A combined virtual element method and the scaled boundary finite element method for linear elastic fracture mechanics

In this paper, we propose a framework that combines the recently introduced virtual element method (VEM) and the scaled boundary finite element method (SBFEM) to evaluate the fracture parameters. The domain is discretized with arbitrary polygons and the element that contains the crack tip is treated within the framework of the SBFEM. This facilitates a semi-analytical treatment of the crack tip singularity allowing the fracture parameters are estimated directly from the definition. The VEM is employed for the rest of the domain. The salient feature of the VEM is that the terms in the stiffness matrix are computed without requiring higher order quadrature schemes. As both the methods satisfy partition of unity and the compatibility condition, the matrices are assembled as in the conventional FEM. The accuracy of the proposed formulation is demonstrated with two standard benchmark examples. The proposed VEM-SBFEM framework yields accurate results.