An accurate approach to simulate friction stir welding processes using adaptive formulation refinement

A novel Adaptive Formulation Refinement (AFR) strategy for Friction Stir Welding (FSW) problems is presented. In FSW, the accurate computation of strains is crucial to correctly predict the highly non-linear material behavior in the stir zone. Based on a posteriori error estimation, AFR switches between two mixed formulations depending on the required accuracy in the different regions of the domain. The higher accuracy formulation is used in the thermo-mechanically affected zone (TMAZ), while a computationally cheaper formulation is used elsewhere. AFR adds to the well-known h- (mesh size), p- (polynomial degree) and r-refinement (spatial distribution) approaches. The considered mixed formulations are the velocity/pressure (u/p) and the velocity/pressure/deviatoric strain rate (u/p/e) formulations-both suitable for isochoric material flow. By applying the AFR strategy, the use of linear elements is preserved, the incompressible flow of the material is captured correctly and any remeshing is avoided. Furthermore, the treatment of the interface between refined and unrefined subdomains is straightforward due to the compatibility of variable fields and lack of hanging nodes. The accuracy of the results obtained from the AFR method compares favorably with reference results of the non-adaptive u/p/e formulation. At the same time, faster build and solve times are achieved.