The Cauchy stress tensor for a material subject to an isotropic internal constraint

The Cauchy stress tensor, T-ij, is considered for an elastic material which is subject to any internal isotropic constraint, apart from the constraint of incompressibility. For a given strain, it is seen that if in a given ba sis one of the eigenvectors of the stress tensor has a zero component, say the alpha th component, and if the arbitrary scalar term in the stress may be chosen so that T-alpha beta(alpha not equal beta) shear stress component is zero, then the stress tensor has a double eigenvalue. This means that t here is a great simplification in the stress field. The given strain may be maintained experimentally by a simple tension superimposed upon a hydrosta tic stress field. Examples are presented for Bell-constrained and Ericksen- constrained materials.