The isotropic material closest to a given anisotropic material

Norris, Andrew

doi:10.2140/jomms.2006.1.223

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The isotropic material closest to a given anisotropic material

Andrew N. Norris

Vol. 1 (2006), No. 2, 223–238

DOI: 10.2140/jomms.2006.1.223

Abstract

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.

Keywords

elastic moduli, anisotropy, Euclidean distance, Riemannian distance

Milestones

Received: 22 September 2005

Revised: 25 November 2005

Accepted: 23 January 2006

Published: 1 June 2006

Authors

Andrew N. Norris
Rutgers University Mechanical and Aerospace Engineering 98 Brett Road Piscataway, NJ 08854-8058 United States
http://mechanical.rutgers.edu/norris

Vol. 1, No. 2, 2006

Andrew N. Norris

Abstract

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