High order mesh-free method for frictional contact

This work concerns numerical simulations of the frictional contact of two elastic deformable bodies and a novel treatment technique of incompatible contact nodes. These numerical simulations are based on a high order mesh-free method coupling the Moving Least Square (MLS) with the Asymptotic Numerical Method (ANM) and on a regularization technique. The obtained nonlinear problem is solved by using ANM applied on strong formulation in order to avoid numerical integrations. According to ANM, the Taylor series development of unknown variables on nodes of nonlinear contact problem leads to a sequence of linear systems to be solved. These linear systems are then discretized by a collocation mesh-free approach by using the MLS functions and a continuation method is adopted to evaluate the solution. The contact problem is identified to boundary conditions which are replaced by force-displacement relations through a regularization technique. The ability of the proposed approach is tested on some contact elastic deformable bi-dimensional examples. The obtained results are compared to an analytical solution and to a numerical solution obtained by the Newton-Raphson method coupled also with MLS approximation.