The isotropic material closest to a given anisotropic material

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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.

Original languageEnglish (US)
Pages (from-to)223-238
Number of pages16
JournalJournal of Mechanics of Materials and Structures
Issue number2
StatePublished - 2006

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Applied Mathematics


  • Anisotropy
  • Elastic moduli
  • Euclidean distance
  • Riemannian distance


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