An implicit ordinary state-based peridynamic framework for quasi-brittle fracture problems

To robustly and accurately predict quasi-brittle fracture problems using peridynamics (PD), irrespective of the restriction of Poisson’ ratio, a rigorous implicit ordinary state-based peridynamic (OSBPD) fracture framework is developed in this study. The stiffness matrix of an OSBPD bond is established firstly on the basis of a complex truss cluster, which consists of a standard truss element and two groups of affiliated non-standard truss elements. And the correction factors in the stiffness matrix for the discretized model are also clearly revisited. Then, a nonlocal CZM is implemented in OSBPD to describe quasi-brittle behaviors of PD bonds, which is composed of an effective combined damage initiation criterion and a well-established degradation curve. Finite elements are also coupled with OSBPD to reduce the computational cost. To accurately predict fracture problems with snap-back phenomenon, the tangent stiffness matrix is explicitly derived and also the indirect displacement-controlled Newton-Raphson method is exploited in detail. Finally, the validity and robustness of the proposed model is well demonstrated through several representative quasi-brittle fracture examples including the overflow-induced fracture of the Koyna dam of 103 m height. More importantly, the proposed model shows grid size independence, and it behaves as a better alternative to the extrinsic CZM in terms of both accuracy and capability for complex crack.