PERIDYNAMIC EQUATION WITH BOUNDARY TRACTION

How to characterize the traction boundary condition is still an open question in peridynamics. This problem is investigated in this paper. We propose a traction-associated peridynamic motion equation, in which the traction boundary condition is introduced by a tensor weight function. The conservation laws of linear and angular momentum are derived from the traction-associated peridynamic motion equation. Meanwhile, the conservation of energy is also acquired, and it has the same form as that in the original peridynamics advanced by Silling. Therefore, the constitutive models of the original peridynamics can be directly applied to the traction-associated peridynamic motion equation. Using the inverse method, we solve for the uniaxial tension of a rod. By matching the transfer function of the boundary traction with the constitutive equations, we acquire the same solution as that in the classical elasticity from the traction-associated peridynamic motion equation. These results show that the traction-associated peridynamic motion equation not only retains all advantages of the original peridynamics, but also can be conveniently used to deal with the traction boundary value problem.

Automated summary

This paper investigates how to characterize the traction boundary condition in peridynamics and proposes a traction-associated peridynamic motion equation. The conservation laws of linear and angular momentum as well as energy are derived from this equation. The results show that the traction-associated peridynamic motion equation not only retains the advantages of the original peridynamics but also conveniently deals with the traction boundary value problem.