## __2014-Sustainable Industrial Processing Summit__

SIPS 2014 Volume 7: Energy Production, Environmental & Multiscale

Editors: | Kongoli F |

Publisher: | Flogen Star OUTREACH |

Publication Year: | 2014 |

Pages: | 528 pages |

ISBN: | 978-1-987820-09-6 |

ISSN: | 2291-1227 (**Metals and Materials Processing in a Clean Environment Series**) |

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## Inclusion of arbitrary polygon with graded eigenstrain in an anisotropic piezoelectric plane

**K.Y.
Xu**^{1};

^{1}SHANGAI UNIVERSITY, Shanghai, China;

**Type of Paper:** Invited

**Id Paper:** 339

**Topic:** 18## Abstract:

This report presents an exact closed-form solution for the Eshelby problem of a polygonal inclusion with a graded eigenstrain in an anisotropic piezoelectric full or half-plane with a traction-free surface condition. 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 solutions are applied to the quantum wires (QWRs) of square, triangular, circular and elliptical shapes within semiconductor GaAs substrates respectively, with results clearly illustrating that there are various influencing factors on the induced fields. The present solution should be particularly appealing to the more realistic nanoscale quantum-wire structure analysis where strain and electric fields could be induced by the non-uniform misfit strain.

## Keywords:

Eshelby problem, Polygonal inclusion, Graded eigenstrain, Greena's function, Anisotropic piezoelectric plane

## Full Text:

Click here to access the Full Text## Cite this article as:

Xu K. Inclusion of arbitrary polygon with graded eigenstrain in an anisotropic piezoelectric plane. In: Kongoli F, editors. Sustainable Industrial Processing Summit SIPS 2014 Volume 7: Energy Production, Environmental & Multiscale. Volume 7. Montreal(Canada): FLOGEN Star Outreach. 2014. p. 501-502.