\(\Gamma \)-convergence for incompressible elastic plates

DOI10.1007/s00526-008-0194-1zbMath1161.74038OpenAlexW2072958247MaRDI QIDQ1017931

Georg Dolzmann, Sergio Conti

Publication date: 13 May 2009

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-008-0194-1

zbMATH Keywords

incompressibility constraintisochoric elastic modulismooth isometries

Mathematics Subject Classification ID

Related Items (20)

Linearization of elasticity models for incompressible materials ⋮ The von Kármán theory for incompressible elastic shells ⋮ Pressure live loads and the variational derivation of linear elasticity ⋮ A Blake-Zisserman-Kirchhoff theory for plates with soft inclusions ⋮ Variational linearization of pure traction problems in incompressible elasticity ⋮ Brittle membranes in finite elasticity ⋮ Infinitesimal isometries on developable surfaces and asymptotic theories for thin developable shells ⋮ Actuation of thin nematic elastomer sheets with controlled heterogeneity ⋮ Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density ⋮ Asymptotic variational analysis of incompressible elastic strings ⋮ Linear elasticity obtained from finite elasticity by \(\Gamma \)-convergence under weak coerciveness conditions ⋮ Approximation of flat \(W ^{2,2}\) isometric immersions by smooth ones ⋮ Fine level set structure of flat isometric immersions ⋮ The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells ⋮ A Griffith–Euler–Bernoulli theory for thin brittle beams derived from nonlinear models in variational fracture mechanics ⋮ A hierarchy of multilayered plate models ⋮ Theories for incompressible rods: A rigorous derivation via Γ-convergence ⋮ Convergence of equilibria for incompressible elastic plates in the von Kármán regime ⋮ Linearized von Kármán theory for incompressible magnetoelastic plates ⋮ On the theory of relaxation in nonlinear elasticity with constraints on the determinant

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Derivation of a plate theory for incompressible materials
• Convexity conditions and existence theorems in nonlinear elasticity
• A justification of nonlinear properly invariant plate theories
• On the justification of the nonlinear inextensional plate model
• Rigorous derivation of nonlinear plate theory and geometric rigidity
• Soft elastic response of stretched sheets of nematic elastomers: A numerical study
• On the Sobolev space of isometric immersions
• Incompressible nonlinearly elastic thin membranes
• The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
• Approximating \(W^{2,2}\) isometric immersions
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• Une justification partielle du modèle de plaque en flexion par -convergence
• MODELING OF A MEMBRANE FOR NONLINEARLY ELASTIC INCOMPRESSIBLE MATERIALS VIA GAMMA-CONVERGENCE
• RELAXATION OF SOME TRANSVERSALLY ISOTROPIC ENERGIES AND APPLICATIONS TO SMECTIC A ELASTOMERS
• Une méthode de Γ-convergence pour un modèle de membrane non linéaire
• The coupling of chiral chains to mechanical distortions in elastomers
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• Derivation of Elastic Theories for Thin Sheets and the Constraint of Incompressibility
• Nonlinear problems of elasticity

This page was built for publication: \(\Gamma \)-convergence for incompressible elastic plates