A 3-D conjugated bond-pair-based peridynamic formulation for initiation and propagation of cracks in brittle solids

In this paper, a novel 3D conjugated bond-pair-based peridynamic model is proposed to simulate the initiation and propagation of cracks in brittle solids. In the proposed numerical method, interacting forces between two material points within one horizon are not only related to the stretch of the bond, but also related to the rotation of the conjugated bond angles, which overcomes the limitation of the fixed Poisson's ratio in the regular bond-based peridynamics. Moreover, the critical stretch of a bond and critical bond shear energy density are respectively used to determine the Mode I (opening) fracture type and Mode II/III (in-plane shearing/tearing) fracture type of bonds. Modified explicit time integration schemes are also proposed to study dynamic and quasi-static/static problems. The performance of the proposed numerical method is demonstrated by three numerical examples that qualitatively and quantitatively illustrate its ability to predict complex crack surfaces in three-dimensional cases.