Aspects of cauchy elastic materials

The Darboux theorem on the classification and canonical forms of first degree exterior differential forms is used to obtain a canonical representation of Cauehy elastic materials. It is shown that the balance of moment of momentum and the principle of material indifference are independent for materials whose Darboux class is greater than 1. By means of the Caratheodory's theorem on inaccessibility it is shown that any homogeneous deformation state can be reached from any other homogeneous deformation state by a path of zero work whenever the Darboux class of the material is 3 or greater.