Implementation of a phase field damage model with a nonlinear evolution equation in an FFT-based solver

This paper focuses on the numerical implementation of phase-field models of fracture using the Fast Fourier Transform (FFT) based numerical method. Recent studies on phase-field models focus on the discussions of the choice of the value of regularization length proposed to smear the discontinuity of the sharp crack. Some studies argue that it should be considered as a material property because it has a significant impact on the mechanical behavior of a material in some phase-field models, for instance, in the model proposed by Miehe. However, our results in this study for heterogeneous materials have shown that the choice of regularization length not only affects the macroscopic mechanical behavior but also the local crack propagation patterns. As a result, it can be challenging to select an appropriate value that produces both accurate macroscopic responses and local crack patterns for certain phase-field models, such as Miehe’s model. Thus, the phase-field model proposed by Wu, which has been proven to reduce the length sensitivity for homogeneous material, has been successfully implemented in an FFT-based solver with the application of Newton–Krylov algorithm.