A computational model for elasto-viscoplastic solids at finite strain with reference to thin shell applications

Abstract

This work extends a previously developed methodology for computational plasticity at finite strains that is based on the exponential map and logarithmic stretches to the context of isotropic elasto-viscoplastic solids. A particular form of the strain-energy function, given in terms of its principal values is employed. It is noticeable that within the proposed framework, the small strain integration algorithms, and the corresponding consistent tangent operators, automatically extend to the finite strain regime. Central to the effort of this formulation is the derivation of the closed form of a tangent modulus obtained by linearization of incremental non-linear problem. This ensures asymptotically quadratic rates of convergence of the Newton–Raphson procedure in the implicit finite element solution. To illustrate the performance of the presented formulation, several numerical examples, involving failure by strain localization and finite deformations, are given. © 1998 John Wiley & Sons, Ltd.