We propose different staggered resolution strategies of the variational phase field fracture formulation using a fully explicit time integration scheme. Parabolic or hyperbolic partial differential equations (PDE) are two alternatives governing the damage evolution and compatible with explicit solvers. We have implemented these models and compared with the standard elliptic damage formulation. The results show globally similar qualitative behavior, but highlight the challenge in the interpretation of additional physical parameters introduced in the damage PDE of the phase field models.