A consistent ordinary state-based peridynamic formulation with high accuracy

Peridynamics has shown great potential in numerical analysis of various engineering problems. However, its accuracy is still not quite satisfactory. In this paper, a consistent ordinary state-based peridynamic formulation (OSB-PD) is presented and significant improvement in computational accuracy is achieved. The starting point of the method is the investigation of the difference between the theoretical horizon and its counterpart in numerical implementation. Due to this difference, the original OSB-PD is inconsistent. The idea of modifying the theoretical horizon to eliminate such difference is proposed, based on which the consistent OSB-PD is developed. Numerical results show that the proposed method remarkably improves the accuracy of the original OSB-PD. Particularly, in calculating strain energy density, it almost achieves machine precision for constant strain field; for linear strain field, it shows orders higher accuracy than the original method. It is worth noting that such high accuracy is achieved with very small horizon and thus the proposed method is very fast. Capability of the proposed method in modeling crack propagation and fragmentation is also demonstrated.