A space–time adaptive solution scheme for phase field fracture model

To accurately capture the crack evolution, a finer mesh is required in the region of crack propagation, resulting in a higher computational cost for the phase field model. In order to improve the computational efficiency, a space–time adaptive solution scheme is proposed in this work. An adaptive remeshing technique is used to adaptively refine the mesh in the space field, the mesh size characteristics are coupled with the phase field variable to control the time incremental changes in the time field. In this scheme, a coarse grid is first used to obtain the initial crack paths and element energy distribution, and the mesh is automatically refined based on the element energy distribution. Second, the time field alteration criterion is presented by coupling the change of the mesh size in the spatial field with the change of the phase field variable. The time increment is adaptively varied based on the changes of mesh size and phase field value in the solution region to reduce the calculated burden. The proposed scheme is validated by some examples. Whether it is a single-mode failure or a mixed-mode failure, the adaptive solution scheme can significantly reduce the number of elements and the computation time. At the same time, complex crack trajectories can be effectively simulated and accurate load–displacement curves obtained, which makes it possible to use the phase field model to the failure analysis of complex structures in practical engineering.