Diffusive-discrete crack transition without remeshing achieved by extended B-spline-based implicit material point method

A novel procedure is proposed to realize a transition from a diffusive to discrete crack topology with the help of extended B-spline (EBS) basis functions in the implicit material point method. The crack initiation and propagation are determined by the crack phase-field model, and a damage field is obtained as the diffusive crack. Based on the damage gradients, the location of the discrete crack surface is identified, and the crack transition is performed by applying the EBS basis functions. Here, the EBS basis functions are constructed so that the support domain of the basis function contains only a single physical domain separated by the crack surface. Accordingly, the crack transition is achieved without additional degrees of freedom to represent the individual movement of separated domains. Additionally, remeshing with reconfiguration of connectivity and reconstruction of tangent matrices are not needed. To verify the performance of the developed scheme, three representative numerical examples are presented.