boundary integral equation framework, by introducing an ad hoc potential, which paves the way for a boundary element formulation of three-dimensional problems of incremental elasticity. Results are used to investigate the behaviour of a material deformed near the limit of ellipticity and to reveal patterns of shear failure. In fact, within the investigated three-dimensional framework, localized deformations emanating from a perturbation are shown to be organized in conical geometries rather than in planar bands, so that failure is predicted to develop through curved and thin surfaces of intense shearing, as can for instance be observed in the cup–cone rupture of ductile metal bars. PMID:25197258
Argani, L P; Bigoni, D; Capuani, D; Movchan, N V
2014-09-08
The infinite-body three-dimensional Green's function set (for incremental displacement and mean stress) is derived for the incremental deformation of a uniformly strained incompressible, nonlinear elastic body. Particular cases of the developed formulation are the Mooney-Rivlin elasticity and the J2-deformation theory of plasticity. These Green's functions are used to develop a boundary integral equation framework, by introducing an ad hoc potential, which paves the way for a boundary element formulation of three-dimensional problems of incremental elasticity. Results are used to investigate the behaviour of a material deformed near the limit of ellipticity and to reveal patterns of shear failure. In fact, within the investigated three-dimensional framework, localized deformations emanating from a perturbation are shown to be organized in conical geometries rather than in planar bands, so that failure is predicted to develop through curved and thin surfaces of intense shearing, as can for instance be observed in the cup-cone rupture of ductile metal bars.
Comparison of experiment and theory for elastic-plastic plane strain crack growth
Hermann, L; Rice, J R
1980-02-01
Recent theoretical results on elastic-plastic plane strain crack growth, and experimental results for crack growth in a 4140 steel in terms of the theoretical concepts are reviewed. The theory is based on a recent asymptotic analysis of crack surface opening and strain distributions at a quasi-statically advancing crack tip in an ideally-plastic solid. The analysis is incomplete in that some of the parameters which appear in it are known only approximately, especially at large scale yielding. Nevertheless, it suffices to derive a relation between the imposed loading and amount of crack growth, prior to general yielding, based on the assumption that a geometrically similar near-tip crack profile is maintained during growth. The resulting predictions for the variation of J with crack growth are found to fit well to the experimental results obtained on deeply cracked compact specimens.
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.
THz elastic dynamics in finite-size CoFeB-MgO phononic superlattices
Ulrichs, Henning Meyer, Dennis; Müller, Markus; Wittrock, Steffen; Mansurova, Maria; Walowski, Jakob; Münzenberg, Markus
2016-10-14
In this article, we present the observation of coherent elastic dynamics in a nano-scale phononic superlattice, which consists of only 4 bilayers. We demonstrate how ultra-short light pulses with a length of 40 fs can be utilized to excite a coherent elastic wave at 0.535 THz, which persist over about 20 ps. In later steps of the elastic dynamics, modes with frequency of 1.7 THz and above appear. All these modes are related to acoustic band gaps. Thus, the periodicity strongly manifests in the wave physics, although the system under investigation has only a small number of spatial periods. To further illustrate this, we show how by breaking the translational invariance of the superlattice, these features can be suppressed. Discussed in terms of phonon blocking and radiation, we elucidate in how far our structures can be considered as useful building blocks for phononic devices.
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-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
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.
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.
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.
Superelastic stress-strain behavior in ferrogels with different types of magneto-elastic coupling.
Cremer, Peet; Löwen, Hartmut; Menzel, Andreas M
2016-09-29
Colloidal magnetic particles embedded in an elastic polymer matrix constitute a smart material called a ferrogel. It responds to an applied external magnetic field by changes in elastic properties, which can be exploited for various applications such as dampers, vibration absorbers, or actuators. Under appropriate conditions, the stress-strain behavior of a ferrogel can display a fascinating feature: superelasticity, the capability to reversibly deform by a huge amount while barely altering the applied load. In previous work, using numerical simulations, we investigated this behavior assuming that the magnetic moments carried by the embedded particles can freely reorient to minimize their magnetic interaction energy. Here, we extend the analysis to ferrogels where restoring torques by the surrounding matrix hinder rotations towards a magnetically favored configuration. For example, the particles can be chemically cross-linked into the polymer matrix and the magnetic moments can be fixed to the particle axes. We demonstrate that these systems still feature a superelastic regime. As before, the nonlinear stress-strain behavior can be reversibly tailored during operation by external magnetic fields. Yet, the different coupling of the magnetic moments causes different types of response to external stimuli. For instance, an external magnetic field applied parallel to the stretching axis hardly affects the superelastic regime but stiffens the system beyond it. Other smart materials featuring superelasticity, e.g. metallic shape-memory alloys, have already found widespread applications. Our soft polymer systems offer many additional advantages such as a typically higher deformability and enhanced biocompatibility combined with high tunability.
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.
Showalter, Brent L; DeLucca, John F; Peloquin, John M; Cortes, Daniel H; Yoder, Jonathon H; Jacobs, Nathan T; Wright, Alexander C; Gee, James C; Vresilovic, Edward J; Elliott, Dawn M
2016-07-01
Tissue strain is an important indicator of mechanical function, but is difficult to noninvasively measure in the intervertebral disc. The objective of this study was to generate a disc strain template, a 3D average of disc strain, of a group of human L4-L5 discs loaded in axial compression. To do so, magnetic resonance images of uncompressed discs were used to create an average disc shape. Next, the strain tensors were calculated pixel-wise by using a previously developed registration algorithm. Individual disc strain tensor components were then transformed to the template space and averaged to create the disc strain template. The strain template reduced individual variability while highlighting group trends. For example, higher axial and circumferential strains were present in the lateral and posterolateral regions of the disc, which may lead to annular tears. This quantification of group-level trends in local 3D strain is a significant step forward in the study of disc biomechanics. These trends were compared to a finite element model that had been previously validated against the disc-level mechanical response. Depending on the strain component, 81-99% of the regions within the finite element model had calculated strains within one standard deviation of the template strain results. The template creation technique provides a new measurement technique useful for a wide range of studies, including more complex loading conditions, the effect of disc pathologies and degeneration, damage mechanisms, and design and evaluation of treatments. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1264-1273, 2016. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.
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.
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.
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.
On the Relationship between Stress and Elastic Strain for Porous and Fractured Rock
Liu, Hui-Hai; Rutqvist, Jonny; Berryman, James G.
2008-02-25
Modeling the mechanical deformations of porous and fractured rocks requires a stress-strain relationship. Experience with inherently heterogeneous earth materials suggests that different varieties of Hook's law should be applied within regions of the rock having significantly different stress-strain behavior, e.g., such as solid phase and various void geometries. We apply this idea by dividing a rock body conceptually into two distinct parts. The natural strain (volume change divided by rock volume at the current stress state), rather than the engineering strain (volume change divided by the unstressed rock volume), should be used in Hooke's law for accurate modeling of the elastic deformation of that part of the pore volume subject to a relatively large degree of relative deformation (i.e., cracks or fractures). This approach permits the derivation of constitutive relations between stress and a variety of mechanical and/or hydraulic rock properties. We show that the theoretical predictions of this method are generally consistent with empirical expressions (from field data) and also laboratory rock experimental data.
A finite difference scheme for the equilibrium equations of elastic bodies
NASA Technical Reports Server (NTRS)
Phillips, T. N.; Rose, M. E.
1984-01-01
A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques.
NASA Astrophysics Data System (ADS)
Lee, Chan; Kim, Hobeom; Kim, Jungdo; Im, Seyoung
2017-06-01
Polyhedral elements with an arbitrary number of nodes or non-planar faces, obtained with an edge-based smoothed finite element method, retain good geometric adaptability and accuracy in solution. This work is intended to extend the polyhedral elements to nonlinear elastic analysis with finite deformations. In order to overcome the volumetric locking problem, a smoothing domain-based selective smoothed finite element method scheme and a three-field-mixed cell-based smoothed finite element method with nodal cells were developed. Using several numerical examples, their performance and the accuracy of their solutions were examined, and their effectiveness for practical applications was demonstrated as well.
NASA Astrophysics Data System (ADS)
Semenova, I. V.; Belashov, A. V.; Garbuzov, F. E.; Samsonov, A. M.; Semenov, A. A.
