  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.
