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We propose a new peridynamic formulation with shear deformation for linearelastic solid. The key idea lies in subtracting the rigid body rotation partfrom the total deformation. Based on the strain energy equivalence betweenclassic local model and non-local model, the bond force vector is derived. Anew damage rule of maximal deviatoric bond strain for elastic brittle fractureis 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 currentperidynamics. The new damage rule is applied to simulate the propagation ofMode I, II and III cracks.

A new peridynamic formulation with shear deformation for elastic solid