Key words: Elasto-plasticity, numerical analysis, EFGM, MLS, transformation method.

Abstract: In this paper, we present a theoretical and numerical analysis of elasto-plastic problems based on the element-free Galerkin method (EFGM) and the numerical analysis. The study has been examined in planar stress analysis around the tip of a crack and in its opening mode of loading. In the EFGM, the implementation of the Moving Least Squares (MLS) approximation is used to obtain the approximation function and the transformation method is proposed to impose the essential boundary conditions. The discritized variational formulation for elasto-plastic materials obeying to the von Mises criterion is presented. To examine the validity of this technique, stress fields in a plate with a crack have been calculated.