A note on the hyperelastic constitutive equation for rotated Biot stress

Abstract

The forward-rotated Biot stress and the right stretch strain are defined, and the virtual work of the rotated stress is found. It is shown that it involves a corotational variation of the Green-McInnis-Naghdi type. For the strain energy assumed in terms of principal invariants of the right stretching tensor, a constitutive equation and a constitutive (4th rank) operator for the Biot stress is derived. Subsequently, they are subjected to the rotate-forward operation, and it is demonstrated how their structure is carried over to the rotated measures.