Biot stress tensor

Biot stress

The Biot stress is useful because it is energy conjugate to the right stretch tensor${\displaystyle {\boldsymbol {U}}}$. The Biot stress is defined as the symmetric part of the tensor ${\displaystyle {\boldsymbol {P}}^{T}\cdot {\boldsymbol {R}}}$ where ${\displaystyle {\boldsymbol {R}}}$ is the rotation tensor obtained from a polar decomposition of the deformation gradient. Therefore, the Biot stress tensor is defined as