Imposing thermodynamic restrictions on the elastic constant-fabric tensor relationship

Zysset and Curnier (1995) rederive the general representation for the fourth rank elasticity tensor in terms of the fabric tensor given originally by Cowin (1985). Zysset and Curnier (1995) then obtain a form of the representation that is sufficiently restricted to satisfy the thermodynamic constraint that the compliance tensor be positive definite. Zysset and Curnier (1995) and Zysset and Curnier (1996) argue that their representation has an advantage over that of Cowin (1985) because it has, a priori, been sufficiently restricted to satisfy the thermodynamic constraint that the compliance tensor be positive definite. The purpose of this note is to point out that the limitations of the Zysset and Curnier (1995) and Zysset and Curnier (1996) sufficiency representation are quite severe, restricting the flexibility of the model by allowing only five of the nine normally independent orthotropic elastic coefficients to be independent. Potential users should consider employing the Cowin (1985) representation and subsequently imposing the condition that the elasticity tensor be positive definite.