2017-06-01
We demonstrate an alternative approach to determination of the third order elastic moduli of materials based on registration of nonlinear bulk strain waves in three basic structural waveguides (rod, plate and shell) and further calculation of the Murnaghan moduli from the recorded wave parameters via simple algebra. These elastic moduli are available in literature for a limited number of materials and are measured with considerable errors, that evidences a demand in novel approaches to their determination.
Scholz, Roger; Hoffmann, Falk; von Sachsen, Sandra; Drossel, Welf-Guntram; Klöhn, Carsten; Voigt, Christian
2013-10-18
In total hip arthroplasty and particularly in revision surgery, computer assisted pre-operative prediction of the best possible anchorage strategy for implant fixation would be a great help to the surgeon. Computer simulation relies on validated numerical models. In the current study, three density-elasticity relationships (No. 1-3) from the literature for inhomogeneous material parameter assignment from CT data in automated finite element (FE) modeling of long bones were evaluated for their suitability for FE modeling of human pelvic bone. Numerical modal analysis was conducted on 10 FE models of hemipelvic bone specimens and compared to the gold standard provided by experimental modal analysis results from a previous in-vitro study on the same specimens. Overall, calculated resonance frequencies came out lower than measured values. Magnitude of mean relative deviation of numerical resonance frequencies with regard to measured values is lowest for the density-elasticity relationship No. 3 (-15.9%) and considerably higher for both density-elasticity relationships No. 1 (-41.1%) and No. 2 (-45.0%). Mean MAC values over all specimens amount to 77.8% (No. 1), 78.5% (No. 2), and 83.0% (No. 3). MAC results show, that mode shapes are only slightly influenced by material distribution. Calculated resonance frequencies are generally lower than measured values, which indicates, that numerical models lack stiffness. Even when using the best suited (No. 3) out of three investigated density-elasticity relationships, in FE modeling of pelvic bone a considerable underestimation of model stiffness has to be taken into account. © 2013 Elsevier Ltd. All rights reserved.
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
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.
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
Shyr, Tien-Wei; Shie, Jing-Wen; Jhuang, Yan-Er
2011-01-01
To use e-textiles as a strain-resistance sensor they need to be both elastic and conductive. Three kinds of elastic-conductive webbings, including flat, tubular, and belt webbings, made of Lycra fiber and carbon coated polyamide fiber, were used in this study. The strain-resistance properties of the webbings were evaluated in stretch-recovery tests and measured within 30% strain. It was found that tensile hysteresis and contact resistance significantly influence the tensile elasticity and the resistance sensitivity of the webbings. The results showed that the webbing structure definitely contributes to the tensile hysteresis and contact resistance. The smaller the friction is among the yarns in the belt webbing, the smaller the tensile hysteresis loss. However the close proximity of the conductive yarns in flat and tubular webbings results in a lower contact resistance. PMID:22319376
Shyr, Tien-Wei; Shie, Jing-Wen; Jhuang, Yan-Er
2011-01-01
To use e-textiles as a strain-resistance sensor they need to be both elastic and conductive. Three kinds of elastic-conductive webbings, including flat, tubular, and belt webbings, made of Lycra fiber and carbon coated polyamide fiber, were used in this study. The strain-resistance properties of the webbings were evaluated in stretch-recovery tests and measured within 30% strain. It was found that tensile hysteresis and contact resistance significantly influence the tensile elasticity and the resistance sensitivity of the webbings. The results showed that the webbing structure definitely contributes to the tensile hysteresis and contact resistance. The smaller the friction is among the yarns in the belt webbing, the smaller the tensile hysteresis loss. However the close proximity of the conductive yarns in flat and tubular webbings results in a lower contact resistance.
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
Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals
NASA Astrophysics Data System (ADS)
Irani, Nilgoon; Remmers, Joris J. C.; Deshpande, Vikram S.
2017-08-01
Plastic size effects in single crystals are investigated by using finite strain and small strain discrete dislocation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip systems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete dislocation plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. However, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bending stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations.
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.
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.
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.
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 role of chemical free energy and elastic strain in the nucleation of zirconium hydride
NASA Astrophysics Data System (ADS)
Barrow, A. T. W.; Toffolon-Masclet, C.; Almer, J.; Daymond, M. R.
2013-10-01
In this work a combination of synchrotron X-ray diffraction and thermodynamic modelling has been used to study the dissolution and precipitation of zirconium hydride in α-Zr establishing the role of elastic misfit strain and chemical free energy in the α → α + δ phase transformation. The nucleation of zirconium hydride is dominated by the chemical free energy where the chemical driving force for hydride precipitation is proportional to the terminal-solid solubility for precipitation and can be predicted by a function that is analogous to the universal nucleation parameter for the bainite transformation in ferrous alloys. The terminal-solid solubility for precipitation was found to be kinetically limited ⩾287 °C at a cooling rate of 5 °C min-1 or greater. The terminal solubilities were established using an offset method applied to the lattice strain data where a resolution of ∼10 wppm H can be achieved in the
Looking-Free Mixed hp Finite Element Methods for Linear and Geometrically Nonlinear Elasticity
1997-06-09
hp mixed methods has been addressed by Stenberg and Suri[20]. They identify sufficient conditions for selecting mixed method spaces on parallelogram...spaces of piecewise polynomials. Math. Modeling Num. Anal., 19:111-143, 1985. [20] R. Stenberg and M. Suri. Mixed hp finite element methods for
Band-gap modulation of graphane-like SiC nanoribbons under uniaxial elastic strain
NASA Astrophysics Data System (ADS)
Gao, Ben-Ling; Xu, Qing-Qiang; Ke, San-Huang; Xu, Ning; Hu, Guang; Wang, Yanzong; Liang, Feng; Tang, Yalu; Xiong, Shi-Jie
2014-01-01
The band-gap modulation of zigzag and armchair graphane-like SiC nanoribbons (GSiCNs) under uniaxial elastic strain is investigated using the density functional theory. The results show that band gap of both structures all decreases when being compressed or tensed. In compression, both zigzag and armchair GSiCNs are semiconductors with a direct band gap. However, in tension, the armchair GSiCNs undergo a direct-to-indirect band-gap transition but the zigzag GSiCNs still have a direct band gap. These results are also proved by HSE06 method. This implies a potential application of the graphane-like SiC nanoribbons in the future pressure sensor and optical electronics nanodevices.
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.
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.
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
Trindade, Flávia Zardo; Valandro, Luiz Felipe; de Jager, Niek; Bottino, Marco Antônio; Kleverlaan, Cornelis Johannes
2016-10-03
To determine the elastic properties of five ceramic systems with different compositions (lithium disilicate vs. feldspathic ceramics) and processing methods and compare the stress distribution in premolars in the interface with inlays made with these systems loaded with the maximum normal bite force (665 N) using 3D finite element analysis (FEA). The elastic properties of five ceramic restoration materials (IPS e.max Press, IPS e.max CAD, Vita PM9, Vita Mark II, Vita VM7) were obtained using the ultrasonic pulse-echo method. Three-dimensional FEA simplified models of maxillary premolars restored with these ceramic materials were created. The models were loaded with a load at the two nodes on the occlusal surface in the middle of the tooth, 2 mm from the outside of the tooth, simulating a loading ball with a radius of 6 mm. The means values of density (g/cm³), Young's modulus (GPa), and Poison's ratio was 2.6 ± 0.3, 82.3 ± 18.3, and 0.22 ± 0.01 for IPS e.max Press; 2.3 ± 0.1, 83.5 ± 15.0, and 0.21 ± 0.01 for IPS e.max CAD; 2.5 ± 0.1, 44.4 ± 11.5, and 0.26 ± 0.08 for PM9; 2.4 ± 0.1, 70.6 ± 4.9, and 0.22 ± 0.01 for Vitamark II; 2.4 ± 0.1, 63.3 ± 3.9, and 0.23 ± 0.01 for VM7, respectively. The 3D FEA showed the tensile stress at the interface between the tooth and the inlay was dependent on the elastic properties of the materials, since the Vita PM9 and IPS e.max CAD ceramics presented the lowest and the highest stress concentration in the interface, respectively. The elastic properties of ceramic materials were influenced by composition and processing methods, and these differences influenced the stress concentration at the bonding interface between tooth and restoration. The lower the elastic modulus of inlays, the lower is the stress concentration at the bonding interfaces. © 2016 by the American College of Prosthodontists.
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.
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
NASA Astrophysics Data System (ADS)
Hung, S. H.; Liao, T. Y.; Sales de Andrade, E.; Liu, Q.
