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:
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