On realizing specific failure initiation criteria in the phase field model

In the phase field model (PFM), fracture timing and direction are determined automatically by the stationary condition of the system’s potential, it is normally considered an advantage since not a failure initiation criterion is required to be appointed. However, it may become an obstacle when a specific failure criterion is required to calculate the fracture timing and direction. In order to solve this issue, we propose a simple way to embed different failure criteria into the PFM in this work. On one hand, an activation parameter is introduced into the PFM’s driving force to control the fracture timing, and the parameter’s value is one if the specified criterion is satisfied and is zero otherwise. On the other hand, a structural tensor is introduced into the PFM’s surface density function to reflect the fracture direction predicted by the specified criterion. The fracture evolution direction is enforced in line with the criterion through a penalty parameter. The proposed PFM is implemented into ABAQUS through using the user-defined element (UEL) subroutine, and comparisons with the extended finite element method (XFEM) and experiments are provided for verification and validation.