An inclusion refers to localized eigenstrains appearing in such processes as thermal expansion and plastic deformation. In view of micromechanics, the existence of inclusions may significantly influence the mechanical properties of the engineering materials. A micromechanical model is proposed to determine the variation of the strain energies in the presence of the near-surface inclusions. The corresponding inclusion problem in a half-space is usually difficult to be solved analytically. In this work, the strain energy is evaluated numerically via the method of images, which superposes the counterpart solutions in full-space and eliminates the tractions on the boundary surface of the half-space. The validity of the present work is confirmed by comparing with the published results and the finite element method (FEM).

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Quantum wires (QWs) and quantum dots (QDs) have been widely applied in semiconductor devices due to their excellent mechanical, electronic, and optical properties. Faux and Downes [J. Appl. Phys. 82 (1997) 3754–3762] have obtained the closed-form solutions for strain distributions produced by QWs, whose cross section is composed of any combination of line elements and circular arcs. In this paper, Eshelby's inclusion model is established to simulate QWs and the closed-form solutions for the resultant displacements are obtained. By employing the method of Green's function, the displacement solutions may be formulated as area integrals and then converted into contour integrals along the boundary of the QW. The present study complements Faux and Downes' work and provides an efficient shortcut for analyzing the displacements of a QW, whose boundary may be discretized into line segments and circular arcs.