A Volume Averaging FEM-Based Fracture Model for Damage Process in Cohesive-Frictional Solids

In this study, a mesh-independent fracture model is implemented in the standard finite-element (FE) framework by leveraging a volume averaging approach. For the tension regime, a cohesive crack model is adopted for the onset and propagation of the crack, in which the direction of a new crack is defined as the eigenvector of the maximum principal stress. For the compression regime, the Coulomb criterion is considered for the onset and propagation of the crack, and the new crack direction is obtained based on the Mohr–Coulomb criterion by employing the residual friction angle. In addition, a new return mapping algorithm, i.e., the general return mapping, is developed for both compression and tension loading conditions to improve the numerical robustness, convergence, and accuracy. Finally, 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 mesh-independence effects of the volume averaging methodology.