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Mathematical Problems in Engineering
Volume 2015, Article ID 486346, 16 pages
Research Article

A Robust Numerical Procedure for the Thermomechanical Flow Simulation of Friction Stir Welding Process Using an Adaptive Element-Free Galerkin Method

1Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94551, USA
2General Motors, 30500 Mound Road, Warren, MI 48090, USA
3Hengstar Technology Corporation, Shanghai 201203, China

Received 24 March 2015; Revised 21 June 2015; Accepted 23 June 2015

Academic Editor: Vladimir Turetsky

Copyright © 2015 C. T. Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A meshfree modeling technique of material flow in the three-dimensional multiphysics thermomechanical friction stir welding process is presented. In this numerical model, the discretization in space is derived by the Element-Free 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 thermomechanical 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 multiphysics thermomechanical coupled friction stir welding problem is analyzed to demonstrate the effectiveness of the present meshfree numerical procedure.