An interpretation of Baker-Ericksen inequalities in uniaxial deformation and stress

We prove that the strong restriction of Baker & Ericksen on the response function of a compressible elastic material is equivalent to require that a simple extension corresponds to simple tension. We also show that under the same restriction, corresponding eigenvalues of the stress tensor and the measure of deformation have the same multiplicity. Finally, a new restriction involving only two response coefficients is proposed.