  This paper presents the Virtual Element Method (VEM) for the modeling of
crack propagation in 2D within the context of linear elastic fracture mechanics
(LEFM). By exploiting the advantage of mesh flexibility in the VEM, we
establish an adaptive mesh refinement strategy based on the superconvergent
patch recovery for triangular, quadrilateral as well as for arbitrary polygonal
meshes. For the local stiffness matrix in VEM, we adopt a stabilization term
which is stable for both isotropic scaling and ratio. Stress intensity factors
(SIFs) of a polygonal mesh are discussed and solved by using the interaction
domain integral. The present VEM formulations are finally tested and validated
by studying its convergence rate for both continuous and discontinuous
problems, and are compared with the optimal convergence rate in the
conventional Finite Element Method (FEM). Furthermore, the adaptive mesh
refinement strategies used to effectively predict the crack growth with the
existence of hanging nodes in nonconforming elements are examined.
