Vol. 6, No. 2, 2018

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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

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.

crack, Eshelby inclusion, inhomogeneity, piezoelectric material, analytic continuation, conformal mapping, field intensity factors
Mathematical Subject Classification 2010
Primary: 30E25, 74B05, 74G70
Received: 3 November 2017
Revised: 9 January 2018
Accepted: 17 February 2018
Published: 29 May 2018

Communicated by David J. Steigmann
Xu Wang
School of Mechanical and Power Engineering
East China University of Science and Technology
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
Edmonton, AB