How to get the update the local material coordinate in large deformation for hyperelasitc rubber-like materials?

Hello, 

I want to ask things about the updation of local material coordinate in large deformation. 

Does there exist two ways for this?

1. Polar decomposition of Gradient Deformation Tensor F to get the rotation tensor.

2. Update each basis vector of local material coordinate system using modified Gradient Deformation Tensor F_bar = F*J^(-1/3).

What I cared about is the second method, is the second method available?

Wish someone could help me, : ). Thanks!!