  In this work, we developed a bond-based cohesive peridynamics model (CPDM)
and apply it to simulate inelastic fracture by using the meso-scale
Xu-Needleman cohesive potential . By doing so, we have successfully developed a
bond-based cohesive continuum mechanics model with intrinsic stress/strain
measures as well as consistent and built-in macro-scale constitutive relations.
The main novelties of this work are: (1) We have shown that the cohesive stress
of the proposed nonlocal cohesive continuum mechanics model is exactly the same
as the nonlocal peridynamic stress; (2) For the first time, we have applied an
irreversible built-in cohesive stress-strain relation in a bond-based cohesive
peridynamics to model inelastic material behaviors without prescribing
phenomenological plasticity stress-strain relations; (3) The cohesive bond
force possesses both axial and tangential components, and they contribute a
nonlinear constitutive relation with variable Poisson's ratios; (4) The
bond-based cohesive constitutive model is consistent with the cohesive fracture
criterion, and (5) We have shown that the proposed method is able to model
inelastic fracture and simulate ductile fracture of small scale yielding in the
nonlocal cohesive continua.
  Several numerical examples have been presented to be compared with the finite
element based continuum cohesive zone model, which shows that the proposed
approach is a simple, efficient and effective method to model inelastic
fracture in the nonlocal cohesive media.
