Elastic moduli approximation of higher symmetry for the acoustical properties of an anisotropic material

Details Elastic moduli approximation of higher symmetry for the acoustical properties of an anisotropic material Elastic moduli approximation of higher symmetry for the acoustical properties of an anisotropic material

2005-11-09

arxiv.org/abs/cond-mat/0511239v2

Journal of the Acoustical Society of America, Vol. 119, No. 4. (2006), pp. 2114-2121.

Physics

Condensed Matter

Materials Science

20 pages

Scientific paper

10.1121/1.2173525

The issue of how to define and determine an optimal acoustical fit to a set of anisotropic elastic constants is addressed. The optimal moduli are defined as those which minimize the mean squared difference in the acoustical tensors between the given moduli and all possible moduli of a chosen higher material symmetry. The solution is shown to be identical to minimizing a Euclidean distance function, or equivalently, projecting the tensor of elastic stiffness onto the appropriate symmetry. This has implications for how to best select anisotropic constants to acoustically model complex materials.

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