IJPAM: Volume 69, No. 2 (2011)

NORM, NORM RATIO CALCULATIONS AND
ANISOTROPY DEGREE

Çiğdem Dinçkal
1464, Avenue 5, 1 Çukurambar, Çankaya
Ankara, 06520, Turkey
e-mail: cigdemdinckal2004@yahoo.com


Abstract. In this paper, for elastic constant tensor, the norm concept, norm ratio and anisotropy degree are described. The norm of a tensor is used as a criterion for comparing the overall effect of the properties of anisotropic materials and norm ratios are used as a criterion to represent the anisotropy degree of the properties of these materials. Norm and norm ratios as well as the measure of ``nearness'' to the nearest isotropic tensor are computed for several examples from various anisotropic materials possessing elastic symmetries such as cubic, transversely isotropic, tetragonal, trigonal and orthorhombic. These computations are used to compare and assess the anisotropy in various anisotropic materials by means of strength or magnitude and also determine the ``nearness'' of the nearest isotropic tensor for the materials with lower symmetry types.

Received: December 28, 2010

AMS Subject Classification: 65A05, 65F35

Key Words and Phrases: norm, norm ratio, anisotropy degree, elastic constant tensor

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 2