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

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...

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Published inComputer 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
LanguageEnglish
Published Elsevier B.V 06.07.1999
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Abstract 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.
AbstractList 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.
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.
Author Findeiss, R.
Wunderlich, W.
Steinl, G.
Cramer, H.
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Cites_doi 10.1016/0045-7825(92)90020-K
10.1016/0045-7825(91)90184-8
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Cramer, Rudolph, Steinl, Wunderlich (bib1) 1996
Ortiz, Quigley (bib3) 1991; 90
Johnson, Hansbo (bib2) 1992; 101
Johnson (10.1016/S0045-7825(98)00336-3_bib2) 1992; 101
Ortiz (10.1016/S0045-7825(98)00336-3_bib3) 1991; 90
Wunderlich (10.1016/S0045-7825(98)00336-3_bib4) 1996
Cramer (10.1016/S0045-7825(98)00336-3_bib1) 1996
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