2014-12-01
The existence of seismic anisotropy in D" has been diagnosed by the evident arrival-time shifts between SVdiff and SHdiff phases and discrepancies in SKS and SKKS splitting. Previous numerical modeling of seismic wave propagation demonstrates that the SVdiff and SHdiff arrivals are not synchronized in time even in an isotropic Earth model due to intrinsically different finite-frequency sensitivity of non-geometrical diffracted S waves between radial and transverse components. Therefore, prior to using diffracted shear wave phases to constrain seismic anisotropy in the lowermost mantle, we need to first clarify the finite-frequency effects of diffracted shear waves propagating through D" velocity heterogeneity. In this study, we collect broadband waveforms from intermediate and deep-focus earthquakes (> 150 km) with epicentral distances of 90-145o and magnitudes greater than 5.8 during 1997-2012. The splitting between the vertically (SV) and transversely (SH) polarized arrivals of S(diff) phases after correcting for upper mantle anisotropy are analyzed to investigate seismic anisotropy in D" induced by anisotropic material elasticity and finite-frequency wave propagation effects. Both positive and negative SVdiff-SHdiff split times are observed in seismically slow regions; however, the proposed viable scenario in which partial melts produced at the base of the hot mantle plumes have been aligned laterally in D" by the basal boundary flow can only explain relatively earlier SHdiff arrivals. Positive SV-SH times (i.e., SH traveling faster) found in high-velocity regions are consistent with the consequences caused by intrinsic LPO of pPv-MgSiO3 in horizontally-lying slabs and different finite-frequency sensitivity between SVdiff and SHdiff in the heterogeneous lowermost mantle. We will differentiate and quantify these two effects on the observed Sdiff splitting through simulating ground-truth finite-frequency shear wave diffraction in the 3-D tomography Earth model and
Finite Strain Analysis of Shock Compression of Brittle Solids Applied to Titanium Diboride
2014-07-01
evolution of microstructure , e.g., accumulated cracks, voids, or dislocations in the material. Here, x is assumed a scalar, but generalization to higher...physics Plasticity Damage Finite strainE-mail address: john.d.clayton1.civ@mail.mil. http://dx.doi.org/10.1016/j.ijimpeng.2014.06.003 0734-743X/Published by...compression). In crystalline materials, these mechanisms can include intergranular fracture, transgranular fracture, pore collapse, dislocation glide
A new high-order finite volume method for 3D elastic wave simulation on unstructured meshes
NASA Astrophysics Data System (ADS)
Zhang, Wensheng; Zhuang, Yuan; Zhang, Lina
2017-07-01
In this paper, we proposed a new efficient high-order finite volume method for 3D elastic wave simulation on unstructured tetrahedral meshes. With the relative coarse tetrahedral meshes, we make subdivision in each tetrahedron to generate a stencil for the high-order polynomial reconstruction. The subdivision algorithm guarantees the number of subelements is greater than the degrees of freedom of a complete polynomial. We perform the reconstruction on this stencil by using cell-averaged quantities based on the hierarchical orthonormal basis functions. Unlike the traditional high-order finite volume method, our new method has a very local property like DG and can be written as an inner-split computational scheme which is beneficial to reducing computational amount. Moreover, the stencil in our method is easy to generate for all tetrahedrons especially in the three-dimensional case. The resulting reconstruction matrix is invertible and remains unchanged for all tetrahedrons and thus it can be pre-computed and stored before time evolution. These special advantages facilitate the parallelization and high-order computations. We show convergence results obtained with the proposed method up to fifth order accuracy in space. The high-order accuracy in time is obtained by the Runge-Kutta method. Comparisons between numerical and analytic solutions show the proposed method can provide accurate wavefield information. Numerical simulation for a realistic model with complex topography demonstrates the effectiveness and potential applications of our method. Though the method is proposed based on the 3D elastic wave equation, it can be extended to other linear hyperbolic system.
Two-particle elastic scattering in a finite volume including QED
NASA Astrophysics Data System (ADS)
Beane, Silas R.; Savage, Martin J.
2014-10-01
The presence of long-range interactions violates a condition necessary to relate the energy of two particles in a finite volume to their S-matrix elements in the manner of Lüscher. While in infinite volume, QED contributions to low-energy charged-particle scattering must be resummed to all orders in perturbation theory (the Coulomb ladder diagrams), in a finite volume the momentum operator is gapped, allowing for a perturbative treatment. The leading QED corrections to the two-particle finite-volume energy quantization condition below the inelastic threshold, as well as approximate formulas for energy eigenvalues, are obtained. In particular, we focus on two spinless hadrons in the A1+ irreducible representation of the cubic group, and truncate the strong interactions to the s-wave. These results are necessary for the analysis of lattice QCD +QED calculations of charged-hadron interactions, and can be straightforwardly generalized to other representations of the cubic group, to hadrons with spin, and to include higher partial waves.
Giordano, Chiara; Kleiven, Svein
2014-11-01
Finite element (FE) models are often used to study the biomechanical effects of traumatic brain injury (TBI). Measures based on mechanical responses, such as principal strain or invariants of the strain tensor, are used as a metric to predict the risk of injury. However, the reliability of inferences drawn from these models depends on the correspondence between the mechanical measures and injury data, as well as the establishment of accurate thresholds of tissue injury. In the current study, a validated anisotropic FE model of the human head is used to evaluate the hypothesis that strain in the direction of fibers (axonal strain) is a better predictor of TBI than maximum principal strain (MPS), anisotropic equivalent strain (AESM) and cumulative strain damage measure (CSDM). An analysis of head kinematics-based metrics, such as head injury criterion (HIC) and brain injury criterion (BrIC), is also provided. Logistic regression analysis is employed to compare binary injury data (concussion/no concussion) with continuous strain/kinematics data. The threshold corresponding to 50% of injury probability is determined for each parameter. The predictive power (area under the ROC curve, AUC) is calculated from receiver operating characteristic (ROC) curve analysis. The measure with the highest AUC is considered to be the best predictor of mTBI. Logistic regression shows a statistical correlation between all the mechanical predictors and injury data for different regions of the brain. Peaks of axonal strain have the highest AUC and determine a strain threshold of 0.07 for corpus callosum and 0.15 for the brainstem, in agreement with previously experimentally derived injury thresholds for reversible axonal injury. For a data set of mild TBI from the national football league, the strain in the axonal direction is found to be a better injury predictor than MPS, AESM, CSDM, BrIC and HIC.
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.
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 .
Strain tensor selection and the elastic theory of incompatible thin sheets
NASA Astrophysics Data System (ADS)
Oshri, Oz; Diamant, Haim
2017-05-01
The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids 57, 762 (2009), 10.1016/j.jmps.2008.12.004]. For a class of simple axisymmetric problems we examine an alternative formulation, defining the strain based on deviations of distances (rather than distances squared) from their rest values. While the two formulations converge in the limit of small slopes and in the limit of an incompressible sheet, for other cases they are found not to be equivalent. The alternative formulation offers several features which are absent in the existing theory. (a) In the case of planar deformations of flat incompatible sheets, it yields linear, exactly solvable, equations of equilibrium. (b) When reduced to uniaxial (one-dimensional) deformations, it coincides with the theory of extensible elastica; in particular, for a uniaxially bent sheet it yields an unstrained cylindrical configuration. (c) It gives a simple criterion determining whether an isometric immersion of an incompatible sheet is at mechanical equilibrium with respect to normal forces. For a reference metric of constant positive Gaussian curvature, a spherical cap is found to satisfy this criterion except in an arbitrarily narrow boundary layer.
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
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
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.
Cong, Alexander; Buijs, Jorn Op Den; Dragomir-Daescu, Dan
2010-01-01
Quantitative computed tomography based finite element analysis of the femur is currently being investigated as a method for non-invasive stiffness and strength predictions of the proximal femur. The specific objective of this study was to determine better conversion relationships from QCT-derived bone density to elastic modulus, in order to achieve accurate predictions of the overall femoral stiffness in a fall-on-the-hip loading configuration. Twenty-two femurs were scanned, segmented and meshed for finite element analysis. The elastic moduli of the elements were assigned according to the average density in the element. The femurs were then tested to fracture and force-displacement data was collected to calculate femoral stiffness. Using a training set of nine femurs, finite element analyses were performed and the parameters of the density-elastic modulus relationship were iteratively adjusted to obtain optimal stiffness predictions in a least-squares sense. The results were then validated on the remaining 13 femurs. Our novel procedure resulted in parameter identification of both power and sigmoid functions for density-elastic modulus conversion for this specific loading scenario. Our in situ estimated power law achieved improved predictions compared to published power laws, and the sigmoid function yielded even smaller prediction errors. In the future, these results will be used to further improve the femoral strength predictions of our finite element models. PMID:21030287
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.
