A reformulation of the strong ellipticity conditions for unconstrained hyperelastic media
From MaRDI portal
Publication:1357196
DOI10.1007/BF00042193zbMath0876.73030MaRDI QIDQ1357196
Publication date: 2 December 1997
Published in: Journal of Elasticity (Search for Journal in Brave)
Related Items (42)
On the Straightening of Compressible, Nonlinearly Elastic, Annular Cylindrical Sectors ⋮ The Convexity Properties of a Class of Constitutive Models for Biological Soft Issues ⋮ Properties and calculation for \(C\)-eigenvalues of a piezoelectric-type tensor ⋮ Convergence of an algorithm for the largest singular value of a nonnegative rectangular tensor ⋮ M-eigenvalue intervals and checkable sufficient conditions for the strong ellipticity ⋮ The exponentiated Hencky-logarithmic strain energy. I: Constitutive issues and rank-one convexity ⋮ On necessary and sufficient conditions of strong ellipticity of equilibrium equations for certain classes of anisotropic linearly elastic materials ⋮ On solving biquadratic optimization via semidefinite relaxation ⋮ \(l^{p/2,q/2}\)-singular values of a real partially symmetric rectangular tensor ⋮ Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints ⋮ \(l^{p, q/2}\)-singular values of a real partially symmetric rectangular tensor ⋮ Positive definiteness of fourth-order partially symmetric tensors ⋮ \(l^{k,s}\)-singular values and spectral radius of rectangular tensors ⋮ Linear convergence of an algorithm for largest singular value of a nonnegative rectangular tensor ⋮ Standard bi-quadratic optimization problems and unconstrained polynomial reformulations ⋮ Bound estimations of bi-block \(M\)-eigenvalues for bi-block symmetric tensors ⋮ The solution methods for the largest eigenvalue (singular value) of nonnegative tensors and convergence analysis ⋮ Criterion of hyperbolicity in hyperelasticity in the case of the stored energy in separable form ⋮ Singular value inclusion sets for rectangular tensors ⋮ An exact solution to the Lame problem for a hollow sphere for new types of nonlinear elastic materials in the case of large deformations ⋮ Positive definiteness of paired symmetric tensors and elasticity tensors ⋮ Semidefinite relaxation approximation for multivariate bi‐quadratic optimization with quadratic constraints ⋮ A new \(S\)-type upper bound for the largest singular value of nonnegative rectangular tensors ⋮ \(l^{k,s}\)-singular values and spectral radius of partially symmetric rectangular tensors ⋮ Singular value inclusion sets of rectangular tensors ⋮ Singular values of a real rectangular tensor ⋮ Criterion for the strong ellipticity of the equations of motion of an anisotropic linear-elastic material ⋮ Generalized Baker-Ericksen inequalities ⋮ Bi-block positive semidefiniteness of bi-block symmetric tensors ⋮ Elasticity \(\mathcal{M} \)-tensors and the strong ellipticity condition ⋮ An \(S\)-type upper bound for the largest singular value of nonnegative rectangular tensors ⋮ On copositiveness identification of partially symmetric rectangular tensors ⋮ Partially symmetric nonnegative rectangular tensors and copositive rectangular tensors ⋮ A semidefinite relaxation algorithm for checking completely positive separable matrices ⋮ An efficient alternating minimization method for fourth degree polynomial optimization ⋮ Stability of classical shock fronts for compressible hyperelastic materials of Hadamard type ⋮ Computing the maximal violation of Bell inequalities for multipartite qubit via partially symmetric tensor ⋮ Conditions for strong ellipticity of anisotropic elastic materials ⋮ Two new singular value inclusion sets for rectangular tensors ⋮ Brualdi-type inclusion sets of \(Z\)-eigenvalues and \(l^{k, s}\)-singular values for tensors ⋮ Conditions for strong ellipticity and M-eigenvalues ⋮ An \(S\)-type singular value inclusion set for rectangular tensors
Cites Work
- Unnamed Item
- Unnamed Item
- On copositive matrices and strong ellipticity for isotropic elastic materials
- The pressurized hollow sphere problem in finite elastostatics for a class of compressible materials
- Ellipticity and deformations with discontinuous gradients in finite elastostatics
- 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)
- A simple derivation of necessary and sufficient conditions for the strong ellipticity of isotropic hyperelastic materials in plane strain
- On the ellipticity of the equations of nonlinear elastostatics for a special material
- On the failure of ellipticity of the equations for finite elastostatic plane strain
- An effective method of verifying Hadamard's condition for a nonlinearly elastic compressible medium
- On the theory of plane strain in finitely deformed compressible materials
- Two New Universal Relations in Nonlinear Elasticity and Some Related Matters
- Plane elastic waves of finite amplitude. Hadamard materials and harmonic materials
This page was built for publication: A reformulation of the strong ellipticity conditions for unconstrained hyperelastic media
