A nonlinear Korn inequality with boundary conditions and its relation to the existence of minimizers in nonlinear elasticity

DOI10.1016/J.CRMA.2011.01.011zbMath1346.74076OpenAlexW2090991332MaRDI QIDQ627762

Christinel Mardare

Publication date: 3 March 2011

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://hal.sorbonne-universite.fr/hal-01077300/file/10existmin-CRAS.pdf

zbMATH Keywords

total energyGreen-Saint Venant strain tensorhyperelastic body

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (4)

A nonlinear Korn inequality based on the Green-Saint Venant strain tensor ⋮ A hybridizable discontinuous Galerkin formulation for non-linear elasticity ⋮ Poincaré meets Korn via Maxwell: extending Korn's first inequality to incompatible tensor fields ⋮ Mixed Kirchhoff stress-displacement-pressure formulations for incompressible hyperelasticity

Cites Work

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• Existence theorems in intrinsic nonlinear elasticity
• Energy minimizers in nonlinear elastostatics and the implicit function theorem
• Continuity of a deformation in \(H^{1}\) as a function of its Cauchy-Green tensor in \(L^{1}\)
• Convexity conditions and existence theorems in nonlinear elasticity
• Critical points in the energy of hyperelastic materials
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity

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