OVERVIEW OF INTEGRATION METHODS FOR ELASTOPLASTICITY Constitutive relations for elastoplasticity are generally expressed in incremental form, as described in an earlier chapter. The relation between incremental stress and incremental strain may be expressed in a general incremental form that incorporates the properties of elasticity, strain additivity, and plastic flow rule. For strain-controll...

We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via Γ-convergence for rate-independent processes that energetic solutions of the quasi-static finite-strain elastoplasticity system converge to the unique strong solution of linearized elastoplasticity.

We study incremental problems in geometrically nonlinear elastoplasticity. Using the multiplicative decomposition Dφ = FelFpl we consider general energy functionals of the form

While elastoplasticity theories at small deformations are well established for various materials, elastoplasticity theories at large deformations are still a subject of controversy and lively discussions. Among the approaches to finite elastoplasticity two became especially popular. The first, implemented in the commercial finite element codes, is based on the introduction of a hypoelastic cons...

Abstract: Many interesting tasks in technology need the solution of complex boundary value problems modeled by the mathematical theory of elasticity and elastoplasticity. Error controlled adaptive strategies should be used in order to achieve a prescribed accuracy of the computed solutions at minimum cost. In this paper, locally computed residual error indicators in the primal form of the finit...

The quasistatic problem of elastoplasticity with combined kinematic-isotropic hardening is formulated as a time-dependent variational inequality (VI) of the mixed kind, that is, it is an inequality involving a nondiierentiable functional and is imposed on a subset of a space. This VI diiers from the standard parabolic VI in that time derivatives of the unknown variable occurs in all of its term...

We consider a Newton-Krylov-FETI-DP algorithm to solve problems in elastoplasticity. First, the material model and its discretization will be described. The model contains a Prandtl-Reuss flow rule and a von Mises flow function. We restrict ourselves to the case of perfect elastoplasticity; thus, there is no hardening. For more information on elastoplasticity; see, e.g., Carstensen and Klose [2...

Optimal control problems for the variational inequality of static elastoplasticity with linear kinematic hardening are considered. The controlto-state map is shown to be weakly directionally differentiable, and local optimal controls are proved to verify an optimality system of B-stationary type. For a modified problem, local minimizers are shown to even satisfy an optimality system of strongly...