Virtual element method for mixed-mode cohesive fracture simulation with element split and domain integral

We present a computational framework for mixed-mode cohesive fracture simulation based on the virtual element method (VEM). To represent an arbitrary crack path, the element splitting scheme is developed on a polygonal mesh to capitalize its flexibility in element shape. For the accurate evaluation of a crack-tip stress field and crack propagation direction, the virtual grid-based stress recovery scheme is tailored for VEM in conjunction with the maximum strain energy release rate criterion. The mixed-mode fracture examples are illustrated to validate the accuracy and robustness of the proposed computational scheme. Numerical results demonstrate that the domain integral method with the stress recovery scheme captures an accurate crack path without oscillation under the biaxial tensile stress state. Furthermore, the computed cracks using the element splitting scheme show that smooth and curved patterns on polygonal elements are in good agreement with the experimental results.