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Linear elasticity
About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.
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TL;DR: In this paper, the authors examined the stresses and displacement gradients in atomistic models of cracks based on an EAM potential devised for aluminum and found that they were in remarkably good agreement to within distances of about one lattice parameter of the crack tip and at the free surface.
Abstract: This paper examines the stresses and displacement gradients in atomistic models of cracks based on an EAM potential devised for aluminum. Methods for computing these quantities are described. Results are presented for two models differing in terms of the orientations of the crack relative to the crystal, a [100] (010) orientation that behaves in a brittle fashion and a [111] (110) orientation that emits partial dislocations prior to extending. Both models display lattice trapping. The stresses in the brittle crack model are compared with the linear elastic prediction and found to be in remarkably good agreement to within distances of about one lattice parameter of the crack tip and at the free surface where contributions from sources other than strain energy (e.g., surface tension) influence the results. Similar results are observed for the ductile model until dislocation emission occurs. The largest stresses that develop just prior to crack extension or dislocation emission are used to estimate the ratio of theoretical tensile strength to shear strength in this material. Eshelby’s conservation integrals, F and M, are also computed. F is found to be essentially contour independent and in agreement with the linear elastic prediction in both models until dislocation emission occurs, at which point a large screening contribution arises from the emitted partials. The contour size dependence of M reveals some interesting features of the crack tip including a slight wobble of the crack tip inside its potential well with changing applied K and the existence of forces acting to move the crack faces apart as blunting occurs.
61 citations
Book•
01 Jan 1976
TL;DR: In this article, the authors present an analysis of variational inequalities with highly oscillating coefficients for nonlinear elasticity problems and their application to the optimisation of a temperature profile.
Abstract: Inequations quasi-variationnelles dans les problemes a frontiere libre en hydraulique.- The alliance of practical and analytical insights into the nonlinear problems of fluid mechanics.- Asymptotic behaviour of solutions of variational inequalities with highly oscillating coefficients.- Application of convex analysis to the treatment of elastoplastic systems.- Theory of mixed and hybrid finite-element approximations in linear elasticity.- Perturbation of domains in elliptic boundary value problems.- Frost propagation in wet porous media.- Viscous fluid flow in chemically reacting and diffusing systems.- Local invertibility conditions for geometrically exact nonlinear rod and shell theories.- Some applications of functional analysis in the mathematical theory of structures.- Functional analysis applied to the optimisation of a temperature profile.- Global free boundary problems and the calculus of variations in the large.- Proof of existence and uniqueness of tidal waves with general vorticity distributions.- A critical appraisal of certain contemporary ship model testing techniques.- Solitary-wave solutions for some model equations for waves in nonlinear dispersive media.- Hilbertian unilateral problems in viscoelasticity.- On the norm-dependence of the concept of stability.- The hodograph method in fluid-dynamics in the light of variational inequalities.- A new formulation of diphasic incompressible flows in porous media.- Convergence of solutions in problems of elastic plastic torsion of cylindrical bars.- On an evolution problem in linear acoustics of viscous fluids.- On the mechanics of materials with fading memory.- Contraction semigroups and trend to equilibrium in continuum mechanics.- The buckling of a thin elastic plate subjected to unilateral conditions.- Problemes de contact entre corps solides deformables.- On the existence and uniqueness of a warpening function in the Elastic-plastic torsion of a cylindrical bar with multiply connected cross-section.- A method for computing the eigenfrequencies of an acoustic resonator.- Secondary bifurcation of a steady solution into an invariant torus for evolution problems of Navier-Stokes' type.- A basic open problem in the theory of elastic stability.- Some applications and methods of nonlinear functional analysis in finite displacement plate theory.- Criteres de validite de la theorie non-lineaire des coques elastiques.- Functional analysis approach for the derivation of hybrid variational functionals.- Stability of equilibrium in elastic-plastic solids.- Solutions in the large for certain nonlinear hyperbolic systems arising in shock-wave theory.- Cauchy problem in a scale of banach spaces and its application to the shallow water theory justification.- Perturbation results and their applications to problems in structural dynamics.- On the physical interpretation of certain inner products as a guide to the application of functional analysis.- Branching and stability for nonlinear shells.- On a free surface problem.- Theoretical constructions of selection of actual events from the virtual ones.- Steadily rotating chains.- Generating functionals and extremum principles in nonlinear elasticity with applications to nonlinear plate and shallow shell theory.- Determination de la configuration d'equilibre d'un plasma.- Elatic-plastic torsion of cylindrical pipes.
61 citations
TL;DR: In this paper, the linear elastic properties of layered silicates on the nanometer scale have been clarified, including tensile moduli, shear moduli and shear properties.
Abstract: Mechanical properties of layered silicates on the nanometer scale have been associated with large uncertainty. We attempt to clarify the linear elastic properties including tensile moduli, shear mo...
61 citations
TL;DR: In this article, a new method is described for the problem of expanding known displacement fields at the boundary of a solid together with the surface tractions on it, towards the solid interior up to the inaccessible part of the boundary.
61 citations
TL;DR: In this article, a simple constitutive model for nonsmared cracking nonlinear finite element analysis of reinforced concrete structures is described, and the effect of biaxial stress conditions on peak strengths is represented by a variation of the Kupfer-Hilsdorf failure curve in stress space, where the compressive and tensile envelopes are separately specified.
Abstract: A simple constitutive model for ‘smeared cracking’ nonlinear finite element analysis of reinforced concrete structures is described. The model divides the uniaxial response curve for concrete into fivedamage regions, described as linear elastic; compressive strain hardening; compressive strain softening; tensile strain softening; and tensile stiffening regions. Recommendations for incorporating strain localization effects into homogenized material properties in the softening regions are given. The effect of biaxial stress conditions on peak strengths is represented by a variation of the Kupfer‐Hilsdorf failure curve in stress space, in which the compressive and tensile envelopes are separately specified. Recommendations for the effects of tensile cracking and confinement on the shear modulus and the compressivesoftening modulus, respectively, are included. The central thrust of the paper is to incorporate those attributes of the constitutive model which affect the prediction of structural failure modes as...
61 citations