A Nonlocal Fracture Model for Cohesive- Frictional Materials via a Volume Averaging Approach

초록

The onset of cracks and their propagation is a critical issue of the mechanical behavior in cohesive- frictional materials, such as rocks. In this study, a nonlocal fracture model is presented based on the volume averaging approach, a homogenization technique for a domain with an intact region and a localized deformation. In this method, the post-localization response is formulated, including a characteristic dimension defined by the ratio of the fractured plane area to the given referential volume, which introduces mesh-independence. A new return mapping algorithm, i.e., the general return mapping, has been developed for both compression and tension loading conditions. Coulomb criterion is used as a failure criterion that triggers the onset of crack under compression loading conditions. For the tensional regime, a cohesive-crack model is adopted for the onset and propagation of the crack. The direction of a new crack under compression is defined based on the Mohr-Coulomb criterion, while the tensional crack propagates along with the eigenvector of the maximum principal stress. The softening behavior is captured via an exponential decay function that includes a constant parameter governing the softening rate. In order to validate the constitutive behavior, a stress-point calculation is performed, followed by boundary value problems to illustrate the robustness of the suggested return mapping algorithms and the nonlocal effect of the volume averaging methodology.