Cohesive fracture evolution within virtual element method

The paper presents a numerical procedure for the nucleation and evolution of cohesive fracture in two-dimensional bodies. The procedure is based on the development of a 12-node virtual element. Initially, the construction bases of the virtual element method (VEM) are illustrated, with specific reference to a four sides 12-node element. The recovery of the stress via complementary energy within the single element is described. The fracture is introduced in the two-dimensional body by splitting the virtual element, called parent element, into two slave elements joined by a cohesive interface. Thus, a damage interface model characterized by bilinear softening and accounting for mode I, mode II and mixed mode of fracture is presented. Then, the numerical procedure for crack nucleation and evolution is proposed. The crack direction is individuated by the maximum tensile principal nonlocal stress computed averaging on the mesh, by means of a weight function, the stress field evaluated via complementary energy within each element. Once the direction is determined, the (parent) 12-node element is split into two (slave) elements joined by the interface. Several numerical applications are developed, illustrating the performance of the 12-node element and the its accuracy in evaluating the stress field. Then, computations concerning typical fracture tests are performed, comparing the obtained results with available experimental evidences and with the ones carried out by using different numerical techniques.