Geodesic
Exact relations for composites: Towards a complete solution
Documenta mathematica, ICM Berlin 1998, Vol. III (1998), pp. 623-632.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Typically, the electrical and elastic properties of composite materials are strongly microstructure dependent. So it comes as a nice surprise to come across exact formulae for (or linking) effective tensor elements that are universally valid no matter what the microstructure is. Here we present a systematic theory of exact relations embracing the known exact relations and establishing new ones. The search for exact relations is reduced to a search for tensor subspaces satisfying certain algebraic conditions. One new exact relation is for the effective shear modulus of a class of three-dimensional polycrystalline materials.
Classification : 35B27, 74E05, 74A60, 74M25, 74E10, 49J45
Keywords: composite materials, polycrystals, microstructure, tensor subspaces 
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     author = {Grabovsky, Yury and Milton, Graeme W.},
     title = {Exact relations for composites: {Towards} a complete solution},
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Grabovsky, Yury; Milton, Graeme W. Exact relations for composites: Towards a complete solution. Documenta mathematica, ICM Berlin 1998, Vol. III (1998), pp. 623-632. http://geodesic.mathdoc.fr/item/DOCMA_1998__S9__a18/