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

• Published in: International journal for numerical methods in engineering Vol. 90; no. 7; pp. 838 - 866
• Main Authors: Tangaramvong, S., Tin-Loi, F., Song, Ch
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 18.05.2012; Wiley
• Subjects: complementarity; elastoplastic analysis; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); material nonlinearity; material nonlinearity, mathematical programming; mathematical programming; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); mixed finite element; Numerical analysis. Scientific computation; Physics; Sciences and techniques of general use; Solid mechanics; Static elasticity (thermoelasticity...); stepwise holonomic; Structural and continuum mechanics; Non linear material; Biaxial stress; material nonlinearity; Iterative method; Complementarity problem; Modeling; Return mapping; Predictor corrector method; Finite element method; elastoplastic analysis; Inelasticity; Algebraic system; Elastoplasticity; Isotropic hardening; complementarity; Von Mises criterion; Mathematical programming; Locking; Stress analysis; Stress strain relation; Wedge; Mixed method; Kinematic hardening; Meshless method; Plane strain; mixed finite element; stepwise holonomic; Mixed problem
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.3346

SUMMARY 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 predictor–corrector procedures associated with the ubiquitous return mapping algorithm. Instead, at each predefined step, the governing formulation—cast in its most natural mathematical programming format known as a mixed complementarity problem—is 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; 141:67–93), 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. Copyright © 2012 John Wiley & Sons, Ltd.