Energy conservation in dynamic crack propagation: Bond-breaking correction and convergence investigations for peridynamic models

Peridynamic models have demonstrated inherent advantages in modeling dynamic crack propagations. The crack initiation and propagation in peridynamics are realized through the breaking of bonds between material points. However, the breakage of the bonds may lead to weak non-conservation of energy in the system, which may further influence the crack propagation and even lead to an incorrect prediction. This work proposed a modification for the breaking bonds, the purpose of which is to ensure energy conservation and obtain correct energy conversion in the system. Then an energy-based quantitative indicator for the study of the convergence of discrete parameters in peridynamic models was provided. In order to verify the correctness of the modification and the effectiveness of the indicator, cases of a typical benchmark problem under different initial and loading conditions were investigated. The results indicate that the modification performs well in maintaining energy conservation of the system during the updating processes and that the energy-based quantitative indicator has been proven to be a robust enabler for convergence investigations. The contributions of this study refine the treatment of breaking bonds and provide a reliable indicator for convergence investigations.