  We propose a new peridynamic formulation with shear deformation for linear
elastic solid. The key idea lies in subtracting the rigid body rotation part
from the total deformation. Based on the strain energy equivalence between
classic local model and non-local model, the bond force vector is derived. A
new damage rule of maximal deviatoric bond strain for elastic brittle fracture
is proposed in order to account for both the tensile damage and shear damage.
2D and 3D numerical examples are tested to verify the accuracy of the current
peridynamics. The new damage rule is applied to simulate the propagation of
Mode I, II and III cracks.
