The Composite Eshelby Tensors and their applications to homogenization Authors R. A. Sauer Department of Civil and Environmental Engineering University of California G. Wang Department of Civil and Environmental Engineering University of California S. Li Department of Civil and Environmental Engineering University of California Article

First Online: 22 November 2007 Received: 25 January 2007 Accepted: 14 August 2007 DOI :
10.1007/s00707-007-0504-2

Cite this article as: Sauer, R.A., Wang, G. & Li, S. Acta Mech (2008) 197: 63. doi:10.1007/s00707-007-0504-2
Summary In recent studies, the exact solutions of the Eshelby tensors for a spherical inclusion in a finite, spherical domain have been obtained for both the Dirichlet- and Neumann boundary value problems, and they have been further applied to the homogenization of composite materials [15], [16]. The present work is an extension to a more general boundary condition, which allows for the continuity of both the displacement and traction field across the interface between RVE (representative volume element) and surrounding composite. A new class of Eshelby tensors is obtained, which depend explicitly on the material properties of the composite, and are therefore termed “the Composite Eshelby Tensors”. These include the Dirichlet- and the Neumann-Eshelby tensors as special cases. We apply the new Eshelby tensors to the homogenization of composite materials, and it is shown that several classical homogenization methods can be unified under a novel method termed the “Dual Eigenstrain Method”. We further propose a modified Hashin-Shtrikman variational principle, and show that the corresponding modified Hashin-Shtrikman bounds, like the Composite Eshelby Tensors, depend explicitly on the composite properties.

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