A modified bond-based peridynamics model without limitations on elastic properties

Abstract

This study proposes a novel Modified Bond-Based PeriDynamic (MBB-PD) model based on the bonds' classification. This classification of bonds is performed on the basis of the equivalent hypothetical local strains and falls into three categories of horizontal normal, vertical normal, and shear bonds. While the classical Bond-Based PD (BB-PD) considers only the stretch of bonds, all components of the bonds' strains are taken into account in the proposed model.A local imaginary element is considered around each bond to estimate the true strains of each bond. The constitutive relations are derived from equating the strain energies of the bonds' deformations to the Classical Continuum Mechanics (CCM) strain energies for a generalized combined loading condition. A novel critical stretch criterion and critical angle criterion are proposed to predict the failure of normal and shear strain bonds, respectively.It is also shown that, unlike the classical BB-PD, the proposed model does not impose any limitations on the value of Poisson's ratio. The model is verified by investigating some intact plane stress and plane strain problems under mechanical and thermal loadings. Moreover, the deformation and damage contours and the corresponding stress-strain responses are presented for different problems with pre-existing defects and validated with the eXtended Finite Element method's (XFEM) analysis