A gradient weighted extended finite element method (GW-XFEM) for fracture mechanics

In this study, a gradient weighted extended finite element method (GW-XFEM) is presented for the analysis of fracture problems. For this method, the domain discretization is the same as the standard XFEM. However, the gradient field is constructed by considering the influences of the element itself and its adjacent elements. Based on the Shepard interpolation, the weighted strain filed can be obtained, which will be utilized to construct the discretized system equations. The validity of the presented method is fully investigated through several numerical examples. From these results, it is shown that compared with standard XFEM, the presented method can achieve much better accuracy, efficiency and higher convergence, when dealing with fracture analysis.