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D.B. Volkov-Bogorodskii and S.A. Lurie, "Eshelby Integral Formulas in Gradient Elasticity," Mech. Solids. 45 (4), 648-656 (2010)
Year 2010 Volume 45 Number 4 Pages 648-656
DOI 10.3103/S0025654410040138
Title Eshelby Integral Formulas in Gradient Elasticity
Author(s) D.B. Volkov-Bogorodskii (Institute of Applied Mechanics, Russian Academy of Sciences, GSP-1, V-334, Leninskii pr-t 32A, Moscow, 117334 Russia, v-b1957@yandex.ru)
S.A. Lurie (Institute of Applied Mechanics, Russian Academy of Sciences, GSP-1, V-334, Leninskii pr-t 32A, Moscow, 117334 Russia, lurie@ccas.ru)
Abstract Eshelby integral formulas play a fundamental role in mechanics of composite materials, because they provide an efficient tool for determining the average properties of dispersion-filled materials. For example, their use in the framework of the self-consistent averaging method actually gives a final and quite precise solution to the problem of determining effective physical and mechanical properties of filled composites up to large relative contents of inclusions and almost all relations between the phase characteristics of the composite. In the present paper, we generalize the Eshelby integral formulas to the gradient theory of elasticity. This provides the possibility for using efficient methods for estimating the average characteristics of micro and nano-structured materials in the framework of gradient theories, which permit taking the scale effects into account correctly, and hence find wider and wider applications in describing the mechanical and physical processes.
Keywords composites, effective properties, gradient theory, special representations of solutions, self-consistency method
References
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Received 11 May 2010
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