Hashin-Shtrikman bounds with eigenfields in terms of texture coefficients for polycrystalline materials

The Hashin-Shtrikman bounds accounting for eigenfields are represented in terms of tensorial texture coefficients for arbitrarily anisotropic materials and arbitrarily textured polycrystals. This requires a short review of the Hashin-Shtrikman bounds with eigenfields, an investigation of the polarization field determined by the stationarity condition and, finally, the analysis of the resulting expressions of the Hashin-Shtrikman bound of the effective potential. The resulting expressions are given naturally in terms of symmetric second-order tensors and minor and major symmetric fourth-order tensors. These properties induce, based on the tensorial Fourier expansion of the crystallite orientation distribution function, a dependency of all Hashin-Shtrikman properties in terms of solely the second-and the fourth-order texture coefficients. This is a new result, which is not self-evident, since an alternative formulation of the polarization field would alter the implied algebraic properties of the Hashin-Shtrikman functional. The results obtained by the polarization field, determined through the stationarity condition of the Hashin-Shtrikman functional, are discussed and demonstrated with an example for linear thermoelasticity in which bounds for elastic and thermoelastic properties are illustrated. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.