A Non-Ordinary State-Based Peridynamic Constitutive Model Based on Three-Body Interaction Potential and Its Implementation on Algorithm

Abstract

In the framework of peridynamics (PD), bond-based constitutive model is more intuitional but less universal than that of state-based one. In order to demonstrate the advantages of these two models, a non-ordinary state-based peridynamic constitutive model is developed based on three-body interaction potential. An explicit general relation between PD material parameters and elastic constants (Young’s modulus and Poisson’s ratio) is rigorously derived, without the need for any particular assumptions about the modes of deformation. Two numerical examples, namely, the uniaxial tension of a bar and the penetration of a plate impacted by a rigid ball, respectively, are presented. Results show that the proposed constitutive model can be used to correctly and effectively characterize the Poisson’s effect of solid deformation and fragmentation caused by impact.