A Piecewise Korn Inequality in SBD and Applications to Embedding and Density Results
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Publication:4577221
DOI10.1137/17M1129982zbMath1391.74227arXiv1604.08416WikidataQ129529934 ScholiaQ129529934MaRDI QIDQ4577221
Publication date: 17 July 2018
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1604.08416
brittle materialscoarea formulavariational fracturefunctions of bounded deformationKorn's inequalityKorn-Poincaré inequality
Variational methods for problems in mechanics (70G75) Brittle fracture (74R10) Methods involving semicontinuity and convergence; relaxation (49J45) Inequalities involving derivatives and differential and integral operators (26D10)
Related Items (24)
Fine properties of functions of bounded deformation -- an approach via linear PDEs ⋮ From atomistic systems to linearized continuum models for elastic materials with voids ⋮ Korn and Poincaré-Korn inequalities for functions with a small jump set ⋮ Compactness and lower semicontinuity in \(GSBD\) ⋮ Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity ⋮ A compactness result in \(GSBV^p\) and applications to \(\varGamma \)-convergence for free discontinuity problems ⋮ Unnamed Item ⋮ Equilibrium Configurations for Nonhomogeneous Linearly Elastic Materials with Surface Discontinuities ⋮ Korn's inequality in anisotropic Sobolev spaces ⋮ Integral representation and \(\Gamma\)-convergence for free-discontinuity problems with \(p(\cdot)\)-growth ⋮ A new proof of compactness in G(S)BD ⋮ Lower semicontinuity for functionals defined on piecewise rigid functions and on \(GSBD\) ⋮ A density result in \(GSBD^p\) with applications to the approximation of brittle fracture energies ⋮ Functionals defined on piecewise rigid functions: integral representation and \(\Gamma \)-convergence ⋮ Phase-field approximation for a class of cohesive fracture energies with an activation threshold ⋮ On the Approximation of SBD Functions and Some Applications ⋮ Phase-field approximation of functionals defined on piecewise-rigid maps ⋮ Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions ⋮ Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy ⋮ Existence of strong solutions to the Dirichlet problem for the Griffith energy ⋮ Approximation of functions with small jump sets and existence of strong minimizers of Griffith's energy ⋮ Integral representation for energies in linear elasticity with surface discontinuities ⋮ Density in SBD and approximation of fracture energies ⋮ Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials
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