Spherical inclusion with time-harmonic eigenfields in strain gradient elasticity considering the effect of micro inertia

Abstract

In the present paper, the complete form of Toupin–Mindlin strain gradient theory of elasticity is utilized to determine the elastic field of a spherical inclusion undergoing a time-harmonic eigenfield in an infinite isotropic body. The theory adopted herein involves three characteristic lengths, two ones of which are present therein due to the incorporation of strain gradients in the strain energy density function of the material under consideration, and the presence of the third one arises from taking into account the role of velocity gradients in its kinetic energy density function, reflecting the effect of micro inertia. After the derivation of an expression for the associated Green’s function of the problem, closed-form solutions are obtained for the interior and exterior elastic fields of a spherical inclusion subjected to a time-harmonic eigenfield whose spatial distribution is expressible as a function of the radial distance of points from the center of the inclusion.