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

• Published in: Computer methods in applied mechanics and engineering Vol. 176; no. 1; pp. 187 - 202
• Main Authors: Cramer, H., Findeiss, R., Steinl, G., Wunderlich, W.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 06.07.1999
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/S0045-7825(98)00336-3

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.