An improved bond-based peridynamic model with shear bonds for eliminating rigid body rotation

Abstract

Peridynamics (PD) is a kind of nonlocal theory based on displacement calculation of material particles around a horizon. The calculation of bond force, which determines the distribution of displacement field, is the key to damage and fracture simulation. Due to introduction of tangential stiffness, the bond-based PD models with shear bonds (PDS models), put forward higher requirements for the calculation of bond force. Because PDS models cannot remove the false shear deformation of bonds caused by rigid body rotation, the calculation of bond force may be inaccurate. To eliminate the influence of rigid body rotation on the calculation of bond force, an improved PDS model is proposed. Based on the principle of minimum energy and the nonlocality of peridynamics, the formula of rigid body rotation is derived. By deducting the influence of rigid body rotation, the improved PDS model ensures the accuracy of bond force calculation. In addition, a new failure criterion, strain-based failure criterion, is developed to improve the accuracy of PD model in calculating fracture energy. The results of deformation and fracture examples with finite rigid body rotation illustrate the necessity of removing the effects of rigid body rotation, and prove that the improved PDS model has high precision in the calculation of elastic displacement and prediction of cracking process. Finally, verification of the developed strain-based failure criterion was tackled with dynamic crack examples.