A direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures

This paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures. Founded on a traditional finite-step formulation, our approach, however, avoids the typically cumbersome implementation of iterative predictorcorrector procedures associated with the ubiquitous return mapping algorithm. Instead, at each predefined step, the governing formulationcast in its most natural mathematical programming format known as a mixed complementarity problemis directly solved by using a complementarity solver run from within a mathematical modeling system. We have chosen the industry-standard General Algebraic Modeling System/PATH mixed complementarity problem solver that is called from within the General Algebraic Modeling System environment. We consider both von Mises and Tresca materials, with perfect or hardening (kinematic and isotropic) behaviors. Our numerical tests, five (benchmark) examples of which are presented in this paper, have been carried out using models constructed from the mixed finite element of Capsoni and Corradi (Comput. Methods Appl. Mech. Eng. 1997; 141:6793), which beneficially offers a locking-free behavior and coarse-mesh accuracy. The results indicate, in addition to an isochoric locking-free behavior, good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of Tresca yield surfaces.