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Mathematics and Mechanics of Solids
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Article

Solutions to the periodic Eshelby inclusion problem in two dimensions

Liping Liu*

University of Houston

* To whom correspondence should be addressed. E-mail: liuliping{at}uh.edu.


  Abstract
We solve the homogeneous Eshelby inclusion problem on a finite unit cell with periodic boundary conditions. The main result is a representation formula of the strain field which is reminiscent of the familiar Green's representation formula. The formula is valid for any smooth inclusion and divergence-free eigenstress. More, it is shown that a Vigdergauz structure does not have the Eshelby uniformity property for symmetric non-dilatational eigenstress unless it degenerates to a laminate.

First published on June 11, 2009
Mathematics and Mechanics of Solids 2009, doi:10.1177/1081286509104492
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