An efficient and robust staggered scheme based on adaptive time field for phase field fracture model

Abstract

The standard staggered scheme in phase field model is computationally slow, so that a large amount of iterations are required. In order to improve the computational efficiency, a novel efficient and robust solution scheme based on adaptive time field is proposed in this paper. This scheme is inspired by the adaptive mesh method for space field, and an error indicator based on phase field and history field variables is established, where the time field is coupled with the phase field and energy field in the space field, so that the time field changes adaptively with the computational iterative process, which improves the convergence rate and reduces the time cost. The numerical results show that the presented novel scheme not only significantly improves the computational efficiency, but also has accurate computational results. Compared with the standard staggered scheme, the time cost of the presented scheme is less than 4% of that of the standard scheme. At the same time, the computational efficiency of the presented solver is faster than the current monolithic BFGS scheme, and it has excellent convergence characteristics.