An Adaptive Meshfree Galerkin Method for the Three-dimensional Thermo-mechanical Flow Simulation of Friction Stir Welding Process

In this paper, new numerical modeling of material flow in the thermo-mechanical friction stir welding process is presented. In this numerical model, the discretization in space is derived by the meshfree Galerkin method using a Lagrangian meshfree convex approximation. The discrete thermal and mechanical equations are weakly coupled as the time advances using a forward difference scheme. A mortar contact algorithm is employed to model the stirring effect and heat generation due to frictional contact. Heat conductance between contacting bodies is considered as a function of contact pressure. A two-way adaptive procedure is introduced to the coupled thermo-mechanical system to surpass potential numerical problems associated with the extensive material deformation and spatial discretization. In each adaptive phase, a consistent projection operation utilizing the first-order meshfree convex approximation is performed to remap the solution variables. Finally, a three-dimensional thermo-mechanical coupled friction stir welding problem is analyzed to demonstrate the effectiveness of the present formulation.