A p ‐version finite element approach for two‐ and three‐dimensional problems of the J 2 flow theory with non‐linear isotropic hardening

In this paper an implementation of a two‐ and three‐dimensional p ‐version approach to the J 2 flow theory with non‐linear isotropic hardening for small displacements and small strains is presented. Based on higher‐order quadrilateral and hexahedral element formulations, a Newton–Raphson iteration scheme combined with a radial return algorithm is applied to find approximate solutions for the underlying physically non‐linear model problem. Curved boundaries are taken care of with the blending function method, allowing an accurate representation of geometry with only a few p ‐elements. Numerical examples demonstrate, that the p ‐version supplies efficient and accurate approximations to this class of physically non‐linear problems. Copyright © 2001 John Wiley & Sons, Ltd.