The peridynamics-based finite element method (PeriFEM) with adaptive continuous/discrete element implementation for fracture simulation

Abstract

The classical finite element method has been successfully applied to many engineering problems but not for the cases with space discontinuity. In our previous work, a peridynamics-based finite element method was presented according to the principle of minimum potential energy, which enables discontinuity. As a continuation of the previous work, on the one hand, we derive the peridynamics-based finite element formulation from a new perspective, i.e., the principle of virtual work. On the other hand, we propose an adaptive continuous/discrete element conversion technique, thus the cracks could be described explicitly without increasing the computational cost significantly. Finally, numerical results are executed to verify the proposed method, including the computational cost, the influence of discretization strategy and critical stretch on crack paths, and the comparison of predicted crack paths with experimental results. Numerical results show the efficiency and accuracy of the proposed method.