An approach to the adaptive finite element analysis in associated and non-associated plasticity considering localization phenomena

摘要

In an adaptive finite element approach elastoplastic problems with associated and non-associated flow rules are investigated. The first part of the paper deals with the underlying numerical formulation for a classical continuum model and a hierarchical h-adaptive mesh refinement strategy. Essential ingredients of the adaptive process are a suitable error indicator and transfer operations for the mapping of history-dependent state variables between different meshes. These are imbedded in a nonlinear incremental finite element procedure. For non-associated plasticity a standard continuum approach may lead to an ill-posed problem. Therefore, in the second part a generalization in the framework of a Cosserat theory is considered. The underlying equations possess a similar structure, and the adaptive finite element formulation can be extended in a straightforward manner. Numerical examples demonstrate the general applicability of the approach to elastoplastic problems including associated as well as non-associated plasticity. They show the superior behaviour of the Cosserat fOrmulation in the case of localization phenomena also for non-associated plasticity.