A simple derivation of necessary and sufficient conditions for the strong ellipticity of isotropic hyperelastic materials in plane strain
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Publication:1198455
DOI10.1007/BF00041893zbMath0759.73013OpenAlexW2083917365MaRDI QIDQ1198455
Publication date: 16 January 1993
Published in: Journal of Elasticity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf00041893
isotropystored energy functiondiagonal matrixLegendre-Hadamard conditionrank one convexitygeneral gradient matrix
Related Items (10)
An example of a one-parameter family of rank-one convex stored energies for isotropic compressible solids ⋮ Necessary and sufficient conditions for isotropic rank-one convex functions in dimension 2 ⋮ A reformulation of the strong ellipticity conditions for unconstrained hyperelastic media ⋮ Rank-one convexity implies polyconvexity in isotropic planar incompressible elasticity ⋮ A thermodynamically compatible splitting procedure in hyperelasticity ⋮ Criterion of hyperbolicity in hyperelasticity in the case of the stored energy in separable form ⋮ Unnamed Item ⋮ A note on strong ellipticity in two-dimensional isotropic elasticity ⋮ Sharp rank-one convexity conditions in planar isotropic elasticity for the additive volumetric-isochoric split ⋮ Stability of classical shock fronts for compressible hyperelastic materials of Hadamard type
Cites Work
- 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
- On the failure of ellipticity of the equations for finite elastostatic plane strain
- Differentiability properties of isotropic functions
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