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.
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