An explicit phase field method for brittle dynamic fracture

In this paper, we propose an explicit phase field model for dynamic brittle fracture. The mechanical field is integrated with a Verlet-velocity scheme, while the phase field is incremented with sub-steps at each step. The sub-stepping is adaptive based on the phase field residual and fast convergence is obtained in a few sub-steps. The numerical difficulty in convergence and the calculation of anisotropic stiffness tensor in the implicit phase field model are avoided in the explicit scheme. The explicit phase field model uses the phase field modulus, rather than the conventional phase field viscosity. The proposed scheme can achieve the same result by the implicit dynamic scheme phase field model. Several numerical examples are presented to validate the explicit method.