Green’s function for an elastic plane with a circular inclusion incorporating surface energy

Summary This paper is concerned with the study of a circular inclusion in an infinite elastic matrix under the combined action of a point force applied at a finite point of the matrix and far away stresses acting in the matrix. The interface between the inclusion and the matrix resists stretching and bending, and may have a prescribed surface prestress. The interface is modeled using the Steigmann-Ogden model of surface elasticity. The problem is solved using the Somigliana identities connecting the stresses and the displacements in the matrix and the inclusion, and the Fourier series expansions of the stresses and displacements on the interface. The solution obtained in this paper can be viewed as Green’s function for a nanosized elastic circular inclusion in an infinite elastic matrix. The obtained Green’s function can serve as a basis solution for numerical studies, such as, for instance, boundary integral equations of elasticity. Parametric studies and comparisons with the known results are given in the paper.