2D Mesh less Solution of Elastoplastic with Damage Problem

The Finite Element Method (FEM) is today the most widely used in numerical simulation of forming processes, due essentially to the continuous improvement of the FEM over the years and the simplicity of its implementation. However, this method has some limitations such as the distortion of elements under large inelastic deformation and the influence of the mesh on the results in several applications. The simulation of metal forming process with large plastic strain is a classical example where the successive re meshing is often the proposed solution in this case. But the re meshing raises the problems of precision and computing time. In this context and in order to avoid the re meshing process, a Meshless method is experimented in the solving of an elastoplastic problem coupled to the isotropic ductile damage. An Element Free Galerkin (EFG) method based on Moving Least Square (MLS) concept is considered in this proposal. A two-dimensional Mechanical problem was studied and solved by a Dynamic-Explicit resolution scheme where the material behaviour is based on an isotropic hardening fully coupled to ductile damage model. In a first step a parametric study is conducted in order to find the most influent parameters on the accuracy of the results. The effect of the number of nodes, of support nodes, of quadrature points, the effect of the time-step and the support domain size are analysed and optimal values are found. In a second step, the meshless results are compared with those of the finite element method and some concluding remarks relative to the accuracy and the computing time are given.