Adaptive phase-field modeling of brittle fracture using a robust combination of error-estimator and markers

Abstract

An error estimator is proposed to carry out adaptive mesh refinement (AMR) for phase-field fracture (PFF) simulation. The proposed error estimator works with the mesh-induced crack (MIC) method for modeling initial cracks, resulting in significant gains in the AMR algorithm’s computational efficiency. The error estimator is derived using the iterative change in the crack driving energy over each element in the mesh. A sensitivity analysis with variation in the control parameter of the marking methods is also carried out to present the robustness of the AMR algorithm with the proposed error estimator. We also study the accuracy of the proposed algorithm by implementing it to standard problems and comparing the responses to the non-adaptive (NA) algorithm. The algorithm adaptively and accurately refines the mesh along the expected crack path to estimate the system’s global force versus displacement response. Compared to the NA algorithm, a reduction of 84%–98% is obtained in the total CPU time with the proposed AMR algorithm.