The Cauchy Relations in Linear Elasticity Theory
  In linear elasticity, we decompose the elasticity tensor into two irreducible pieces with 15 and 6 independent components, respectively. The {\it vanishing} of the piece with 6 independent components corresponds to the Cauchy relations. Thus, for the first time, we recognize the group-theoretical underpinning of the Cauchy relations. 
Friedrich W. Hehl (Cologne) and Yakov Itin (Jerusalem)