A nonlocal fracture criterion and its effect on the mesh dependency of GraFEA

Recently, Khodabakhshi et al. (Meccanica 51(12):3129–3147, 2016. https://doi.org/10.1007/s11012-016-0560-6 ) presented a new method (by the name GraFEA) capable of studying fracture based on edge breakage within a classical FEA scheme which combines the best features of FEA and bond-breakage methods in a single framework. In this study, an attempt is made to investigate the mesh dependency of GraFEA by a set of numerical examples, and it is shown that using a local fracture criterion for edge failure will yield mesh-dependent results, as is already well known. A physically motivated nonlocal fracture criterion is implemented along with the edge breakage model, and its efficacy in eliminating the mesh sensitivity is investigated. The nonlocal criterion introduces a length scale into the problem. It is shown that by increasing the magnitude of the length scale parameter from zero, the damage pattern moves from localized fracture to diffuse damage pattern, yet with complete material separation (fracture) across a certain plane. It is shown by numerical results that, as expected, the introduction of the nonlocal fracture criterion eliminates the issue of mesh sensitivity, and thus predictions of the approximate crack paths and damage zone can be done within the classical FEA framework without the need for special formulations.