A numerical mesh-free model for elasto-plastic contact problems

A numerical mesh-free model applied to a strong formulation for simulating elasto-plastic structures with contact is developed in the context of large deformation. This numerical mesh-free model is based on the Asymptotic Numerical Method (ANM) which is used in the meshless collocation framework to extend its application field to elasto-plastic problems with contact. The efficiency of this model is to take into account of large deformations and to avoid the meshing distortion problem. According to (ANM) techniques, the development in Taylor series is performed to obtain a sequence of linear systems to be solved. These linear systems are then discretized by a collocation meshless approach by using the Moving Least Squares (MLS) functions and a continuation method is adopted to evaluate the solution. The unilateral contact problem is identified to boundary conditions which are replaced by force-displacement relations through a regularization technique. The performance of the proposed approach is tested on several elasto-plastic bi-dimensional examples without and with contact. The obtained results are compared to those computed by the Newton-Raphson method.