Multi-scale finite element modeling of strain localization in geomaterials with strong discontinuity
NASA Astrophysics Data System (ADS)
Lai, Timothy Yu
2002-01-01
Geomaterials such as soils and rocks undergo strain localization during various loading conditions. Strain localization manifests itself in the form of a shear band, a narrow zone of intense straining. It is now generally recognized that these localized deformations lead to an accelerated softening response and influence the response of structures at or near failure. In order to accurately predict the behavior of geotechnical structures, the effects of strain localization must be included in any model developed. In this thesis, a multi-scale Finite Element (FE) model has been developed that captures the macro- and micro-field deformation patterns present during strain localization. The FE model uses a strong discontinuity approach where a jump in the displacement field is assumed. The onset of strain localization is detected using bifurcation theory that checks when the governing equations lose ellipticity. Two types of bifurcation, continuous and discontinuous are considered. Precise conditions for plane strain loading conditions are reported for each type of bifurcation. Post-localization behavior is governed by the traction relations on the band. Different plasticity models such as Mohr-Coulomb, Drucker-Prager and a Modified Mohr-Coulomb yield were implemented together with cohesion softening and cutoff for the post-localization behavior. The FE model is implemented into a FORTRAN code SPIN2D-LOC using enhanced constant strain triangular (CST) elements. The model is formulated using standard Galerkin finite element method, applicable to problems under undrained conditions and small deformation theory. A band-tracing algorithm is implemented to track the propagation of the shear band. To validate the model, several simulations are performed from simple compression test of soft rock to simulation of a full-scale geosynthetic reinforced soil wall model undergoing strain localization. Results from both standard and enhanced FE method are included for comparison. The
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.
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
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. Copyright © 2013 Elsevier Ltd. All rights reserved.
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.
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.
NASA Astrophysics Data System (ADS)
Bilham, R.; Feldl, N.
2005-12-01
In view of the absence of historical precedent for the 1600 km long Sumatra/Andaman rupture of the eastern edge of the Indian plate in 2004, we question whether similar earthquakes without historical precedent could also occur in the Himalaya. A seismic slip deficit corresponding to a single Mw=8.7 earthquake currently exists, and although no great earthquake has ruptured the Himalayan frontal thrusts in the past 300 years, evidence that larger earthquakes have done so between 900 and 1505 is now available in the form of trench investigations of slip in the range 5-21 m, over rupture lengths of 200-300 km. The magnitude of these and possibly larger earthquakes is unknown. We investigate possibly magnitudes for Himalayan earthquakes by developing a synthetic scaling law relating renewal time to rupture length. We first emulate the accumulation of present-day elastic strain near the southern edge of the Tibet plateau using 3D boundary element methods, and then, after incrementing this strain by a time interval of many hundreds of years, we investigate the amount of slip that corresponds to different rupture lengths. Our interseismic model uses the inferred subsurface geometry of the Indian plate (20-40 km depth) and the observed GPS velocity field to 1000 km north of the Himalaya as constraints, with minor adjustments to the shallow geometry beneath the Greater Himalaya as our only variable. Assuming that frictionless aseismic slip occurs beneath the plateau, we find that its rate decays to zero 25 km south of what we have previously considered the locking line, with dip increasing to 15 deg. at 12-18 km depth, consistent with focal mechanisms in this region. An unexpected result is that vertical deformation is twice the width (70 km) & half the amplitude (3 mm/yr) of that assoicated with uniform-slip elastic models, though still consistent with the lower error envelope of leveling data. To account for the 14-21 mm/yr long term advance of the Himalaya over India we
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
Analysis of shear strain imaging for classifying breast masses: finite element and phantom results.
Xu, Haiyan; Varghese, Tomy; Madsen, Ernest L
2011-11-01
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). 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. 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. Finite element and tissue-mimicking phantom results demonstrate the feasibility of utilizing both the normalized axial-shear and full-shear strain area features to
Elastic Fluctuations and Rubber Elasticity
NASA Astrophysics Data System (ADS)
Xing, Xiangjun; Goldbart, Paul; Rradzihovsky, Leo
2006-03-01
A coarse-grained phenomenological model is constructed to describe both phonon fluctuations and elastic heterogeneities in rubbery materials. It is a nonlocal, spatially heterogeneous generalization of the classical model of rubber elasticity, and with a tunable repulsion interaction. This model can also be derived from the Vulcanization theory. The residual stress and the non-affine deformation field, as well as their correlations, are calculated perturbatively, to the leading order of quenched randomness. It is explicitly shown that the interplay between the repulsive interaction and quenched randomness induces non- affine deformation. The spatial correlations of the non- affine deformation field and residual stress exhibit power-law scaling, with no characteristic length scale. We also calculate the contributions to the elastic free energy from both thermal and quenched fluctuations for arbitrary deformation. We find that they naturally explain the universal features in the Mooney-Rivlin plot of the stress-strain curve for rubbery materials. The (disorder averaged) thermal fluctuation of monomers is shown to depend on deformation, and becomes anisotropic upon shear deformation, as long as the repulsive interaction is finite.
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 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)
Pettit, J. R.; Walker, A.; Lowe, M. J. S.
2015-01-01
A common goal when using Finite Element (FE) modelling in time domain wave scattering problems is to minimise model size by only considering a region immediately surrounding a scatterer or feature of interest. The model boundaries must simulate infinite space by minimising the reflection of incident waves. This is a significant and long-standing challenge that has only achieved partial success. Industrial companies wishing to perform such modelling are keen to use established commercial FE packages that offer a thorough history of validation and testing. Unfortunately, this limits the flexibility available to modellers preventing the use of popular research tools such as Perfectly Matched Layers (PML). Unlike PML, Absorbing Layers by Increasing Damping (ALID) have proven successful offering practical implementation into any solver that has representation of material damping. Despite good performance further improvements are desirable. Here, a Stiffness Reduction Method (SRM) has been developed and optimised to operate within a significantly reduced spatial domain. The technique is applied by altering damping and stiffness matrices, inducing decay of incident waves. Variables are expressed as a function of known model constants, easing implementation for generic problems. Analytical and numerical solutions have shown that SRM out performs ALID, with results approaching those of PML.
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)
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)
Liu, Liwu; Liu, Yanju; Zhang, Zhen; Yu, Kai; Deng, Gang; Sun, Shouhua; Shi, Liang; Leng, Jinsong
2009-03-01
Dielectric elastomers (DE) are the most promising electroactive polymer materials capable of being applied in smart actuators. When the DE film sandwiched between two compliant electrodes is applied high electric field, due to the electrostatic force between two electrodes, the film expands in-plane and contracts out-of-plane such that its thickness becomes thinner. The thinner thickness results in higher electric field which inversely squeezes the film again. This positive feedback induces a mode of instability, known as electromechanical instability or pull-in instability. When the electric field exceeds certain critical value, the DE film collapses. In this paper, the elastic strain energy function with two material constants is applied to analyze the stability of dielectric elastomers, which facilitates to understand fully Suo's nonlinear theory. The results verify again the truth of this theory and exploit larger application spectrum. The method is capable of analyzing the stability of different dielectric materials with different values of k and the result can be useful on design of the dielectric elastomer actuator.
Method for measuring compliances and crack length by strain gauge and 3D finite element calculation
Riedle, J.; Wulf, J.; Schmauder, S.
1995-05-01
A method for determining compliances and crack lengths of round CT specimen geometries (RCT) by measuring the notch opening displacement (NOD) with strain gauges, combined with 3D finite element calculations to correlate the NOD to the loading point displacements, is presented. The method has been verified for tungsten and it is shown that measured and calculated compliances are in excellent agreement. A general equation is presented correlating compliances and NOD which allows to implicitly determine crack lengths by simply measuring the NOD of RCT specimens. 5 refs.
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.
