Grabovsky, Yury; Milton, Graeme W. Exact relations for composites: Towards a complete solution. (English) Zbl 0896.35013 Doc. Math., Extra Vol. ICM Berlin 1998, vol. III, 623-632 (1998). Summary: 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. Cited in 1 Document MSC: 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 74E05 Inhomogeneity in solid mechanics 74A60 Micromechanical theories 74M25 Micromechanics of solids 74E10 Anisotropy in solid mechanics 49J45 Methods involving semicontinuity and convergence; relaxation Keywords:composite materials; polycrystals; microstructure; tensor subspaces PDFBibTeX XMLCite \textit{Y. Grabovsky} and \textit{G. W. Milton}, Doc. Math. Extra Vol., 623--632 (1998; Zbl 0896.35013) Full Text: EuDML EMIS