Numerical implementation of the coupled criterion: Matched asymptotic and full finite element approaches

An implementation of the coupled criterion (CC) for crack initiation simulation in the commercial finite element (FE) code Abaqus/Standard is proposed. This finite fracture mechanics approach allows crack initiation to be modeled by fulfilling simultaneously a stress and an energy conditions, which results in the determination of the loading level and crack length at initiation. Two procedures are considered and compared: the first one relies on matched asymptotic expansions while the second one is based on full FE calculations. The asymptotic approach is computationally more efficient than the second one since it requires less calculations to be performed. However, it is restricted to cases for which the crack initiation length remains small compared to the smallest characteristic dimensions of the studied structure. For such cases, both methods leads to similar results as illustrated by crack initiation modeling of notched specimen under three point bending. The provided source codes and the tutorials help understanding and applying the CC for crack initiation modeling