Two-dimensional Eshelby’s problem for piezoelectric materials with a parabolic boundary
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We use complex variable techniques to obtain analytic solutions of Eshelby’s problem consisting of an inclusion of arbitrary shape in an anisotropic piezoelectric plane with a parabolic boundary. The region of the physical plane below the parabola is mapped onto the lower half of the image plane. The problem is then more conveniently studied in the image plane rather than in the physical plane. The critical step in our approach lies in the construction of certain auxiliary functions in the image plane which allow for the technique of analytic continuation to be applied to an inclusion of arbitrary shape.
KeywordsEshelby inclusion Piezoelectric material Parabolic boundary Stroh octet formalism Analytic solution
This work is supported by the National Natural Science Foundation of China (Grant No. 11272121) and through a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No: RGPIN – 2017 - 03716115112).
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Conflict of interest
The authors declare that they have no conflict of interest.
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