A fully coupled thermo-mechanical model was developed to study the temperature fields and the plastic deformations of alloy AL6061-T6 under different process parameters during the friction stir welding （FSW） process. Three-dimensional results under different process parameters were presented. Results indicate that the maximum temperature is lower than the melting point of the welding material. The higher temperature gradient occurs in the leading side of the workpiece. The calculated temperature field can be fitted well with the one from the experimental test. A lower plastic strain region can be found near the welding tool in the trailing side on the bottom surface, which is formed by the specific material flow patterns in FSW. The maximum temperature can be increased with increasing the welding speed and the angular velocity in the current numerical modelling.
Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.