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)
Borisov, Dmitry; Singh, Satish C.; Fuji, Nobuaki
2015-09-01
Seismic full waveform inversion is an objective method to estimate elastic properties of the subsurface and is an important area of research, particularly in seismic exploration community. It is a data-fitting approach, where the difference between observed and synthetic data is minimized iteratively. Due to a very high computational cost, the practical implementation of waveform inversion has so far been restricted to a 2-D geometry with different levels of physics incorporated in it (e.g. elasticity/viscoelasticity) or to a 3-D geometry but using an acoustic approximation. However, the earth is three-dimensional, elastic and heterogeneous and therefore a full 3-D elastic inversion is required in order to obtain more accurate and valuable models of the subsurface. Despite the recent increase in computing power, the application of 3-D elastic full waveform inversion to real-scale problems remains quite challenging on the current computer architecture. Here, we present an efficient method to perform 3-D elastic full waveform inversion for time-lapse seismic data using a finite-difference injection method. In this method, the wavefield is computed in the whole model and is stored on a surface above a finite volume where the model is perturbed and localized inversion is performed. Comparison of the final results using the 3-D finite-difference injection method and conventional 3-D inversion performed within the whole volume shows that our new method provides significant reductions in computational time and memory requirements without any notable loss in accuracy. Our approach shows a big potential for efficient reservoir monitoring in real time-lapse experiments.
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.
Shock-Wave and Finite-Strain Equations of State at Large Expansion
NASA Astrophysics Data System (ADS)
Jeanloz, Raymond
The empirically observed linear relationship between shock-wave velocity and particle velocity is compatible with the Eulerian finite-strain equation of state under tension as well as compression, identifying an ideal value of dynamic strength -PH = K0S/(K0S' + 1) and dynamic cohesive energy EH - E0 = 8V0K0S/(K0S' + 1)2 (V, K and K' are volume, bulk modulus and its pressure derivative; subscripts 0, S and H refer to zero-pressure, isentrope and Hugoniot states). The corresponding finitestrain estimate of the isentropic cohesive energy is ES - E0 = 9V0K0S(2 + 2n - K0S')/(2n3), with strain parameter n = 2 for the Eulerian (spatial) frame of reference.
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.
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
Pettit, J. R.; Lowe, M. J. S.; Walker, A. E.
2015-03-31
Pulse-echo ultrasonic NDE examination of large pressure vessel forgings is a design and construction code requirement in the power generation industry. Such inspections aim to size and characterise potential defects that may have formed during the forging process. Typically these defects have a range of orientations and surface roughnesses which can greatly affect ultrasonic wave scattering behaviour. Ultrasonic modelling techniques can provide insight into defect response and therefore aid in characterisation. However, analytical approaches to solving these scattering problems can become inaccurate, especially when applied to increasingly complex defect geometries. To overcome these limitations a elastic Finite Element (FE) method has been developed to simulate pulse-echo inspections of embedded planar defects. The FE model comprises a significantly reduced spatial domain allowing for a Monte-Carlo based approach to consider multiple realisations of defect orientation and surface roughness. The results confirm that defects aligned perpendicular to the path of beam propagation attenuate ultrasonic signals according to the level of surface roughness. However, for defects orientated away from this plane, surface roughness can increase the magnitude of the scattered component propagating back along the path of the incident beam. This study therefore highlights instances where defect roughness increases the magnitude of ultrasonic scattered signals, as opposed to attenuation which is more often assumed.
Perruisseau-Carrier, A; Bahlouli, N; Bierry, G; Vernet, P; Facca, S; Liverneaux, P
2017-04-03
Augmented reality could help the identification of nerve structures in brachial plexus surgery. The goal of this study was to determine which law of mechanical behavior was more adapted by comparing the results of Hooke's isotropic linear elastic law to those of Ogden's isotropic hyperelastic law, applied to a biomechanical model of the brachial plexus. A model of finite elements was created using the ABAQUS(®) from a 3D model of the brachial plexus acquired by segmentation and meshing of MRI images at 0°, 45° and 135° of shoulder abduction of a healthy subject. The offset between the reconstructed model and the deformed model was evaluated quantitatively by the Hausdorff distance and qualitatively by the identification of 3 anatomical landmarks. In every case the Hausdorff distance was shorter with Ogden's law compared to Hooke's law. On a qualitative aspect, the model deformed by Ogden's law followed the concavity of the reconstructed model whereas the model deformed by Hooke's law remained convex. In conclusion, the results of this study demonstrate that the behavior of Ogden's isotropic hyperelastic mechanical model was more adapted to the modeling of the deformations of the brachial plexus. Copyright © 2017 Elsevier Masson SAS. All rights reserved.
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
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
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.
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.
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.
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.
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.
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 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; 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.
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
Johnson, P.A. |; Rasolofosaon, P.N.J.
1995-11-01
Nonlinear elastic response in rock is established as a robust and representative characteristic of rock rather than a curiosity. This behavior is illustrated from a variety of experiments conducted over many orders of magnitude in strain and frequency. The evidence leads to a pattern of unifying behavior in rock: (1) Nonlinear response in rock is enormous; (2) the response takes place over a large frequency interval (dc--10{sup 6} Hz at least); (3) the response not only occurs, as is commonly appreciated, at large strains but also at small strains where nonlinear response and the manifestations of this behavior are commonly disregarded. Nonlinear response may manifest itself in a variety of manners, including a nonlinear stress{minus}strain relation (hysteretic/discrete memory), nonlinear dissipation, harmonic generation, and resonant peak shift, all of which are related. The experiments described include: quasistatic stress{minus}strain tests (strains of 10{sup -4}--10{sup -1} at frequencies near dc-1Hz); torsional oscillator experiments (strains of 10{sup {minus}4}--10{sup {minus}7}, frequencies between 0.1 and 100Hz); resonant bar experiments (strains of 10{sup {minus}4}--10{sup {minus}8}, frequencies between 10{sup 3} and 10{sup 4} Hz); and dynamic, propagating wave experiments (strains of 10{sup {minus}6}--10{sup {minus}9}, frequencies between 10{sup 3} and 10{sup 6} Hz). [Work supported by OBES/DOE through the University of California and the Institut Francais du Petrole.
Ponce-García, Néstor; Ramírez-Wong, Benjamín; Torres-Chávez, Patricia I; Figueroa-Cárdenas, Juan de Dios; Serna-Saldívar, Sergio O; Cortez-Rocha, Mario O; Escalante-Aburto, Anayansi
2017-03-01
The aim of this research was to evaluate the visco-elastic properties of conditioned wheat kernels and their doughs by applying the compression test under a small strain. Conditioned wheat kernels and their doughs, from soft and hard wheat classes were evaluated for total work (Wt ), elastic work (We ) and plastic work (Wp ). Soft wheat kernels showed lower We than Wp , while the hard wheat kernels had a We that was higher than Wp . Regarding dough visco-elasticity, cultivars from soft and hard wheat showed higher Wp than We . The degree of elasticity (DE%) of the conditioned wheat kernel related to its dough decreased ∼46% in both wheat classes. The Wt , We and Wp from the soft wheat kernel and dough correlated with physico-chemical and farinographic flour tests. The Wt , Wp and the maximum compression force (Fmax ) of the dough from hard wheat class presented highly significant negative correlations with wet gluten. The visco-elasticity parameters from compression test presented significant differences among conditioned wheat classes and their doughs. © 2016 Society of Chemical Industry. © 2016 Society of Chemical Industry.
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.
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.
NASA Astrophysics Data System (ADS)
Vattré, A.
2017-08-01
The long- and short-range interactions as well as planar reactions between two infinitely periodic sets of crossing dislocations are investigated using anisotropic elasticity theory in face- (fcc) and body- (bcc) centered cubic materials. Two preliminary cases are proposed to examine the substantial changes in the elastic stress states and the corresponding strain energies due to a slight rearrangement in the internal dislocation geometries and characters. In general, significant differences and discrepancies resulting from the considered cubic crystal structure and the approximation of isotropic elasticity are exhibited. In a third scenario, special attention is paid to connecting specific internal dislocation structures from the previous cases with non-equilibrium configurations predicted by the quantized Frank-Bilby equation for the (111) fcc and (110) bcc twist grain boundaries. The present solutions lead to the formation of energetically favorable dislocation junctions with non-randomly strain-relaxed configurations of lower energy. In particular, the local dislocation interactions and reactions form equilibrium hexagonal-shaped patterns with planar three-fold dislocation nodes without producing spurious far-field stresses.Numerical application results are presented from a selection of cubic metals including aluminum, copper, tantalum, and niobium. In contrast to the fcc materials, asymmetric dislocation nodes occur in the anisotropic bcc cases, within which the minimum-energy paths for predicting the fully strain-relaxed dislocation patterns depend on the Zener anisotropic factor with respect to unity. The associated changes in the dislocation structures as well as the removal of the elastic strain energy upon relaxations are quantified and also discussed.
