Conditions for strong ellipticity of anisotropic elastic materials
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Publication:1039335
DOI10.1007/s10659-009-9205-5zbMath1252.74006OpenAlexW2085795790MaRDI QIDQ1039335
Deren Han, Liqun Qi, Hui-Hui Dai
Publication date: 27 November 2009
Published in: Journal of Elasticity (Search for Journal in Brave)
Full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.728.3663
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Cites Work
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- On copositive matrices and strong ellipticity for isotropic elastic materials
- Ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids
- Ellipticity and deformations with discontinuous gradients in finite elastostatics
- Eigenvalues and invariants of tensors
- Spatial estimates for the constrained anisotropic elastic cylinder
- Sufficient conditions for strong ellipticity for a class of anisotropic materials
- On the strong ellipticity of the anisotropic linearly elastic materials
- The degree of the E-characteristic polynomial of an even order tensor
- Z-eigenvalue methods for a global polynomial optimization problem
- Discontinuous deformation gradients in plane finite elastostatics of incompressible materials
- On the ellipticity of the equations of nonlinear elastostatics for a special material
- A reformulation of the strong ellipticity conditions for unconstrained hyperelastic media
- Instabilities and loss of ellipticity in fiber-reinforced compressible nonlinearly elastic solids under plane deformation.
- Strong ellipticity of transversely isotropic elasticity tensors
- Eigenvalues of a real supersymmetric tensor
- Rank and eigenvalues of a supersymmetric tensor, the multivariate homogeneous polynomial and the algebraic hypersurface it defines
- Necessary and sufficient conditions for strong ellipticity of isotropic functions in any dimension
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