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An arbitrarily
shaped Eshelby inclusion interacting with a circular
piezoelectric inhomogeneity penetrated by a semi-infinite
crack
Xu Wang and Peter Schiavone
Vol. 6 (2018), No. 2, 125–136
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Abstract |
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We study the interaction between an Eshelby inclusion of arbitrary shape and a circular piezoelectric inhomogeneity penetrated by a semi-infinite crack under antiplane mechanical and in-plane electrical loading in a linear piezoelectric solid. The Eshelby inclusion undergoes uniform antiplane eigenstrains and in-plane eigenelectric fields. Through the use of a conformal mapping, the cracked piezoelectric plane is first mapped onto the lower half of the image plane. The corresponding boundary value problem is then studied in this image plane. The interaction problem is solved through the construction of an auxiliary function and the application of analytic continuation across straight and circular boundaries. We obtain concise expressions for the resultant stress and electric displacement intensity factors at the crack tip. |
Keywords
crack, Eshelby inclusion, inhomogeneity, piezoelectric
material, analytic continuation, conformal mapping, field
intensity factors
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Mathematical Subject Classification 2010
Primary: 30E25, 74B05, 74G70
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Milestones
Received: 3 November 2017
Revised: 9 January 2018
Accepted: 17 February 2018
Published: 29 May 2018
Communicated by David J. Steigmann
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Authors |
| Xu Wang | |
| School of Mechanical and Power
Engineering East China University of Science and Technology Shanghai China |
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| Peter Schiavone | |
| Department of Mechanical
Engineering University of Alberta Edmonton, AB Canada |
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