an efficient implementation of phase field method with explicit time integration

The phase field method integrates the griffith theory and damage mechanics approach to predict crack initiation, propagation, and branching within one framework. no crack tracking topology is needed, and complex crack shapes can be captures without user intervention. in this paper, a detailed description of how the phase field method is implemented with explicit dynamics into lsdyna is provided. the displacement field and the damage field are solved in a staggered approach and the phase field equation is solved every nth time step (n is refered to as calculation cycle) to save computational time. an n value smaller than 1/400 of the total time step numbers is suggested. several simulations are presented to demonstrate the feasibility of this solving scheme.