Application of the proper generalized decomposition to elasto-plastic finite element analysis

Abstract

The aim of this paper is to develop the PGD for time dependent elastoplastic problems with cyclic loadings. The objective is to show that the PGD can be well suited for simulating a ratchet effect by separating space and time, and using a finite element approximation for both variables. The first part of this paper is dedicated to the mechanical formulation of the problem and especially the nonlinear behavior of the material. Then, the PGD approximation and the finite element discretization are presented, as well as the computational strategy. Finally, two examples are presented to show the capability of the method.