For modelling FSW a thermo-mechanical apporach should be adopted to take into account all the different phenomena enabling the determination of strain, strain rate and temperature in weld zones.
Different approaches were introduced from researchers. A semi-analytical model can be found for example in the following manuscript: http://www.sciencedirect.com/science/article/pii/S0924013605007570
Please refer the following article for useful info.
Integrated modeling of friction stir welding of 6xxx series Al alloys: Process, microstructure and properties, Progress in Materials Science 57 (2012) 95–183.