The non-singular Green tensor of gradient anisotropic elasticity of Helmholtz type

• Theory of gradient anisotropic elasticity of Helmholtz type is presented.
• The non-singular (3D) Green tensor, which is the regularized anisotropic Green tensor, is given.
• The gradients of the non-singular Green tensor are calculated.

In this paper, we derive the three-dimensional Green tensor of the theory of gradient anisotropic elasticity of Helmholtz type, a particular version of Mindlin's theory of gradient elasticity with only one characteristic parameter. In contrast with classical anisotropic elasticity, it is found that in gradient anisotropic elasticity of Helmholtz type both the Green tensor and its gradient are non-singular at the origin. On the other hand, the Green tensor rapidly converges to its classical counterpart a few characteristic lengths away from the origin. Therefore, the Green tensor of gradient anisotropic elasticity of Helmholtz type can be used as a physically-based regularization of the classical anisotropic Green tensor. Using the non-singular Green tensor, the Kelvin problem is studied in the framework of gradient anisotropic elasticity.