Strain-gradient solution to elastodynamic scattering from a cylindrical inhomogeneity

Abstract

In this paper, Mindlin’s first strain-gradient theory is adopted for the first time to come up with a solution to the problem of the elastic scattering of an anti-plane time-harmonic wave incident upon an isolated circular cylindrical inhomogeneity embedded in an infinite body. The effect of micro-inertia is also captured in this analysis, which alongside the strain-gradient effect enhances the adopted theory to account for different aspects of the size effect on the elastodynamic fields developed in the medium. The general case of an elastic inhomogeneity and two special cases of a rigid immovable obstacle and a cavity are addressed and the analytical expressions for the corresponding displacement fields are obtained. These solutions reveal the existence of some kind of decaying standing waves in the medium, which cannot be predicted by the classical elastodynamic theory. Moreover, the analytical expressions for the differential and total scattering cross-sections of the cylindrical inhomogeneity are determined. The results demonstrate that, if the cross-sectional radius of the inhomogeneity or the wave-length of the incident wave is comparable with the characteristic lengths of the medium, then the size effect will be significant and the discrepancies between the solutions obtained by the adopted theory and their counterparts in the classical elastodynamic theory will be pronounced.