Vol. 1, No. 2, 2006

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The isotropic material closest to a given anisotropic material

Andrew N. Norris

Vol. 1 (2006), No. 2, 223–238

The isotropic elastic moduli closest to a given anisotropic elasticity tensor are defined using three definitions of elastic distance: the standard Frobenius (Euclidean) norm, the Riemannian distance for tensors, and the log-Euclidean norm. The closest moduli are unique for the Riemannian and the log-Euclidean norms, independent of whether the difference in stiffness or compliance is considered. Explicit expressions for the closest bulk and shear moduli are presented for cubic materials, and an algorithm is described for finding them for materials with arbitrary anisotropy. The method is illustrated by application to a variety of materials, which are ranked according to their distance from isotropy.

elastic moduli, anisotropy, Euclidean distance, Riemannian distance
Received: 22 September 2005
Revised: 25 November 2005
Accepted: 23 January 2006
Published: 1 June 2006
Andrew N. Norris
Rutgers University
Mechanical and Aerospace Engineering
98 Brett Road
Piscataway, NJ 08854-8058
United States