An implicit iterative algorithm, based on the continuous moving least square (CMLS), is developed to simulate material mixing in Friction Stir Welding (FSW) process. Strong formulation is chosen for the modeling of the mechanical problem in Lagrangian framework to avoid the drawback of numerical integration. This algorithm is well adapted to large deformations in the mixing zone in the neighborhood of the welding tool. We limit ourselves to bidimensional viscoplastic problem to show the performance of the proposed implicit algorithm. The results show that the proposed algorithm can be employed to simulate FSW. 1. Introduction Friction stir welding (FSW) [1] is a solid state welding process used to join two pieces (plates, tubes, spheres, etc.) of aluminum alloys. Joining two workpieces by FSW consists in heat generation mainly due to the shoulder and material mixing thanks to the pin that provokes both extremely high plastic deformation and also a high heat generation. Numerical simulation of friction stir welding process is important in industry to control the product quality and optimize the fabrication cost and avoid the traditional tests. It has been investigated by several authors considering thermal or thermomechanical framework [2–8]. The difficulty in modeling this welding type resides to large deformations generated by the material mixing. Different formulations have been proposed in Eulerian, Lagrangian, or Arbitrary Lagrangian Eulerian frameworks. Eulerian formulation is appropriate to describe material flow for large deformations thanks to fixed mesh grid but this formulation cannot be used for problems involving free surfaces. Lagrangian formulation is well adapted for history dependence in solids and for simulation of material flow with free surfaces but mesh distortions require special procedure as remeshing. The ALE formulation has been proposed to benefit from both advantages of Eulerian and Lagrangian formulations [3]. In this technique, one has to describe the motion of the mesh and material particles separately with respect to a reference domain. ALE has been applied successfully in many fields and particularly in metal forming processes. Despite the intensive development of these techniques, material mixing in FSW process remains very difficult to achieve numerically and especially when using finite element method [2, 3]. An alternative solution for the simulation of this process is the use of meshless methods. Indeed, these techniques are developed for several decades to solve partial differential equations. They aim to avoid
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