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.
2015-07-01
approximate 3D solution for the stress distribution around a circular cylindrical hole in an infinite plate of arbitrary thickness. They did this by...UNCLASSIFIED UNCLASSIFIED Linear-Elastic 2D and 3D Finite Element Contact Analysis of a Hole Containing a Circular Insert in a Fatigue Test...large numbers of circular holes that are fitted with fasteners such as bolts or rivets. During the service life of aircraft, fatigue damage often occurs
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Lopez-Pamies, Oscar; Goudarzi, Taha; Danas, Kostas
2013-01-01
In Part I, an exact solution was determined for the problem of the overall nonlinear elastic response of Gaussian (or Neo-Hookean) rubber reinforced by a dilute isotropic distribution of rigid particles. Here, this fundamental result is utilized to construct an approximate solution for non-Gaussian rubber reinforced by an isotropic distribution of rigid particles at finite concentration. This is accomplished by means of two different techniques in two successive steps. First, the dilute solution is utilized together with a differential scheme in finite elasticity to generate a solution for Neo-Hookean rubber filled with an isotropic distribution of rigid particles of polydisperse sizes and finite concentration. This non-dilute result is then employed within the context of a new comparison medium method — derived as an extension of Talbot-Willis (1985) variational framework to the non-convex realm of finite elasticity — to generate in turn a corresponding solution for filled non-Gaussian rubber wherein the underlying elastomeric matrix is characterized by any I1-based stored-energy function Ψ(I1) of choice. The solution is fully explicit and remarkably simple. Its key theoretical and practical merits are discussed in detail. Additionally, the constructed analytical solution is confronted to 3D finite-element simulations of the large-deformation response of Neo-Hookean and non-Gaussian rubber reinforced by isotropic distributions of rigid spherical particles with the same size, as well as with different sizes. Good agreement is found among all three sets of results. The implications of this agreement are discussed.
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.
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.
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.
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.
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.
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.
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.
Nguyen, Ba N.; Kunc, Vlastimil; Phelps, Jay H; TuckerIII, Charles L.; Bapanapalli, Satish K
2009-01-01
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 an anisotropic rotary diffusion model recently developed for LFTs. An incremental procedure using Eshelby's equivalent inclusion method and the Mori-Tanaka assumption 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 latter is then obtained from the solution for the aligned-fiber composite by averaging over all fiber orientations. Failure during incremental loading is predicted using the Van Hattum-Bernado model. The model is validated against the experimental stress-strain results obtained for long-glass-fiber/polypropylene specimens.
NASA Astrophysics Data System (ADS)
Treutenaere, S.; Lauro, F.; Bennani, B.; Matsumoto, T.; Mottola, E.
2015-09-01
The use of fabric reinforced polymers in the automotive industry is growing significantly. The high specific stiffness and strength, the ease of shaping as well as the great impact performance of these materials widely encourage their diffusion. The present model increases the predictability of explicit finite element analysis and push the boundaries of the ongoing phenomenological model. Carbon fibre composites made up various preforms were tested by applying different mechanical load up to dynamic loading. This experimental campaign highlighted the physical mechanisms affecting the initial mechanical properties, namely intra- and interlaminar matrix damage, viscoelasticty and fibre failure. The intralaminar behaviour model is based on the explicit formulation of the matrix damage model developed by the ONERA as the given damage formulation correlates with the experimental observation. Coupling with a Maxwell-Wiechert model, the viscoelasticity is included without losing the direct explicit formulation. Additionally, the model is formulated under a total Lagrangian scheme in order to maintain consistency for finite strain. Thus, the material frame-indifference as well as anisotropy are ensured. This allows reorientation of fibres to be taken into account particularly for in-plane shear loading. Moreover, fall within the framework of the total Lagrangian scheme greatly makes the parameter identification easier, as based on the initial configuration. This intralaminar model thus relies upon a physical description of the behaviour of fabric composites and the numerical simulations show a good correlation with the experimental results.
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 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.
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)
Graba, M.
2017-02-01
This paper provides a numerical analysis of selected parameters of fracture mechanics for double-edge notched specimens in tension, DEN(T), under plane strain conditions. The analysis was performed using the elastic-plastic material model. The study involved determining the stress distribution near the crack tip for both small and large deformations. The limit load solution was verified. The J-integral, the crack tip opening displacement, and the load line displacement were determined using the numerical method to propose the new hybrid solutions for calculating these parameters. The investigations also aimed to identify the influence of the plate geometry and the material characteristics on the parameters under consideration. This paper is a continuation of the author's previous studies and simulations in the field of elastic-plastic fracture mechanics.
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.
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
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 Astrophysics Data System (ADS)
Rosi, Giuseppe; Scala, Ilaria; Nguyen, Vu-Hieu; Naili, Salah
2017-06-01
This article is about ultrasonic wave propagation in microstructured porous media. The classic Biot's model is enriched using a strain gradient approach to be able to capture high-order effects when the wavelength approaches the characteristic size of the microstructure. In order to reproduce actual transmission/reflection experiments performed on poroelastic samples, and to validate the choice of the model, the computation of the time domain response is necessary, as it allows for a direct comparison with experimental results. For obtaining the time response, we use two strategies: on the one hand we compute the closed form solution by using the Laplace and Fourier transforms techniques; on the other hand we used a finite element method. The results are presented for a transmission/reflection test performed on a poroelastic sample immersed in water. The effects introduced by the strain gradient terms are visible in the time response and in agreement with experimental observations. The results can be exploited in characterization of mechanical properties of poroelastic media by enhancing the reliability of quantitative ultrasound techniques.
Filardi, Vincenzo; Simona, Portaro; Cacciola, Giorgio; Bertino, Salvatore; Soliera, Luigi; Barbanera, Andrea; Pisani, Alessandro; Milardi, Demetrio; Alessia, Bramanti
2017-06-01
In humans, vertical posture acquisition caused several changes in bones and muscles which can be assumed as verticalization. Pelvis, femur, and vertebral column gain an extension position which decreases muscular work by paravertebral muscles in the latter. It's widely known that six different morphological categories exist; each category differs from the others by pelvic parameters and vertebral column curvatures. Both values depend on the Pelvic Incidence, calculated as the angle between the axes passing through the rotation centre of the two femur heads and the vertical axis passing through the superior plate of the sacrum. The aim of this study is to evaluate the distribution of stress and the resulting strain along the axial skeleton using finite element analysis. The use of this computational method allows performing different analyses investigating how different bony geometries and skeletal structures can behavior under specific loading conditions. A computerized tomography (CT) of artificial bones, carried on at 1.5 mm of distance along sagittal, coronal and axial planes with the knee at 0° flexion (accuracy 0.5 mm), was used to obtain geometrical data of the model developed. Lines were imported into a commercial code (Hypermesh by Altair(®)) in order to interpolate main surfaces and create the solid version of the model. In particular six different models were created according Roussoly's classification, by arranging geometrical position of the skeletal components. Loading conditions were obtained by applying muscular forces components to T1 till to L5, according to a reference model (Daniel M. 2011), and a fixed constrain was imposed on the lower part of the femurs. Materials were assumed as elastic with an Elastic modulus of 15 GPa, a Shear Modulus of 7 GPa for bony parts, and an Elastic modulus of 6 MPa, a Shear Modulus of 3 MPa for cartilaginous parts. Six different simulations have been carried out in order to evaluate the mechanical behavior
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.
Barabash, O.M.; Santella, M.; Barabash, R.I.; Ice, G.E.; Tischler, J.
2011-12-14
The indentation-induced elastic-plastic zone in an IN 740 Ni-based superalloy was studied by three-dimensional (3-D) x-ray microdiffraction and electron back scattering diffraction (EBSD). Large lattice reorientations and the formation of geometrically necessary dislocations are observed in the area with a radius of {approx}75 {mu}m. A residual compression zone is found close to the indent edge. An elastic-plastic transition is observed at {approx}20 {mu}m from the indent edge. Depth dependent dislocation densities are determined at different distances from the indent edge.
