Explicit consistent tangent moduli with a return mapping algorithm for pressure-dependent elastoplasticity models

Abstract

In order to preserve the quadratic rate of asymptotic convergence, for the widely-used iterative schemes based on Newton's method, it is crucial to ensure consistency between the tangent moduli and the integration algorithm. By exact linearization of the algorithm and decomposition of the stresses into hydrostatic and deviatoric parts, a method is presented whereby an explicit expression for the tangent moduli consistent with a closest point return mapping algorithm may be developed for generalized pressure-dependent elastolasticity models. One significant advantage of this method is that no matrix inversion is necessary in the consistent tangent moduli expression. For classical J 2 elastoplasticity associated with an isotropic hardening rule problem, the present consistent tangent moduli coincide with consistent tangent moduli given by others. Application is made to fixed Gurson-based model as well as Gurson-based model. The excellent convergence performance of the consistent tangent moduli is illustrated in numerical experiments.