  This paper is concerned with the energy decomposition of various nonlocal
models, including elasticity, thin plates, and gradient elasticity, to arrive
at bond-based nonlocal models in which the bond force depends only on the
deformation of a single bond. By assuming an appropriate form of bond force and
using energy equivalence between local and nonlocal models, several very
concise bond-based models are derived. We also revisit the nonlocal operator
methods and study the simplified form of second-order NOM in the symmetric
support domain. A bent-bond consisting of three points is proposed to describe
the curvature and moment. To model the damage, a rule based on Griffith theory
for the critical normal strain of the bond is proposed in analogy to the phase
field model, which can be applied individually to each bond and provides strain
localization. With this rule, the crack direction can be automatically
predicted by simply cutting the bond, giving comparable results to the phase
field method. At the same time, a damage rule for critical shear strains in
shear fractures is proposed. Furthermore, an incremental form of the plasticity
model for bond reaction force is derived. Several numerical examples are
presented to further validate the nonlocal bond-based models.
