Commutability of homogenization and linearization at identity in finite elasticity and applications

DOI10.1016/j.anihpc.2011.07.002zbMath1256.35004OpenAlexW1975342759MaRDI QIDQ654167

Antoine Gloria, Stefan Neukamm

Publication date: 28 December 2011

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.anihpc.2011.07.002

zbMATH Keywords

linearizationhomogenizationnonlinear elasticity\(G\)-convergencestochastic homogenization\(\Gamma \)-convergenceKorn inequality\(\Gamma \)-closureMeyers estimate

Mathematics Subject Classification ID

Bounds on effective properties in solid mechanics (74Q20) Composite and mixture properties (74E30) Methods involving semicontinuity and convergence; relaxation (49J45) Homogenization in equilibrium problems of solid mechanics (74Q05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (13)

Homogenization theory: periodic and beyond. Abstracts from the workshop held March 14--20, 2021 (online meeting) ⋮ Stochastic homogenisation of singularly perturbed integral functionals ⋮ Linearization for finite plasticity under dislocation-density tensor regularization ⋮ A homogenized bending theory for prestrained plates ⋮ Rigorous derivation of a homogenized bending-torsion theory for inextensible rods from three-dimensional elasticity ⋮ Quantitative nonlinear homogenization: control of oscillations ⋮ Derivation of a homogenized bending-torsion theory for rods with micro-heterogeneous prestrain ⋮ Linearized plasticity is the evolutionary \(\Gamma\)-limit of finite plasticity ⋮ Lipschitz estimates and existence of correctors for nonlinearly elastic, periodic composites subject to small strains ⋮ Variance reduction using antithetic variables for a nonlinear convex stochastic homogenization problem ⋮ Geometric linearization of theories for incompressible elastic materials and applications ⋮ Quantitative homogenization in nonlinear elasticity for small loads ⋮ Derivation of Linear Elasticity for a General Class of Atomistic Energies

Cites Work

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• Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion
• Stochastic homogenization of nonconvex integral functionals
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• On local the representations of \(G\)-closure.

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