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Modelling and Simulation in Engineering
Volume 2013, Article ID 716383, 14 pages
Research Article

An Implicit Algorithm Based on Continuous Moving Least Square to Simulate Material Mixing in Friction Stir Welding Process

1Laboratoire d’Ingénierie et Matériaux LIMAT, Faculte des Sciences Ben M’Sik, Université Hassan II Mohammedia-Casablanca, Sidi Othman, BP 7955, Casablanca, Morocco
2Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux LEM3, CNRS UMR 7239, Université de Lorraine, Ile du Saulcy, 57045 Metz Cedex 01, France

Received 25 June 2013; Revised 16 September 2013; Accepted 30 September 2013

Academic Editor: Jean-Michel Bergheau

Copyright © 2013 Abdelaziz Timesli 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.


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.