A novel h‐adaptive finite element method for standard dissipative media at finite strains based on energy minimization

Abstract

AbstractA novel h‐adaptive finite element strategy for standard dissipative media at finite strains based on energy minimization is presented. The method can be applied to any (incremental) minimization problem to be analyzed by finite elements. Similarly to an error estimator by Babǔska & Rheinboldt, the proposed error indicator is based on solving a local Dirichlet‐type problem. However, in contrast to the original work, a different error indicator is considered. Provided the underlying physical problem is governed by a minimization problem, the difference between the energy of the elements defining the local problem computed from the initial finite element interpolation and that associated with the local Dirichlet‐type problem is used as an indicator. If this difference reaches a certain threshold, the elements defining the local problem are refined by applying a modified longest edge bisection according to Rivara. Since this re‐meshing strategy leads to a nested family of triangulations, the transfer of history variables necessary to describe dissipative materials is relatively inexpensive. The presented h‐adaption is only driven by energy‐minimization. As a consequence, anisotropic meshes may evolve if they are energetically favorable. The versatility and rate of convergence of the resulting approach are illustrated by means of selected numerical examples. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)