Necessary and sufficient conditions for isotropic rank-one convex functions in dimension 2

DOI10.1007/BF00042440zbMath0828.73015MaRDI QIDQ1898367

Gilles Aubert

Publication date: 17 September 1995

Published in: Journal of Elasticity (Search for Journal in Brave)

zbMATH Keywords

quasiconvexityexistence of minimizersstored energy function

Mathematics Subject Classification ID

Related Items (12)

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 ⋮ Criterion of hyperbolicity in hyperelasticity in the case of the stored energy in separable form ⋮ A note on strong ellipticity in two-dimensional isotropic elasticity ⋮ On rank one connectedness, for planar objective functions ⋮ On isotropic rank 1 convex functions ⋮ 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 ⋮ Quasiconvex relaxation of isotropic functions in incompressible planar hyperelasticity ⋮ Stability of classical shock fronts for compressible hyperelastic materials of Hadamard type

Cites Work

• Unnamed Item
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• On copositive matrices and strong ellipticity for isotropic elastic materials
• Sur la faible fermeture de certains ensembles de contraintes en élasticité non-linéaire plane. (Weak closure of certain sets of constraints in plane nonlinear elasticity)
• On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics
• An example of a quasiconvex function that is not polyconvex in two dimensions
• A simple derivation of necessary and sufficient conditions for the strong ellipticity of isotropic hyperelastic materials in plane strain
• On the relation between polyconvexity and rank-one convexity in nonlinear elasticity
• Quelques remarques sur les notions de $1-$rang convexité et de polyconvexité en dimensions 2 et 3
• Rank-one convexity does not imply quasiconvexity
• 60.6 Some probabilities in the simple race game
• Semicontinuity problems in the calculus of variations

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