Lipton, Robert Variational methods, bounds, and size effects for composites with highly conducting interface. (English) Zbl 0969.74571 J. Mech. Phys. Solids 45, No. 3, 361-384 (1997). Cited in 21 Documents MSC: 74Q20 Bounds on effective properties in solid mechanics 74E30 Composite and mixture properties 78A48 Composite media; random media in optics and electromagnetic theory Keywords:effective conductivity tensor; anisotropic two-phase electric conductors; surface energy tensor; two-point correlation functions; component volume fractions; interfacial geometric parameters; lower bounds; isotropic polydisperse suspensions of spheres; constitutive behaviour; inhomogeneous material; variational calculus PDFBibTeX XMLCite \textit{R. Lipton}, J. Mech. Phys. Solids 45, No. 3, 361--384 (1997; Zbl 0969.74571) Full Text: DOI References: [1] Chandrasekhar, S., The stability of a rotating liquid drop, (Proc. Roy. Soc. Lond. (A), 286 (1965)), 1-26 · Zbl 0137.23004 [2] Ekeland, I.; Temam, R., Convex Analysis and Variational Problems (1976), North-Holland: North-Holland Amsterdam [3] Hashin, Z.; Shtrikman, S., A variational approach to the theory of effective magnetic permeability of multiphase materials, J. Appl. Phys., 33, 3125-3131 (1962) · Zbl 0111.41401 [4] Kobayashi, S.; Nomizu, K., (Foundations of Differential Geometry, Vol. 2 (1969), Interscience: Interscience New York) · Zbl 0175.48504 [5] Kohn, R. V.; Milton, G. W., Variational bounds on the effective moduli of anisotropic composites, J. Mech. Phys. Solids, 36, 597-629 (1988) · Zbl 0672.73012 [6] Lipton, R., Reciprocal relations, bounds, and size effects for composites with highly conducting interface, IMA Preprint 1339 (1995) [7] to appear in SIAM J. Appl. Math.; to appear in SIAM J. Appl. Math. [8] Lipton, R.; Vernescu, B., Composites with imperfect interface, (Proc. Roy. Soc. Lond. (A), 452 (1996)), 329-358 · Zbl 0872.73033 [9] Lipton, R.; Vernescu, B., Variational methods, size effects and extremal microgeometries for elastic composites with imperfect interface, Math. Models Methods Appl. Sci., 8, 1139-1173 (1995) · Zbl 0848.73041 [10] Lurie, K. A.; Cherkaev, A. V., Effective characteristics of composite materials and the optimal design of structural elements, Uspekhi Mekhaniki, Advances in Mechanics, 9 (1986) · Zbl 0623.73011 [11] Murat, F.; Tartar, L., Calcul des Variations et homogégéisation: Théorie et Applications en Physique, (Coll. de la Dir. des Etudes et Reserches de Electr. del France. Coll. de la Dir. des Etudes et Reserches de Electr. del France, Eyrolles, Paris (1985)), 319-370 [12] Pham Huy, H.; Sanchez-Palencia, E., Phénomènes de à traverse des couches minces de conductivité élevée, J. Math. Anal. Appl., 47, 284-309 (1974) · Zbl 0286.35007 [13] Torquato, S.; Rintoul, M. D., Effect of the interface on the properties of composite media, Phys. Rev. Lett., 75, 4067-4070 (1995) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.