VEM-based tracking algorithm for cohesive/frictional 2D fracture

The present paper proposes an innovative nucleation and propagation algorithm for fracture evolution in 2D cohesive media, based on virtual element method (VEM) technology. Initially, an interface cohesive law is described, which is able to account for the crack opening due to the evolution of a damage variable in mode I, mode II, and in mixed mode; the model includes unilateral contact and frictional effects. The VEM, which is used to model the elastic behavior of the bulk material, is presented in a simple and viable way, illustrating the projection operation necessary for defining strain and stress in a typical element, and discussing the stabilization technique. Then, the numerical algorithm for reproducing the crack nucleation, the fracture path generation and evolution is described. The procedure fundamentally consists in two steps, i.e. the nucleation and propagation criteria, and the topological adaptive mesh refinement. Numerical applications are developed in order to assess the ability of the proposed procedure to satisfactorily reproduce the crack nucleation and growth in solids. Comparisons with numerical results available in literature are reported, remarking the reliability of the implemented algorithm.