Journal of Elasticity 46: 151–180, 1997. 151 c 1997 Kluwer Academic Publishers. Printed in the Netherlands. Averaging Anisotropic Elastic Constant Data STEPHEN C. COWIN and GUOYU YANG Department of Mechanical Engineering, The School of Engineering of The City College and The Graduate School of The City University of New York, New York, NY 10031, U.S.A. e-mail: scccc@cunyum.cuny.edu Received 23 October 1996; in revised form 8 February 1997 Abstract. A method of averaging the data on the anisotropic elastic constants of a material is presented. The anisotropic elastic constants are represented by the elasticity tensor which is expressed as a second rank tensor in a space of six dimensions. The method consists of averaging eigenbases of different measurements of the elasticity tensor, then averaging the eigenvalues referred to the average eigenbasis. The eigenvalues and eigenvectors are obtained by using a representation of the stress–strain relations due, in principle, to Kelvin [17, 18]. The formulas for the representation of the averaged elasticity tensor are simple and concise. The applications of these formulas are illustrated using previously reported data, and are contrasted with the traditional analysis of the same data by Hearmon [9]. An interesting result that emerges from this analysis is a method dealing with variable composition anisotropic elastic materials whose elastic constants depend upon the particular composition. In the case of porous isotropic materials, for example, it is customary to regress the Young’s modulus against porosity. The results of this paper suggest a structure or paradigm for extending to anisotropic materials this empirical method of regressing elastic constant data against composition or porosity. Mathematics Subject Classifications (1991): 73B40, 73C02. Key words: elasticity, anisotropy, averaging, elasticity tensor, compliance tensor. 1. Introduction A method of averaging the data on the anisotropic elastic constants of a material is presented. The method is based on the idea of averaging the eigenbases of different measurements of the elasticity tensor, then averaging the eigenvalues referred to the average eigenbasis. The elasticity tensor may be expressed either as a fourth rank tensor, with components , in a space of three dimensions or as a second rank tensor, with components , in a space of six dimensions. The averaging processes are applied here to the six eigenvalues of the matrix c and to the eigenbasis of c; or, equivalently, to the inverse of c, the compliance tensor s. This averaging process is, basically, an averaging process for the simultaneous invariants of c and s. The second rank tensor c in six dimensions whose components are appears in a representation of the stress–strain relations due, in principle, to Kelvin [17, 18], but expressed by Rychlewski [16] and Mehrabadi and Cowin [12] in contemporary