Strain rate dependence of the mesh objectivity in dynamic fracture analyses with the crack band model

The crack band model (CBM) is one of the most widely employed energy regularization techniques in continuum scale finite element fracture analyses. We demonstrate here that for dynamic fracture problems, the CBM regularization works only below a threshold strain rate, above which it should be bypassed. This is because, in dynamic fracture, higher strain rates make fractures increasingly branched and diffused, implying suppression of localization. This is demonstrated by considering the dynamic fracture of an isotropic brittle material, modeled via a scalar damage model in conjunction with the CBM regularization. Dynamic mode-I fracture in a thin plate is simulated under various strain rates such that results include localized, slightly branched, highly branched, and extensively branched diffused cracks. It is revealed that CBM yields mesh objective results only for a localized or slightly branched crack. For diffused or highly branched cracks, results are mesh size-dependent if CBM is used, but objective results are obtained if CBM is bypassed. CBM is found to work when the energy dissipation scales linearly with element size, which only occurs for localized or slightly branched cracks. This finding has great implications for applications involving finite element modeling of dynamic fracture.