Eshelby formalism for nano-inhomogeneities

Duan, Huiling, Wang, J., Huang, Z. P. and Karihaloo, Bhushan Lal ORCID: https://orcid.org/0000-0003-0657-2678 2005. Eshelby formalism for nano-inhomogeneities. Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences 461 (2062) , pp. 3335-3353. 10.1098/rspa.2005.1520

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Abstract

The Eshelby formalism for inclusion/inhomogeneity problems is extended to the nano-scale at which surface/interface effects become important. The interior and exterior Eshelby tensors for a spherical inhomogeneous inclusion with the interface stress effect subjected to an arbitrary uniform eigenstrain embedded in an infinite alien matrix, and the stress concentration tensors for a spherical inhomogeneity subjected to an arbitrary remote uniform stress field are obtained. Unlike their counterparts at the macro-scale, the Eshelby and stress concentration tensors are, in general, not uniform inside the inhomogeneity but are position-dependent. They have the property of radial transverse isotropy. It is also shown that the size-dependence of the Eshelby tensors and the stress concentration tensors follow very simple scaling laws. Finally, the Eshelby formula to calculate the strain energy in the presence of the interface effect is given.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Uncontrolled Keywords:	Eshelby formalism; interface stress; inhomogeneity; Eshelby tensor
ISSN:	1471-2946
Last Modified:	17 Oct 2022 09:04
URI:	https://orca.cardiff.ac.uk/id/eprint/1963

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