The von Kármán theory for incompressible elastic shells

DOI10.1007/s00526-012-0549-5zbMath1314.74043OpenAlexW1990638184WikidataQ61442422 ScholiaQ61442422MaRDI QIDQ368547

Milena Chermisi, Hui Li

Publication date: 23 September 2013

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

Full work available at URL: https://doi.org/10.1007/s00526-012-0549-5

Mathematics Subject Classification ID

Plates (74K20) Shells (74K25)

Related Items

Plates with incompatible prestrain of high order, Asymptotic justification of equations for von Kármán membrane shells, On a consistent finite-strain shell theory for incompressible hyperelastic materials, Asymptotic variational analysis of incompressible elastic strings, Nonlinear higher-order shell theory for incompressible biological hyperelastic materials, A refined dynamic finite-strain shell theory for incompressible hyperelastic materials: equations and two-dimensional shell virtual work principle, 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
• The uniform Korn-Poincaré inequality in thin domains
• Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density
• The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells
• Derivation of a plate theory for incompressible materials
• A nonlinear theory for shells with slowly varying thickness
• \(\Gamma \)-convergence for incompressible elastic plates
• An introduction to \(\Gamma\)-convergence
• Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence.
• Incompressible nonlinearly elastic thin membranes
• Asymptotic considerations shedding light on incompressible shell models
• The membrane shell model in nonlinear elasticity: A variational asymptotic derivation
• The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
• Infinitesimal isometries on developable surfaces and asymptotic theories for thin developable shells
• Confining thin elastic sheets and folding paper
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• Reduced Theories in Nonlinear Elasticity
• A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry
• The Föppl-von Kármán equations for plates with incompatible strains
• MODELING OF A MEMBRANE FOR NONLINEARLY ELASTIC INCOMPRESSIBLE MATERIALS VIA GAMMA-CONVERGENCE
• Convergence of Equilibria of Thin Elastic Plates - The Von Karman Case
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• The Infinite Hierarchy of Elastic Shell Models: Some Recent Results and a Conjecture
• Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity
• Derivation of Elastic Theories for Thin Sheets and the Constraint of Incompressibility