On the inadequacy of the scaling of linear elasticity for 3D-2D asymptotics in a nonlinear setting

DOI10.1016/S0021-7824(01)01204-1zbMath1029.35216WikidataQ127012797 ScholiaQ127012797MaRDI QIDQ1606242

Irene Fonseca, Gilles A. Francfort

Publication date: 24 July 2002

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

zbMATH Keywords

dimension reductionrelaxation\(\Gamma\)-convergenceplate models

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Plates (74K20) Thin films (74K35) Homogenization in equilibrium problems of solid mechanics (74Q05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (4)

Nonlinear boundary conditions in Kirchhoff-Love plate theory ⋮ 3D-2D Asymptotic Analysis for Micromagnetic Thin Films ⋮ THE REISSNER–MINDLIN PLATE IS THE Γ-LIMIT OF COSSERAT ELASTICITY ⋮ Equi-integrability results for 3D-2D dimension reduction problems

Cites Work

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• \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
• A justification of nonlinear properly invariant plate theories
• An introduction to \(\Gamma\)-convergence
• The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
• A-Quasiconvexity: Relaxation and Homogenization
• 3D-2D Asymptotic Analysis for Inhomogeneous Thin Films
• Quasi-Convex Integrands and Lower Semicontinuity in $L^1 $
• Semicontinuity problems in the calculus of variations
• Nonlinear problems of elasticity
• Direct methods in the calculus of variations

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