Virtual element method with non-matching and adaptive meshes for phase field fracture

This work presents a stabilization-free virtual element method (VEM) for phase field fracture. The distinctive feature of the virtual element method is its ability to utilize elements of general shape. However, the existence of additional stabilization term in the traditional virtual element method has some drawbacks when solving complex phase field fracture models. Different from the conventional virtual element method, the approach employed in this work eliminates the need for additional stabilization terms, making it more suitable for the phase field modeling of fracture. In this work, the anisotropic phase field fracture model is considered. In order to improve the calculation efficiency, the non-matching mesh ability of VEM and adaptive technique are employed. Since the virtual element method is automatically applicable to elements with general shape, it is easy to handle an arbitrary number of nodes and thus also hanging nodes resulting from the non-matching meshes used to adapt the meshes. Several representative benchmarks show the accuracy and efficiency of the proposed method.