Error estimators and enrichment procedures for the finite element analysis of thin sheet large deformation processes

An essentially geometric error measure capable of estimating the accuracy with which a faceted element mesh describes the continjous exact geometry of a deforming sheet is presented in this paper. This error is based on an estimated strain tensor between discrete and approximate geometries. Additionally, the paper describes the enrichment process which, at a reasonable computational cost, ensures that the error targets are met whilst generating as few elements as possible. In particular, the enrichment algorithm is based on a judicious combination of two simple operations, namely, side splitting and diagonal swapping. Finally, several applications relating to superplastic forming components are presented.