Peridynamics in dynamic fracture modeling

A two-dimensional ordinary state-based peridynamic formulation is utilized for evaluating dynamic fracture parameters. At first, mixed-mode dynamic stress intensity factors are extracted by interaction integrals for stationary cracks under dynamic loading. The spatial derivatives of physical quantities are evaluated by moving least squares approximation in cooperation with diffraction method to take into account the discontinuities. The same peridynamic formulation is then extended for simulating the dynamic crack propagation and arrest. To suppress the oscillations caused by sudden release of the peridynamic bonds, the transition bond concept is proposed, in which the bond forces are reduced gradually once a certain failure condition is met. The crack propagation is assessed by conventional fracture mechanics parameters, i.e., dynamic stress intensity factors rather than the critical stretch-based failure criterion. In the crack arrest part, the application (prediction) phase is studied. In the application phase, both dynamic stress intensity factors and final crack lengths are evaluated (predicted) by the present formulation. In general, obtained dynamic fracture parameters are in good agreement with the reference values available in the literature.