Numerical algorithm for solving the elasto-plastic problem with isotropic hardening and the plane stress state

In this paper a numerical approach of the elasto-plastic problem with mixed hardening in the plane stress state, within the classical constitutive framework of small deformation, is proposed. In the formalized problem, the non-zero normal component of the strain (namely, the component in the direction perpendicular to the plane of stress) is considered to be compatible with the plane stress. We eliminate the rate of strains which develop normal to the plane and we solve an appropriate plane problem in the strain setting. The numerical algorithm (which is an incremental one) consists of the Radial Return Mapping Algorithm, originally proposed by Simo and Hughes [21], adapted to the stress plane problem and coupled with a pseudo-elastic problem. The proposed algorithm has been called the revisited Simo algoritm and it is applied to exemplify the mode of integration of the bidimensional problem. Key–Words: elasto-plastic model, finite element method, variational formulation, plain stress, Radial Return Mapping Algorithm, numerical simulation