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.
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