Elastic plastic deformation

DOI10.1007/BF01448387zbMath0522.73029OpenAlexW2071096182MaRDI QIDQ1056254

David Kinderlehrer, Robert M. Hardt

Publication date: 1983

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01448387

zbMATH Keywords

potential energy functionalsolid continuumduality of first problem and regularity properties of solutionelastic plastic deformationexistence of elastic and plastic statesfirst variations gives equilibrium equationsstress expressed in terms of straintransition to fracture

Mathematics Subject Classification ID

Related Items (22)

Strong solution for an elastic-plastic plate ⋮ Improved Lp-estimates for the strain velocities in hardening problems ⋮ On time flows of minimizers of general convex functionals of linear growth with variable exponent in BV space and stability of pseudosolutions ⋮ Regularity results for two standard models in elasto-perfect-plasticity theory with hardening ⋮ Equilibrium configurations of crystals ⋮ Total variation time flow with quantile regression for image restoration ⋮ On Prandtl-Reuss Mixtures ⋮ The obstacle problem for an elastoplastic body ⋮ The Incompatibility Operator: from Riemann’s Intrinsic View of Geometry to a New Model of Elasto-Plasticity ⋮ An evolution problem for plastic antiplanar shear ⋮ A partial regularity result for an anisotropic smoothing functional for image restoration in BV space ⋮ A revision of results for standard models in elasto-perfect-plasticity theory ⋮ Analysis of a new variational model for image multiplicative denoising ⋮ Differentiability properties of weak solutions of certain variational problems in the theory of perfect elastoplastic plates ⋮ Differential properties of solutions of variational problems for functionals of linear growth ⋮ Local minima of nonconvex problems ⋮ Dislocation microstructures and the effective behavior of single crystals ⋮ The Euler Equation for Functionals with Linear Growth ⋮ Fractional differentiability for the stress velocities to the solution of the Prandtl-Reuss problem ⋮ Convex duality and uniqueness for BV-minimizers ⋮ A class of convex non-coercive functionals and masonry-like materials ⋮ On Carathéodory Quasilinear Functionals for BV Functions and Their Time Flows for a Dual $$ H^{1}$$ Penalty Model for Image Restoration

Cites Work

• Dual spaces of stresses and strains, with applications to Hencky plasticity
• Existence of the displacements field for an elasto-plastic body subject to Hecky's law and von Mises yield condition
• On the existence of the fields of stresses and displacements for an elasto-perfectly plastic body in static equilibrium
• Functions of bounded deformation
• New integral estimates for deformations in terms of their nonlinear strains
• The Lipschitz character of the stress tensor, when twisting an elastic plastic bar
• The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
• Multiplicateur de Lagrange en torsion elasto-plastique
• Sublinear functions of measures and variational integrals
• Un espace fonctionnel pour les équations de la plasticité
• On the continuity of the trace of vector functions with bounded deformation
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
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