Effective moduli of an anisotropic material with elliptical holes of arbitrary orientational distribution

E€ective moduli of a two-dimensional anisotropic solid with elliptical holes having an arbitrary (non-random) orientational distribution are given in closed form. The results are derived in the non-interacting approximation. Besides being rigorous at small defect densities, this approximation constitutes the basic building block for various approximate schemes. Proper tensorial parameters of defect density (dependent on ellipsesʹ eccentricity and their orientations relative to the matrix anisotropy axes) are identi®ed. When derived in terms of such parameters, expressions for the e€ective moduli cover, in a uni®ed way, mixtures of holes of diverse eccentricities and arbitrary orientational distribution. A number of special cases (circles, cracks of various orientational distributions) are discussed. If the ®eld of defects is ``geometrically isotropicʹʹ (holes of the circular shapes, or randomly oriented cracks), it reduces the matrix anisotrop