The phase-field fracture model enriched by interpolation cover functions for brittle fracture problems

Abstract

In this study, interpolation cover functions were introduced into the phase-field fracture model (PFM) to improve its convergence and efficiency. The traditional PFM has proven to be successful in simulating brittle fracture problems. However, one disadvantage is that it requires a relatively dense mesh. The PFM model enriched by interpolation cover functions (EPFM) was used for numerical fracture analysis under a relatively coarse mesh. The rank deficiency problem caused by the introduction of interpolation cover functions was resolved using the rank deficiency repair technique. Higher gradients were captured by introducing interpolation cover functions without changing the mesh structure. The numerical examples showed the improvement in convergence. The high efficiency of the proposed EPFM was demonstrated through a series of numerical examples. The numerical results of the EPFM and PFM under different length-scale parameters and meshes were also compared. The results showed that the proposed EPFM is an excellent alternative for evaluating engineering fracture problems.