A peridynamic differential operator-based scheme for the extended bond-based peridynamics and its application to fracture problems of brittle solids

In order to describe the mechanical behavior of solids with arbitrary Poisson's ratio values, an extended bond-based peridynamic (XBB-PD) model was developed in the authors’ previous work by taking both the bond longitudinal and tangential deformations into account. In the current work, a peridynamic differential operator based implementation scheme is presented for the XBB-PD model. An energy-based failure criterion is introduced to describe the failure and crack propagation in brittle solids. First, two elastic examples are solved to validate the proposed approach. The m- and δ- convergence studies are carried out. Subsequentially, several numerical examples of crack propagation problems are simulated. All simulations show good agreement with the results reported in the references, demonstrating the flexibility and capabilities of the developed approach in the simulation of crack propagation in brittle solids.