A Virtual Element Method for Crack Propagation

In this contribution, a crack propagation within brittle materials is presented by means of a novel technique, the virtual element method (VEM) [1]. In comparison to FEM, VEM allows usage of arbitrary polygonal (2D) and polyhedral (3D) elements. Such a method can be extremely useful for simulation of crack propagation problems, which may be providing an alternative approach for XFEM and remeshing. Based on the stress intensity factor, calculated by the interaction integral, the direction of the crack propagation is predicted by using the maximum circumferential stress criterion. For domain discretization, we used arbitrary polygonal elements with arbitrary number of nodes. Without changing the element formulations, the crack path is constructed by splitting the elements in the direction of growth. Also, if the crack growth stops within the element, this can be easily accomplished. Finally, a numerical example is provided to demonstrate the performance of the model.