Tracking of material orientation in updated Lagrangian SPH

This contribution demonstrates a continuum-mechanics-based method which yields the possibility of material orientation tracking within the smoothed particle hydrodynamics framework. The functionality provides the information on local orientation of particles, which is necessary for anisotropic material models, e.g., the kinematic hardening rule proposed by Prager. Such a model is expected to provide a possibility of a more precise simulation of complex industrial processes such as friction stir welding with three-dimensional material flow. The derivation of the method is presented for the updated Lagrangian formulation, in which the increment of the quaternion for the material point can be extracted from the gradient of velocity, following the continuum mechanics description. The examples of different complexity are demonstrated in order to verify the method: the rotating cylinder, torsion test, and industrial turning process. Additionally, the importance of kernel gradient correction adoption in order to preserve angular momentum in the presence of rotations is showcased.