Straight Disclinations in Fractional Nonlocal Medium.

The constitutive equation for a nonlocal stress tensor is represented as an integral with the suitable kernel function. In this paper, the nonlocality kernel is chosen as the Green function of the Cauchy problem for the fractional diffusion equation with the Caputo derivative with respect to the nonlocality parameter. The solutions of nonlocal elasticity problems for the straight wedge and twist disclinations in an infinite medium are obtained in the framework of this new nonlocal theory of elasticity. The Laplace integral transform with respect to the nonlocality parameter is used. It is necessary to emphasize that the transition from the nonlocal to local stress tensor is described by the limiting value of the nonlocality parameter τ→0. The obtained stress fields do not contain nonphysical singularities at the disclination lines.