Inclusion of arbitrary polygon with graded eigenstrain in an anisotropic piezoelectric full plane |
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Authors: | LG Sun KY Xu E Pan |
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Institution: | 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Department of Mechanics, Shanghai University, Shanghai 200072, China;2. The School of Mechanical Engineering, Zhengzhou University, Zhengzhou, Henan 450001, China;3. Department of Civil Engineering, The University of Akron, OH 44325-3905, USA |
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Abstract: | In this paper, an exact closed-form solution for the Eshelby problem of a polygonal inclusion with a graded eigenstrain in an anisotropic piezoelectric full plane is presented. For this electromechanical coupling problem, by virtue of Green’s function solutions, the induced elastic and piezoelectric fields are first expressed in terms of line integrals on the boundary of the inclusion. Using the line-source Green’s function, the line integral is then carried out analytically for the linear eigenstrain case, with the final expression involving only elementary functions. Finally, the solution is applied to the semiconductor quantum wire (QWR) of square, triangle, circle and ellipse shapes within the GaAs (0 0 1) substrate. It is demonstrated that there exists significant difference between the induced field by the uniform eigenstrain and that by the linear eigenstrain. Since the misfit eigenstrain in most QWR structures is actually non-uniform, the present solution should be particularly appealing to nanoscale QWR structure analysis where strain and electric fields are coupled and are affected by the non-uniform misfit strain. |
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