On isotropic rank 1 convex functions

DOI10.1017/S0308210500031085zbMath0945.26018MaRDI QIDQ4934086

Šilhavý, Miroslav

Publication date: 27 March 2000

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

nonlinear elasticityrank 1 convexity

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Methods involving semicontinuity and convergence; relaxation (49J45) Convexity of real functions of several variables, generalizations (26B25)

Related Items (10)

Phase equilibria in isotropic solids ⋮ Automatic quasiconvexity of homogeneous isotropic rank-one convex integrands ⋮ Rank-one convexity implies polyconvexity in isotropic planar incompressible elasticity ⋮ Morrey's conjecture for the planar volumetric-isochoric split: least rank-one convex energy functions ⋮ The exponentiated Hencky-logarithmic strain energy. I: Constitutive issues and rank-one convexity ⋮ Consequences of the Coleman‐Noll inequality for isotropic materials ⋮ The exponentiated Hencky-logarithmic strain energy. II: Coercivity, planar polyconvexity and existence of minimizers ⋮ Four applications of majorization to convexity in the calculus of variations ⋮ Sharp rank-one convexity conditions in planar isotropic elasticity for the additive volumetric-isochoric split ⋮ On Semiconvexity Properties of Rotationally Invariant Functions in Two Dimensions

Cites Work

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• On copositive matrices and strong ellipticity for isotropic elastic materials
• Ellipticity and deformations with discontinuous gradients in finite elastostatics
• On the failure of ellipticity of the equations for finite elastostatic plane strain
• Convexity conditions and existence theorems in nonlinear elasticity
• Confluent Cauchy and Cauchy-Vandermonde matrices
• Necessary and sufficient conditions for isotropic rank-one convex functions in dimension 2
• An introduction to continuum mechanics
• An inversion formula and fast algorithms for Cauchy-Vandermonde matrices
• Direct methods in the calculus of variations

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