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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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02 Dec 2010
TL;DR: In this article, the authors present a mathematical foundation for the Kinematics of Crystalline Solids, including the Thermomechanics of the solids, and the Thermo-elasticity and elastoplasticity.
Abstract: Introduction.- Mathematical foundations.- Kinematics of Crystalline Solids.- Thermomechanics of Crystalline Solids.- Thermoelasticity.- Elastoplasticity.- Residual Deformation from Lattice Defects.- Mechanical Twinning in Crystal Plasticity.- Generalized Inelasticity.- Dielectrics and piezoelectricity.- Chrystal Symmetries and Elastic Constants.- Lattice Statics and Dynamics.- Discrete Defects in Linear Elasticity.- SI Units and Fundamental Constants.- Kinematic Derivations.- References.- Index.

211 citations

Journal ArticleDOI
TL;DR: In this article, the authors argue that the usual interpretation of what one means by "elasticity" is much too insular and illustrate their thesis by introducing implicit constitutive theories that can describe the non-dissipative response of solids.
Abstract: In this note we assert that the usual interpretation of what one means by “elasticity” is much too insular and illustrates our thesis by introducing implicit constitutive theories that can describe the non-dissipative response of solids. There is another important aspect to the introduction of such an implicit approach to the non-dissipative response of solids, the development of a hierarchy of approximations wherein, while the strains are infinitesimal the relationship between the stress and the linearized strain is non-linear. Such approximations would not be logically consistent within the context of explicit theories of Cauchy elasticity or Green elasticity that are currently popular.

210 citations

Journal ArticleDOI
TL;DR: In this article, a strain smoothing procedure for the extended finite element method (XFEM) is presented, which is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM.

210 citations

Journal ArticleDOI
TL;DR: In this paper, the elastic field of complex shape ensembles of dislocation loops is developed as an essential ingredient in the dislocation dynamics method for computer simulation of mesoscopic plastic deformation.
Abstract: The elastic field of complex shape ensembles of dislocation loops is developed as an essential ingredient in the dislocation dynamics method for computer simulation of mesoscopic plastic deformation. Dislocation ensembles are sorted into individual loops, which are then divided into segments represented as parametrized space curves. Numerical solutions are presented as fast numerical sums for relevant elastic field variables (i.e., displacement, strain, stress, force, self-energy, and interaction energy). Gaussian numerical quadratures are utilized to solve for field equations of linear elasticity in an infinite isotropic elastic medium. The accuracy of the method is verified by comparison of numerical results to analytical solutions for typical prismatic and slip dislocation loops. The method is shown to be highly accurate, computationally efficient, and numerically convergent as the number of segments and quadrature points are increased on each loop. Several examples of method applications to calculations of the elastic field of simple and complex loop geometries are given in infinite crystals. The effect of crystal surfaces on the redistribution of the elastic field is demonstrated by superposition of a finite-element {ital image force} field on the computed results. {copyright} {ital 1999} {ital The American Physical Society}

209 citations

Journal ArticleDOI
TL;DR: In this article, a method for the stress analysis of plane cracks of any shape in a stressed three-dimensional linear elastic space is presented, which utilizes a system of integral equations which is defined over the crack area only.

209 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202386
2022223
2021318
2020317
2019312
2018335