A micromechanics-based nonlocal constitutive equation for transversely-isotropic random composites

An explicit, micromechanics-based nonlocal constitutive equation for random linear elastic composite materials exhibiting transversely-isotropic macroscopic behaviour is derived by employing a generalization of the Hashin-Shtrikman variational formulation. A random distribution of isotropic, non-overlapping identical inclusions with fixed spheroidal shape is considered, wherein the inclusions have random spatial location but aligned orientation in an isotropic matrix. The analysis builds on that of Drugan and Willis (1996, J Mech Phys Solids 44, 497-524), here extended to the case of transversely-isotropic composites. New explicit results will be shown, and the effects of inclusion alignment will be highlighted by comparing these results with those previously obtained by Monetto and Drugan (2004, J Mech Phys Solids 52, 359-393) for spheroidal inclusions having random orientation as well as location.