The calculation of the overall anisotropic response of materials with variations in properties on a scale short compared to the wavelength of the imposed stressfield is complicated but, when the variations in structure are one-dimensional, a straightforward averaging technique exists. This method, originated by Riznichenko (1949) and Postma (1955), and further developed by Backus (1962), has been cast into a convenient matrix form by Helbig and Schoenberg (1987). Schoenberg and Douma (1988) have shown that distributions of parallel cracks may also be incorporated into the system by representation as layers in the limit of vanishing thickness and stiffness. Finally, Schoenberg and Muir (1989) cast the whole calculation into a form in which the rules of group theory apply, and suggest that distributions of intersecting sets of parallel cracks in fine layering can be manipulated in this way.

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