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.

A non-ordinary state decomposition method for three-body potential peridynamics model

“…As is well known, there exists Poisson’s ratio limitation in original BB PD model due to central potential assumption. To eliminate this limitation, the authors proposed the TBP PD model [28–31] based on a micropotential w ij combined with three-body interaction potential. The expression shown in equation (2) is the so-called novel TBP defined in Li and Hao [29] (or modified TBP in Li and Hao [31]) and will be the basis of this study.…”

“…In OSB-PD models above, the PD force density vectors between two points are assumed to be parallel to their relative position vector in deformed state, leading to the limitation of shear deformation for bond vectors. By comparison, three-body potential (TBP) PD model [28][29][30][31], belonging to non-ordinary state-based (NOSB) PD models such as those in the literature [9,[32][33][34][35][36][37][38][39][40] among others, can resolve this limitation due to introducing three-body interaction potential between material points, which enables the shear deformability of bond vectors. Meanwhile, as researched in Li and Hao [29], if a specific expression, provided by novel TBP, is used, this PD model will take bond shear form in the hypothesis of small deformation conditions and be equivalent to the one presented by Madenci et al [40], that is, the PD model considering bond rotation.…”

“…Meanwhile, as researched in Li and Hao [29], if a specific expression, provided by novel TBP, is used, this PD model will take bond shear form in the hypothesis of small deformation conditions and be equivalent to the one presented by Madenci et al [40], that is, the PD model considering bond rotation. However, no matter in the TBP PD model or the one considering bond rotation, the PD SED and force functions are directly expressed in terms of bond stretch and shear deformations [28][29][30][31]40]. Also, the decomposition method appearing in OSB-PD model [9,25] could not be directly used to obtain the required decomposition forms for them due to the bond shear deformability .…”