 If we pull back formula_16 to the reference configuration, we have
or, 

The PK2 stress (formula_5) is symmetric and is defined via the relation
Therefore,

The Biot stress is useful because it is energy conjugate to the right stretch tensor formula_36.The Biot stress is defined as the symmetric part of the tensor formula_37 where formula_38 is the rotation tensor obtained from a polar decomposition of the deformation gradient.Therefore, the Biot stress tensor is defined as
The Biot stress is also called the Jaumann stress.