Effective stress-based finite element error estimation for composite bodies

Abstract

This paper presents a discretization error estimator for displacement-based finite element analysis applicable to multi-material bodies such as composites. The proposed method applies a specific stress continuity requirement across the intermaterial boundary consistent with physical principles. This approach estimates the discretization error by comparing the discontinuous finite element effective stress function with a smoothed ( C 0 continuous) effective stress function for non-intermaterial boundary elements with a smoothed pseudo-effective stress function for elements which lie on the intermaterial boundary. Examples are presented which illustrate the effectiveness of the multi-material error estimator. The pointwise pseudo-effective stress and the L 2 norm of the estimated stress error are seen to converge with mesh refinement, while Zienkiewicz and Zhu's error estimator failed to converge for elements on the intermaterial boundary due to the physically admissible stress discontinuities that exist on the intermaterial boundary.