Karatolios, Konstantinos; Wittek, Andreas; Nwe, Thet Htar; Bihari, Peter; Shelke, Amit; Josef, Dennis; Schmitz-Rixen, Thomas; Geks, Josef; Maisch, Bernhard; Blase, Christopher; Moosdorf, Rainer; Vogt, Sebastian
2013-11-01
Aortic wall strains are indicators of biomechanical changes of the aorta due to aging or progressing pathologies such as aortic aneurysm. We investigated the potential of time-resolved three-dimensional ultrasonography coupled with speckle-tracking algorithms and finite element analysis as a novel method for noninvasive in vivo assessment of aortic wall strain. Three-dimensional volume datasets of 6 subjects without cardiovascular risk factors and 2 abdominal aortic aneurysms were acquired with a commercial real time three-dimensional echocardiography system. Longitudinal and circumferential strains were computed offline with high spatial resolution using a customized commercial speckle-tracking software and finite element analysis. Indices for spatial heterogeneity and systolic dyssynchrony were determined for healthy abdominal aortas and abdominal aneurysms. All examined aortic wall segments exhibited considerable heterogenous in-plane strain distributions. Higher spatial resolution of strain imaging resulted in the detection of significantly higher local peak strains (p ≤ 0.01). In comparison with healthy abdominal aortas, aneurysms showed reduced mean strains and increased spatial heterogeneity and more pronounced temporal dyssynchrony as well as delayed systole. Three-dimensional ultrasound speckle tracking enables the analysis of spatially highly resolved strain fields of the aortic wall and offers the potential to detect local aortic wall motion deformations and abnormalities. These data allow the definition of new indices by which the different biomechanical properties of healthy aortas and aortic aneurysms can be characterized. Copyright © 2013 The Society of Thoracic Surgeons. Published by Elsevier Inc. All rights reserved.
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.
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
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.
An experimental method to obtain the elastic strain energy function from torsion-tension tests
NASA Technical Reports Server (NTRS)
Peng, S. T. J.; Landel, R. F.
1976-01-01
It is shown that by employing a torsion-tension test, it is possible to have a complete mapping near the origin of the two principal strain invariants associated with the rate of change of the strain energy function. However, the mathematical representation of the twist moment and normal forces vs strain and the strain energy function are complex. This problem is solved by using a set of solid cylindrical bars with different diameters such that the difference in diameter of two successive bars is small. The stress-strain equations can be grossly oversimplified by considering differences in twist moment and normal force as a function of difference in radius.
Plane stress-strain state of a circular cylindrical bushing due to a finite out-of-plane shear
NASA Astrophysics Data System (ADS)
Zhukov, B. A.
2017-01-01
The paper deals with the determination of the stress-strain state due to a finite longitudinal shear in a circular cylindrical bushing manufactured from the Mooney-Rivlin material. Some expressions for the internal stresses and displacements in the plane perpendicular to the longitudinal shear are obtained.
NASA Astrophysics Data System (ADS)
Okudur, O. O.; Vanstreels, K.; De Wolf, I.; Hangen, U.
2016-01-01
Continuous scaling of integrated circuits has led to the introduction of highly porous low dielectric constant (low-k) materials, whose inferior mechanical properties raise concerns regarding the reliability of integrated circuits. Nanoindentation is proven to be a straightforward method to study mechanical properties of films. However, in the case of low-k, the measurement and analysis are complex due to the porous nature of the films and reduced film thicknesses which give rise to substrate effects. A methodology that combines nanoindentation experiments with finite-element simulations is proposed and validated in this study to extract the substrate-free elastic modulus of porous ultra-thin low-k films. Furthermore, it is shown that imperfections of the nanoindentation probe significantly affect the finite-element results. An effective analytical method that captures the actual nanoindenter behavior upon indentation is proposed by taking both tip radius and conical imperfections into account. Using this method combined with finite element modeling, the elastic modulus of sub-100 nm thick low-k films is successfully extracted. Standard indentation tests clearly overestimated the actual modulus for such thin films, which emphasizes the importance of the proposed methodology.
Small Strain Compatibility Conditions of an Elastic Solid in Cylindrical Coordinates
2013-04-01
Intermediate Mechanics of Materials, McGraw-Hill, New York, 2001. 4. Timoshenko , S. P., Goodier, J. N., Theory of Elasticity, 3rd Ed., McGraw-Hill, New York...1970. 5. Timoshenko , S. P., Woinowsky-Krieger, S., Theory of Plates and Shells, 2nd Ed., McGraw- Hill, New York, 1959. 6. Boresi, Arthur P
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.
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.
Nakayama, M; Ariji, Y; Nishiyama, W; Ariji, E
2015-01-01
To verify the use of a single coupling agent as a reference to obtain the elasticity index (EI) ratios and to investigate the EI ratios of the masseter muscles of healthy volunteers. Muscle phantoms with known elasticity (20, 40 and 60 kPa in the Young's modulus) were examined by strain-type sonoelastography using a coupling agent as the reference. Eight examiners tested soft (with 7 kPa) and hard (with 40 kpa) reference coupling agents separately. The correlation coefficients were determined between the EI ratio and Young's modulus of muscle phantoms. The interclass correlation coefficients were calculated for inter- and intraexaminer agreement. Strong correlations were found between the EI ratios and Young's modulus for both soft and hard references. The variations of the EI ratios were larger with soft coupling agents than those with hard coupling agents, and they increased in phantoms with 60 kPa elasticity. There were no differences in the EI ratios of the masseter muscle at rest between males and females or between the right and left sides. The ratio increased during clenching. The hard reference coupling agent was suitable for obtaining EI ratio of the masseter muscle. No differences were found in the EI ratios of the masseter muscle either between sexes or between the right and left sides at rest, and the ratios increased with the widening of their variations during clenching.
Ariji, Y; Nishiyama, W; Ariji, E
2015-01-01
Objectives: To verify the use of a single coupling agent as a reference to obtain the elasticity index (EI) ratios and to investigate the EI ratios of the masseter muscles of healthy volunteers. Methods: Muscle phantoms with known elasticity (20, 40 and 60 kPa in the Young's modulus) were examined by strain-type sonoelastography using a coupling agent as the reference. Eight examiners tested soft (with 7 kPa) and hard (with 40 kpa) reference coupling agents separately. The correlation coefficients were determined between the EI ratio and Young's modulus of muscle phantoms. The interclass correlation coefficients were calculated for inter- and intraexaminer agreement. Results: Strong correlations were found between the EI ratios and Young's modulus for both soft and hard references. The variations of the EI ratios were larger with soft coupling agents than those with hard coupling agents, and they increased in phantoms with 60 kPa elasticity. There were no differences in the EI ratios of the masseter muscle at rest between males and females or between the right and left sides. The ratio increased during clenching. Conclusions: The hard reference coupling agent was suitable for obtaining EI ratio of the masseter muscle. No differences were found in the EI ratios of the masseter muscle either between sexes or between the right and left sides at rest, and the ratios increased with the widening of their variations during clenching. PMID:25411712
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
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.
Elastic unbalance of composite rim flywheels
Portnov, G.G.; Barinov, I.N.; Kulakov, V.L.
1995-01-01
Elastic unbalance of a composite flywheel is considered to be caused by different strain character of the rotating rim due to the distributed material density homogeneity or the corrective mass balancing it in the static state. An analysis has been carried out on the effect of elasticity of the rim flywheel on the linear elastic unbalance and its magnitude for an actual composite flywheel has been calculated. A procedure has been developed for the elimination of unbalance using two corrective masses. The problem of angular unbalance of a rim flywheel has also been considered. The finite element method has been used for computation.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Mozafari, E.; Shulumba, N.; Steneteg, P.; Alling, B.; Abrikosov, Igor A.
2016-08-01
We present a theoretical scheme to calculate the elastic constants of magnetic materials in the high-temperature paramagnetic state. Our approach is based on a combination of disordered local moments picture and ab initio molecular dynamics (DLM-MD). Moreover, we investigate a possibility to enhance the efficiency of the simulations of elastic properties using the recently introduced method: symmetry imposed force constant temperature-dependent effective potential (SIFC-TDEP). We have chosen cubic paramagnetic CrN as a model system. This is done due to its technological importance and its demonstrated strong coupling between magnetic and lattice degrees of freedom. We have studied the temperature-dependent single-crystal and polycrystalline elastic constants of paramagentic CrN up to 1200 K. The obtained results at T = 300 K agree well with the experimental values of polycrystalline elastic constants as well as the Poisson ratio at room temperature. We observe that the Young's modulus is strongly dependent on temperature, decreasing by ˜14 % from T = 300 K to 1200 K. In addition we have studied the elastic anisotropy of CrN as a function of temperature and we observe that CrN becomes substantially more isotropic as the temperature increases. We demonstrate that the use of Birch law may lead to substantial errors for calculations of temperature induced changes of elastic moduli. The proposed methodology can be used for accurate predictions of mechanical properties of magnetic materials at temperatures above their magnetic order-disorder phase transition.
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
Elastic strain field due to an inclusion of a polyhedral shape with a non-uniform lattice misfit
NASA Astrophysics Data System (ADS)
Nenashev, A. V.; Dvurechenskii, A. V.
2017-03-01
An analytical solution in a closed form is obtained for the three-dimensional elastic strain distribution in an unlimited medium containing an inclusion with a coordinate-dependent lattice mismatch (an eigenstrain). Quantum dots consisting of a solid solution with a spatially varying composition are examples of such inclusions. It is assumed that both the inclusion and the surrounding medium (the matrix) are elastically isotropic and have the same Young's modulus and Poisson ratio. The inclusion shape is supposed to be an arbitrary polyhedron, and the coordinate dependence of the lattice misfit, with respect to the matrix, is assumed to be a polynomial of any degree. It is shown that, both inside and outside the inclusion, the strain tensor is expressed as a sum of contributions of all faces, edges, and vertices of the inclusion. Each of these contributions, as a function of the observation point's coordinates, is a product of some polynomial and a simple analytical function, which is the solid angle subtended by the face from the observation point (for a contribution of a face), or the potential of the uniformly charged edge (for a contribution of an edge), or the distance from the vertex to the observation point (for a contribution of a vertex). The method of constructing the relevant polynomial functions is suggested. We also found out that similar expressions describe an electrostatic or gravitational potential, as well as its first and second derivatives, of a polyhedral body with a charge/mass density that depends on coordinates polynomially.
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.
NASA Astrophysics Data System (ADS)
Søe-Knudsen, A.; Sorokin, S. V.
2010-09-01
The combined methodology of boundary integral equations and finite elements is formulated and applied to study the wave propagation phenomena in compound piping systems consisting of straight and curved pipe segments with compact elastic supports. This methodology replicates the concept of hierarchical boundary integral equations method proposed by L. I. Slepyan to model the time-harmonic wave propagation in wave guides, which have components of different dimensions. However, the formulation presented in this article is tuned to match the finite element format, and therefore, it employs the dynamical stiffness matrix to describe wave guide properties of all components of the assembled structure. This matrix may readily be derived from the boundary integral equations, and such a derivation is superior over the conventional derivation from the transfer matrix. The proposed methodology is verified in several examples and applied for analysis of periodicity effects in compound piping systems of several alternative layouts.
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.
NASA Astrophysics Data System (ADS)
Shaina, P. R.; Sakorikar, Tushar; Sarkar, Biporjoy; Kavitha, M. K.; Vayalamkuzhi, Pramitha; Jaiswal, Manu
2017-06-01
We investigate temperature-dependent charge transport in reduced graphene oxide (rGO) films coated on flexible polydimethylsiloxane (PDMS) substrates which are subject to uniaxial strain. Variable strain, up to 10%, results in an anisotropic morphology comprising of quasi-periodic linear array of deformations which are oriented perpendicular to the direction of strain. The anisotropy is reflected in the charge transport measurements, when conduction in the direction parallel and perpendicular to the applied strain are compared. Temperature dependence of resistance is measured for different values of strain in the temperature interval 80-300 K. While the resistance increases significantly upon application of strain, the temperature-dependent response shows anomalous decrease in resistance ratio R 80 K/R 300 K upon application of strain. This observation of favorable conduction processes under strain is further corroborated by reduced activation energy analysis of the temperature-dependent transport data. These anomalous transport features can be reconciled based on mutually competing effects of two processes: (i) thinning of graphene at the sites of periodic deformations, which tends to enhance the overall resistance by a purely geometrical effect, and (ii) locally enhanced inter-flake coupling in these same regions which contributes to improved temperature-dependent conduction.
DT-REFinD: Diffusion Tensor Registration With Exact Finite-Strain Differential
Vercauteren, Tom; Fillard, Pierre; Peyrat, Jean-Marc; Pennec, Xavier; Golland, Polina; Ayache, Nicholas; Clatz, Olivier
2014-01-01
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. PMID:19556193
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.
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.
Forman, Jason L; de Dios, Eduardo del Pozo; Kent, Richard W
2010-12-01
Injury-predictive finite element (FE) models of the chest must reproduce the structural coupling behavior of the costal cartilage accurately. Gross heterogeneities (the perichondrium and calcifications) may cause models developed based on local material properties to erroneously predict the structural behavior of cartilage segments. This study sought to determine the pseudo-elastic effective material properties required to reproduce the structural behavior of the costal cartilage under loading similar to what might occur in a frontal automobile collision. Twenty-eight segments of cadaveric costal cartilage were subjected to cantilever-like, dynamic loading. Three limited-mesh FE models were then developed for each specimen, having element sizes of 10 mm (typical of current whole-body FE models), 3 mm, and 2 mm. The cartilage was represented as a homogeneous, isotropic, linear elastic material. The elastic moduli of the cartilage models were optimized to fit the anterior-posterior (x-axis) force versus displacement responses observed in the experiments. For a subset of specimens, additional model validation tests were performed under a second boundary condition. The pseudo-elastic effective moduli ranged from 4.8 to 49 MPa, with an average and standard deviation of 22 ± 13.6 MPa. The models were limited in their ability to reproduce the lateral (y-axis) force responses observed in the experiments. The prediction of the x-axis and y-axis forces in the second boundary condition varied. Neither the effective moduli nor the model fit were significantly affected (Student's t-test, p < 0.05) by the model mesh density. The average pseudo-elastic effective moduli were significantly (p < 0.05) greater than local costal cartilage modulus values reported in the literature. These results are consistent with the presence of stiffening heterogeneities within the costal cartilage structure. These effective modulus values may provide guidance for the representation of the costal
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.
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.
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.
Effect of the electronic kinetic energy on the elastic strain in metallic multilayers
NASA Astrophysics Data System (ADS)
Huberman, M. L.; Grimsditch, M.
1992-09-01
A recent theory of induced strain in metallic multilayers, caused by electron transfer effects, is revised by taking into account the electronic kinetic energy. When this is done, it is found that the predicted sign of the strain is opposite to what was found previously. For a multilayer having abrupt composition changes, the predicted magnitude of the strain is greater by a factor of 9/5 than what was found previously, whereas for a multilayer having smooth composition changes, it is the same as what was found previously.
Xiong, Jiang; Wang, Shen Ming; Zhou, Wei; Wu, Jan Guo
2008-07-01
The maximal strain, stress, elastic modulus, and stress-strain curve fitting of abdominal aortic aneurysms (AAA) and bidirectional nonaneurysmal abdominal aorta (NAA) were measured and analyzed to obtain the ultimate mechanical properties, the more approximate stress-strain curve-fitting, and the elastic modulus formula of AAA and NAA. Fourteen human AAA samples were harvested from patients undergoing elective aneurysm repair. Twelve NAA samples comprised of six longitudinal-circumferential pairs of NAA from six cadaveric organ donors were used as controls. Samples were mounted on a tensile-testing machine and force was applied until breakage occurred. The maximal strain, stress, and elastic modulus were calculated and a stress-strain curve was plotted for each sample. Exponential and second-order polynomial curves were used to fit the stress-strain curve, and the means were estimated by comparing the R2 (coefficient of determination that represents the strength of a curve fitting). Coefficients of elastic modulus were calculated and analyzed, and the incremental tendency of each modulus was evaluated by comparing the difference of coefficients. There was no significant difference in maximal stress among AAA, circumferential aortic aneurysms (CAA), and longitudinal aortic aneurysms (LAA). However, AAA maximal strain was significantly less (P < .01) than that of bidirectional NAA. AAA maximal elastic modulus was significantly greater than that of CAA and LAA (P < .01 and .05, respectively). R2 of AAA for second-order polynomial curve was significantly greater (P < .05) than that for the exponential curve. For the elastic modulus formula from the second-order polynomial curve, E = 2ax + b, the average value of a for the AAA was significantly greater (P < .01) than that for the bidirectional NAA, but there was no significant difference (P > .05) among the three groups for the average value of b. Tensile test measurements can successfully analyze ultimate mechanical
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.
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.
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. Copyright © 2014 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.
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 e