Localizing gradient damage model with micro inertia effect for dynamic fracture

A localizing gradient damage model with micro inertia effect is proposed for the dynamic fracture of quasi-brittle materials. The objective is to achieve mesh independent solutions, and to avoid spurious effects associated with the conventional nonlocal enhancement. The proposed localizing gradient damage model closely resembles the conventional gradient enhancement, albeit with an interaction domain that decreases with damage, complemented by a micro inertia effect. We first consider a classical crack branching problem, where the localizing gradient damage model is shown to resolve the mesh sensitivity issue, as well as to correctly reproduce the crack profile. Moreover, the micro inertia effect is observed to retard the crack velocity. Next, the tensile loading of a Polymethyl Methacrylate plate is considered. It is shown that the proposed model effectively captures the experimentally observed transition of crack profiles as the loading rate increases, i.e. from a straight crack propagation, to sub-branching, and finally to macro branching. Numerical results in terms of crack patterns, crack velocities, and fracture energies are in good agreement with the experimental data. To furthermore demonstrate the superior performance of the localizing gradient damage model, the macro branching problem is solved using the conventional gradient enhancement with micro inertia. It is shown that a spurious damage growth and an erroneous interaction between closely spaced cracks suppress the development of macro branching, even though reasonable values are obtained for the fracture energy and crack velocity. The localizing gradient damage model is able to fully resolve these issues.