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Solutions to the Eshelby Conjectures

Liu, Liping (2007) Solutions to the Eshelby Conjectures. . (Unpublished)

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We present solutions to the Eshelby conjectures based on a variational inequality. We first discuss the meanings of the original Eshelby's statement. By Fourier analysis, we establish the connection between the homogeneous Eshelby inclusion problem and the classic Newtonian potential problem. We then proceed to the solutions of the Eshelby conjectures. Under some hypothesis on the material properties and restricted to connected inclusions with Lipschitz boundary, we show that one version of the Eshelby conjectures is valid in all dimensions and the other version is valid in two dimensions. We also show the existence of multiply-connected inclusions in all dimensions and the existence of non-ellipsoidal connected inclusions in three and higher dimensions such that, in physical terms and in the context of elasticity, some uniform eigenstress of the inclusion induces uninform strain on the inclusion. We numerically calculate these special inclusions based on the finite element method.

Item Type:Report or Paper (Discussion Paper)
Group:Solid Mechanics Research Group
Record Number:CaltechSOLIDS:2007.001
Persistent URL:
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28617
Deposited By: Imported from CaltechSOLIDS
Deposited On:29 Nov 2007
Last Modified:03 Oct 2019 03:34

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