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

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