Modeling and simulation of kinked cracks by virtual node XFEM

In the present work, virtual node extended finite element method (VNXFEM) is proposed for modeling and simulation of kinked cracks in a single element. The kinked crack growth in an element is performed using the concept of virtual nodes to model and improve the accuracy of the solution. The virtual nodes are enriched with additional degrees of freedom. In the proposed approach, an actual tip element is divided into one virtual tip element and one virtual split element with the help of virtual nodes. Special five-node transition elements are used to ensure the continuity in the displacement fields. A polygon law is proposed to determine the positions of the Gauss points with respect to a crack face in the virtual split elements for the purpose of integration. Several crack growth problems in homogeneous and bi-materials are solved to verify the proposed method. The results obtained by VNXFEM are compared with those available in literature and standard XFEM solutions.