Error indicators and adaptive remeshing in large deformation finite element analysis

We present and use a system of adaptive procedures for large-deformation finite element analysis of elastic and elastoplastic problems using the h-refinement approach. The procedures include a pointwise indicator for error in stresses, a pointwise indicator for error in plastic strain increments, a quadrilateral element mesh generator for generating completely new meshes on the deformed configuration of the body, and several mapping schemes for transferring state variables and history-dependent variables accurately across models. These procedures constitute the ingredients of a proposed adaptive scheme that is demonstrated to be effective in solutions of two-dimensional stress analysis problems including contact conditions. An important observation is that with coarse finite element meshes and no error indicator used, crucial physical phenomena may be completely missed in the analysis.