Robust Symmetric Formulations for Nonassociated Plasticity Problems

Abstract

Most engineering material behaviors can be described by using nonassociated plasticity models, but their use leads to the formation of unsymmetric matrices that have, to date, been resolved by nonsymmetric solvers, the initial stiffness method, and, more recently, some symmetrization techniques. Some of these methods have proved to be inefficient due to large core storage requirements, excessive iteration, and slow rate of convergence; or the existence of regions of numerical instability within the mapping process. Some robust techniques are outlined in this paper that are capable of providing solutions of acceptable accuracy for nonassociated plasticity problems, by adapting them for banded, symmetric solvers and by returning CPU times comparable to the best available solution techniques. Numerical solutions to problems in both soil and nongranular plasticity are provided to illustrate the capability of the proposed techniques, and the problem of numerical instability inherent in a previous symmetrization technique is addressed.