Energy minimizers in nonlinear elastostatics and the implicit function theorem

DOI10.1007/BF00375399zbMath0734.73009OpenAlexW2036386469MaRDI QIDQ811156

Kewei Zhang

Publication date: 1991

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00375399

zbMATH Keywords

null Lagrangianstability problemgeneral smooth solutionhomogeneous compressible hyperelasticpolyconvex stored energy functionpure displacement boundary value problem

Mathematics Subject Classification ID

Related Items (21)

A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation ⋮ On the uniqueness of energy minimizers in finite elasticity ⋮ Well-posedness and regularity for a polyconvex energy ⋮ A nonlinear Korn inequality with boundary conditions and its relation to the existence of minimizers in nonlinear elasticity ⋮ A uniqueness criterion and a counterexample to regularity in an incompressible variational problem ⋮ (High frequency-) uniqueness criteria for \(p\)-growth functionals in in- and compressible elasticity ⋮ Lipschitz estimates and existence of correctors for nonlinearly elastic, periodic composites subject to small strains ⋮ A continuously perturbed Dirichlet energy with area-preserving stationary points that `buckle' and occur in equal-energy pairs ⋮ Compensated convexity and its applications ⋮ Uniqueness of equilibrium with sufficiently small strains in finite elasticity ⋮ Elastostatics in the presence of a temperature distribution or inhomogeneity ⋮ Existence theorems in intrinsic nonlinear elasticity ⋮ On the symmetry of energy-minimising deformations in nonlinear elasticity. I: Incompressible materials ⋮ Mixed Kirchhoff stress-displacement-pressure formulations for incompressible hyperelasticity ⋮ Quantitative homogenization in nonlinear elasticity for small loads ⋮ Minimizers with topological singularities in two dimensional elasticity ⋮ Twists and shear maps in nonlinear elasticity: explicit solutions and vanishing Jacobians ⋮ Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems ⋮ The pure displacement problem in nonlinear three-dimensional elasticity: Intrinsic formulation and existence theorems ⋮ On bifurcation in finite elasticity: Buckling of a rectangular rod ⋮ Resolution of some hyperelastic image-matching problems

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