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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access published online on December 4, 2007
The Quarterly Journal of Mechanics and Applied Mathematics, doi:10.1093/qjmam/hbm024
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© The author 2007. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

ESHELBY'S CONJECTURE IN FINITE PLANE ELASTOSTATICS

C. I. Kim

( Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada )

M. Vasudevan

( Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2J1, Canada
JLR Engineering Solutions, 111 SE Everett Mall Way, E-201, Everett, WA 98208, USA )

P. Schiavone{dagger}

( Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada )

{dagger} Corresponding author < p.schiavone{at}ualberta.ca>

Received 29 March 2007. Accepted 19 September 2007.


  Abstract

We consider an inhomogeneity–matrix system from a particular class of compressible hyper- elastic materials of harmonic type undergoing finiteplane deformations. We discuss the analogue of Eshelby's conjecture for this class of materials. Specifically, we examine whether the stress distribution inside an inhomogeneity is uniform if and only if the inhomogeneity is elliptic when the system is subjected to uniform remote stress.


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