A new mixed-mode fracture criterion for large-scale lattice models

Reasonable fracture criteria are crucial for the modeling of dynamic failure in computational lattice models. Successful criteria exist for experiments on the micro-and on the mesoscale, which are based on the stress that a bond experiences. In this paper, we test the applicability of these failure criteria to large-scale models, where gravity plays an important role in addition to the externally applied deformation. Brittle structures, resulting from these criteria, do not resemble the outcome predicted by fracture mechanics and by geological observations. For this reason we derive an elliptical fracture criterion, which is based on the strain energy stored in a bond. Simulations using the new criterion result in realistic structures. It is another great advantage of this fracture model that it can be combined with classic geological material parameters: the tensile strength sigma(0) and the shear cohesion sigma(0). The proposed fracture criterion is much more robust with regard to numerical strain increments than fracture criteria based on stress (e. g., Drucker-Prager). While we tested the fracture model only for large-scale structures, there is strong reason to believe that the model is equally applicable to lattice simulations on the micro-and on the mesoscale.