On the uniqueness of energy minimizers in finite elasticity
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Publication:2424211
DOI10.1007/s10659-018-9671-8zbMath1415.74042OpenAlexW2785950014MaRDI QIDQ2424211
Spector, Scott J., Sivaloganathan, Jeyabal
Publication date: 24 June 2019
Published in: Journal of Elasticity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10659-018-9671-8
uniquenessnonlinear elasticityfinite elasticityenergy minimizersequilibrium solutionsnonuniquenessstrict polyconvexitystrongly polyconvexuniform polyconvexity
Variational inequalities (49J40) Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) Optimization of other properties in solid mechanics (74P10) Uniqueness of solutions of equilibrium problems in solid mechanics (74G30) PDEs in connection with mechanics of deformable solids (35Q74) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Boundary value problems for second-order elliptic systems (35J57)
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Cites Work
- Unnamed Item
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- Radially symmetric steady states of nonlinearly elastic plates and shells
- Normality condition in elasticity
- Existence theorems in intrinsic nonlinear elasticity
- Surface interaction potentials in elasticity
- \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
- Energy minimizers in nonlinear elastostatics and the implicit function theorem
- Non-uniqueness of minimizers for strictly polyconvex functionals
- Direct approach to the problem of strong local minima in calculus of variations
- The generalised Hamilton-Jacobi inequality and the stability of equilibria in nonlinear elasticity
- On the symmetry of energy-minimising deformations in nonlinear elasticity. II: Compressible materials
- Neohookean deformations of annuli, existence, uniqueness and radial symmetry
- Weak local minimizers in finite elasticity
- On bifurcation in finite elasticity: Buckling of a rectangular rod
- Quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity
- Quasiconvexity and partial regularity in the calculus of variations
- Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity
- Fine phase mixtures as minimizers of energy
- The remarkable nature of radially symmetric equilibrium states of aeolotropic nonlinearly elastic bodies
- Regularity properties of deformations with finite energy
- On uniqueness in finite elasticity with general loading
- On stability and uniqueness in finite elasticity
- The eversion of thick spherical shells
- New integral estimates for deformations in terms of their nonlinear strains
- Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems
- Quasiconformal mappings and spaces of functions with generalized first derivatives
- Convexity conditions and existence theorems in nonlinear elasticity
- An isoperimetric estimate and \(W^{1,p}\)-quasiconvexity in nonlinear elasticity
- Partial regularity of strong local minimizers in the multi-dimensional calculus of variations
- On the convexity of nonlinear elastic energies in the right Cauchy-Green tensor
- An introduction to continuum mechanics
- On configuration-dependent loading
- \(H^p\) spaces of several variables
- A remark on polyconvex functions with symmetry
- Biting theorems for Jacobians and their applications
- Extending the Knops-Stuart-Taheri technique to $C^{1}$ weak local minimizers in nonlinear elasticity
- ON RIGID AND INFINITESIMAL RIGID DISPLACEMENTS IN THREE-DIMENSIONAL ELASTICITY
- Some Open Problems in Elasticity
- Higher integrability of determinants and weak convergence in L1.
- On functions of bounded mean oscillation
- Sufficient conditions for strong local minima: The case of $C^{1}$ extremals
- Polyconvexity, generalised twists and energy minimizers on a space of self-maps of annuli in the multi-dimensional calculus of variations
- Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
- Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions
- Stability of pure homogeneous deformations of an elastic cube under dead loading
- On homotopy conditions and the existence of multiple equilibria in finite elasticity
- Quasiconvexity and uniqueness of stationary points in the multi-dimensional calculus of variations
- Uniqueness of non-linear elastic equilibrium for prescribed boundary displacements and sufficiently small strains
- A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
- Variational Methods in Nonlinear Elasticity
- Twists and shear maps in nonlinear elasticity: explicit solutions and vanishing Jacobians
- Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance
- Direct methods in the calculus of variations
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