Adaptive method for phase-field fracture using a volume weighted Quickselect algorithm

The phase-field fracture method (PFM) requires an extremely fine mesh to accurately capture the crack topology, which is computationally expensive. In this work, a new adaptive mesh refinement method is proposed for phase-field fracture. Based on the phase field increment, a volume weighted Quickselect algorithm is used to determine the coarsen region and the refined region. The speed of the crack propagation is predicted to control the size of the refined region, which reduces unnecessary degrees of freedom. Several benchmark numerical examples are simulated and the results demonstrate the efficiency and accuracy of the proposed method. In the numerical examples, the computational time using this method is reduced by about 90% compared with the standard PFM.