DOCUMENTA MATHEMATICA, Extra Volume ICM III (1998), 623-632

Yury Grabovsky and Graeme W. Milton

Title: Exact Relations for Composites: Towards a Complete Solution

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. 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.

1991 Mathematics Subject Classification: Primary 35B27, 73B27, 73S10; Secondary 73B40, 49J45

Keywords and Phrases: Composites, homogenization, polycrystals, exact relations

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