Orientation-preserving condition and polyconvexity on a surface: application to nonlinear shell theory

DOI10.1016/j.matpur.2012.10.006zbMath1288.74049OpenAlexW2007384806MaRDI QIDQ387983

Radu Gogu, Philippe G. Ciarlet, Christinel Mardare

Publication date: 18 December 2013

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

Full work available at URL: https://doi.org/10.1016/j.matpur.2012.10.006

zbMATH Keywords

Sobolev spaceexistencecoercivityminimizerstored energy function

Mathematics Subject Classification ID

Energy minimization in equilibrium problems in solid mechanics (74G65) Shells (74K25)

Related Items (8)

Polyconvexity and existence theorem for nonlinearly elastic shells ⋮ Crack Nucleation in Shells with Through-the-Thickness Microstructure ⋮ Energy minimizing configurations for single-director Cosserat shells ⋮ Existence theorem for a nonlinear elliptic shell model ⋮ A notion of polyconvex function on a surface suggested by nonlinear shell theory ⋮ The isotropic Cosserat shell model including terms up to \(O(h^5)\). I: Derivation in matrix notation ⋮ The isotropic Cosserat shell model including terms up to \(O(h^5)\). II: Existence of minimizers ⋮ An existence theorem for a two-dimensional nonlinear shell model of Koiter’s type

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A notion of polyconvex function on a surface suggested by nonlinear shell theory
• Injectivity and self-contact in nonlinear elasticity
• Null Lagrangians, weak continuity, and variational problems of arbitrary order
• Convexity conditions and existence theorems in nonlinear elasticity
• An existence theorem for nonlinearly elastic `flexural' shells
• Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence.
• The membrane shell model in nonlinear elasticity: A variational asymptotic derivation
• An introduction to continuum mechanics
• On the thermostatics of continuous media
• Non-polyconvexity of the stored energy function of a Saint Venant-Kirchhoff material
• Global invertibility of Sobolev functions and the interpenetration of matter
• Un modèle bi-dimensionnel non linéaire de coque analogue à celui de W.T. Koiter
• Remarks on Nonlinear Membrane Shell Problems
• Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids
• Nonlinear problems of elasticity
• Justification of a two-dimensional nonlinear shell model of Koiter's type

This page was built for publication: Orientation-preserving condition and polyconvexity on a surface: application to nonlinear shell theory