Phase-field approach is widely adopted for crack simulations since it can naturally treat complex crack patterns such as merging and branching. In this work, we extend our recently proposed limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) method to model crack propagation in weakly coupled thermomechanical problems. Particularly, this method is introduced to overcome the convergence issues caused by the nonconvex energy functional. The adaptive mesh refinement (AMR) is further integrated into the L-BFGS scheme to reduce the computational cost. Several numerical examples are provided to demonstrate the capabilities and computational efficiency of the developed solving scheme. The performance of the developed method is reported and compared with the commonly used staggered approach in the phase-field simulations. This work offers an efficient solving strategy for other types of coupled phase-field problems.
Hu et al. (Thu,) studied this question.