Based on a proper decomposition of the nonlocal diffusion operator, we systematically developed nonlocal traction constraints in one-dimensional space. This nonlocal traction constraint is proved to eliminate ghost force for affine deformations. We also proved that the static nonlocal diffusion problem with the proposed traction boundary conditions has O( delta) modeling error, and converges to the local diffusion problem with classical Neumann boundary conditions as the horizon size delta goes to zero. In addition, we conducted several numerical tests to confirm our theories. This work is done with Qiang Du, Jianfeng Lu and Xiaochuan Tian.

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