Lipton, Robert; Vernescu, Bogdan Composites with imperfect interface. (English) Zbl 0872.73033 Proc. R. Soc. Lond., Ser. A 452, No. 1945, 329-358 (1996). The authors present a new variational principle and bounds to describe the effective conductivity tensor for anisotropic two-phase heat conducting composites with interfacial surface resistance between phases. New upper bounds are given in terms of the two-correlation functions, component volume fractions, and the moment of inertia tensor for the surface of each heterogeneity. A new lower bound is given in terms of the interfacial surface area, component volume fractions, and a scale-free matrix parameter which corresponds to the effective conductivity associated with the same geometry of non-conducting inclusions. Finally, the method is applied to predict the occurrence of size effect phenomena. Reviewer: H.Demiray (İstanbul) Cited in 41 Documents MSC: 74E30 Composite and mixture properties Keywords:variational principle; effective conductivity tensor; anisotropic two-phase heat conducting composites; interfacial surface resistance; upper bounds; two-correlation functions; lower bound; interfacial surface area; scale-free matrix parameter; size effect phenomena PDFBibTeX XMLCite \textit{R. Lipton} and \textit{B. Vernescu}, Proc. R. Soc. Lond., Ser. A 452, No. 1945, 329--358 (1996; Zbl 0872.73033) Full Text: DOI Link