Irreducible decompositions of the elasticity tensor under the linear and orthogonal groups and their physical consequences

Yakov Itin; Friedrich W. Hehl

doi:10.1088/1742-6596/597/1/012046

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arXiv · 1411.5104

Irreducible decompositions of the elasticity tensor under the linear and orthogonal groups and their physical consequences

Yakov Itin·Friedrich W. Hehl

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Abstract

We study properties of the fourth rank elasticity tensor C within linear elasticity theory. First C is irreducibly decomposed under the linear group into a "Cauchy piece" S (with 15 independent components) and a "non-Cauchy piece" A (with 6 independent components). Subsequently, we turn to the physically relevant orthogonal group, thereby using the metric. We find the finer decomposition of S into pieces with 9+5+1 and of A into those with 5+1 independent components. Some reducible decompositions, discussed earlier by numerous authors, are shown to be inconsistent. --- Several physical consequences are discussed. The Cauchy relations are shown to correspond to A=0. Longitudinal and transverse sound waves are basically related by S and A, respectively.

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Yakov Itin, Friedrich W. Hehl. 2014-11-19. Irreducible decompositions of the elasticity tensor under the linear and orthogonal groups and their physical consequences. https://doi.org/10.1088/1742-6596%2F597%2F1%2F012046

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