An auto-adaptive sub-stepping algorithm for phase-field modeling of brittle fracture

Abstract

In this work, we propose an auto-adaptive displacement stepping algorithm to auto-adaptively adjust the displacement step size while solving the quasi-static brittle fracture propagation problem with the phase-field method. We employ a step size controller based on an ‘a posteriori’ error estimator to achieve adaptivity in the displacement step size. To capture correct crack propagation behavior near peak load, we propose an energy-based conditional. The conditional is evaluated in a sub-step of the primary displacement step, and it decides whether to accept or reject the step. Based on the step size controller algorithm and the sub-stepping algorithm, we formulate the auto-adaptive sub-stepping algorithm. We investigate the accuracy and computational cost of the proposed algorithm on several benchmark problems from the literature and compare it to the standard alternate minimization (AM) approach. The algorithm auto-adaptively adjusts the size of the displacement step and allows us to use step sizes that may vary by even three orders of magnitude. As compared to the standard AM algorithm, this results in a reduction of 78–90% in the CPU time required to reach peak reaction force, and 56–78% reduction in the CPU time needed to complete analysis, and always maintains the accuracy in crack path prediction.