The non-singular Green tensor of Mindlin's anisotropic gradient elasticity with separable weak non-locality

•Theory of Mindlin's anisotropic gradient elasticity with separable weak non-locality is presented.•The non-singular (3D) Green tensor is given.•The gradient of the non-singular Green tensor is calculated.

In this paper, we derive the Green tensor of anisotropic gradient elasticity with separable weak non-locality, a special version of Mindlin's form II anisotropic gradient elasticity theory with up to six independent length scale parameters. The framework models materials where anisotropy is twofold, namely the bulk material anisotropy and a weak non-local anisotropy relevant at the nano-scale. In contrast with classical anisotropic elasticity, it is found that both the Green tensor and its gradient are non-singular at the origin, and that they rapidly converge to their classical counterparts away from the origin. Therefore, the Green tensor of Mindlin's anisotropic gradient elasticity with separable weak non-locality can be used as a physically-based regularization of the classical Green tensor for materials with strong anisotropy.