Eshelby problem of polygonal inclusions in anisotropic piezoelectric full- and half-planes

This paper presents an exact closed-form solution for the Eshelby problem of polygonal inclusion in anisotropic piezoelectric fulland half-planes. Based on the equivalent body-force concept of eigenstrain, the induced elastic and piezoelectric 4elds are 4rst expressed in terms of line integral on the boundary of the inclusion with the integrand being the Green’s function. Using the recently derived exact closed-form line-source Green’s function, the line integral is then carried out analytically, with the 4nal expression involving only elementary functions. The exact closed-form solution is applied to a square-shaped quantum wire within semiconductor GaAs fulland half-planes, with results clearly showing the importance of material orientation and piezoelectric coupling. While the elastic and piezoelectric 4elds within the square-shaped quantum wire could serve as benchmarks to other numerical methods, the exact closed-form solution should be useful to the analysis of nanoscale quantum-wire structures where large strain and electric 4elds could be induced by the mis4t strain. ? 2003 Elsevier Ltd. All rights reserved.