A robust explicit algorithm for phase-field modeling of quasi-brittle fracture

The phase-field modeling of quasi-brittle fracture accounting for the irreversible growth of the regularization variable is considered. As a consequence of this irreversibility, the minimization problem turns into a variational inequality. A staggered solution scheme is employed to decouple the optimization algorithm. This leads to two sub-problems for the displacement and the phase field. The spatial discretization transforms the phase-field sub-problem into a symmetric linear complementarity problem. The present paper shows a robust and explicit algorithm to solve this problem.