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Elastic anisotropy of crystals
Throughout this letter, anisotropy/isotropy will implicitly refer to the anisotropy/isotropy of the second-order elastic constants of crystalline materials.
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index seeks to quantify how directionally dependent the properties of a system are. In
this article, the focus is on quantifying the elastic anisotropy of crystalline
Previous elastic anisotropy indices are reviewed and their shortcomings discussed. A new
scalar log-Euclidean anisotropy measure A
proposed, which overcomes these deficiencies. It is based on a distance measure in a
log-Euclidean space applied to fourth-rank elastic tensors.
L is an absolute measure of anisotropy where the limiting
case of perfect isotropy yields zero. It is a universal measure of anisotropy applicable to all
crystalline materials. Specific examples of strong anisotropy are highlighted. A
material provides an anisotropy table giving the
values of A
L for 2,176 crystallite
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