Multi-level adaptive mesh refinement technique for phase-field method

In order to solve the contradiction between the calculation efficiency and accuracy of the phase -field method (PFM), a multi-level adaptive mesh refinement technique suitable for PFM was developed and improved. A multi-level mesh refinement method of 2-D quadrilateral elements including three-layer transition elements without hanging nodes is designed, and the automatic refinement crack tip elements is realized by combining the phase field value. The local element coarsening technique is adopted to solve the problem of rapid elements number growth and reduce elements number in the calculation process. Combined with backtracking algorithm and "tree structure" node information storage technique, crack propagation is simulated. Through the benchmark example, the accuracy of the multi-level adaptive mesh refinement technique and the applicability to non-orthogonal mesh are verified, and the efficiency is greatly improved. For more complex crack propagation, the simulation results are also in good agreement with the experimental results. The critical gradient method proposed at last can find the refinement range more accurately and reduce elements number, which shows a great prospect in engineering applications.