stretch ratio

Hi.

I found a very useful explanation about hyperelasticity here: http://en.wikipedia.org/wiki/Hyperelastic_material#cite_note-Ogden-1

 In the proof3, there is a good explanation (I can't found anything better than this one) of how we can express the Cauchy stresses in terms of the principal streches.

I am interested to incompressible material, so this is the equation: