Exactly solvable spherically anisotropic thermoelastic microstructures
Résumé
Microstructures possessing local spherical anisotropy are considered in this paper. An example is a spherulitic polymer which can be modelled by an assemblage of spheres of all sizes in which a radial direction in every sphere is an axis of local transverse isotropy. Our purpose is to construct effectively isotropic microstructures, with spherically anisotropic and thermoelastic constituents, whose effective bulk modulus, thermal stress and specific heat can be exactly determined. The basic microstructure for which this is achieved in the present paper is the nested composite sphere assemblage of Milgrom and Shtrikman (J. Appl. Phys. 66 (1989) 3429) which was originally formulated for isotropic constituents, in the settings of conductivity and coupled fields with scalar potentials. Here, we allow the phases of this microstructure to be spherically thermoelastic with a symmetry class which can be trigonal, tetragonal, transversely isotropic, cubic or isotropic with respect to a local spherical coordinate system. A rich class of new exact results for two-phase composites and polycrystals are obtained. (C) 2004 Elsevier Ltd. All rights reserved.