Symmetrization Method for the Generalized Plasticity Model with Nonassociated Plastic Flow Rule

Abstract

When the generalized plasticity model with nonassociated flow rule is utilized to simulate the mechanical behaviors of sands, the asymmetric elastoplastic matrices or coefficient matrix has to be encountered in finite-element (FE) computations, posing a great challenge to the solution of large-scale asymmetric linear systems of equations. In this study, a simple symmetrization method for the asymmetric stiffness matrix attributable to the generalized plasticity model is presented and then verified by simulating a series of triaxial tests involving the asymmetric stiffness matrices. Furthermore, the symmetric and asymmetric preconditioned iterative methods are employed to solve the asymmetric and symmetrized FE linear systems of equations, respectively, arising from a three-dimensional earth dam example. Finite-element elastoplastic dynamic analyses of the dam show that compared with the solution method based on the asymmetric FE equation, the symmetrization method can produce accurate results, but with remarkably less computational time and random-access memory (RAM) requirement.