Revisiting the peridynamic motion equation due to characterization of boundary conditions

The peridynamic motion equation was investigated once again. The origin of incompatibility between boundary conditions and peridynamics was analyzed. In order to eliminate this incompatibility, we proposed a new peridynamic motion equation in which the effects of boundary traction and boundary displacement constraint were introduced. The new peridynamic motion equation is invariant under the transformations of rigid translation and rotation. Meanwhile, it also satisfies the requirements of total linear and angular momentum equilibrium. By this motion equation, three kinds of boundary value problems containing the displacement boundary condition, the traction boundary condition and mixed boundary condition are characterized in peridynamics. As examples, we calculated static tension and longitudinal vibration of a finite rod. The acquired solutions exhibit obvious nonlocal features, and the vibration has the dispersion similar to one dimensional atom chain vibration.