The following table lists conversion rules for the three stress measures

• first Piola-Kirchhoff stress $\tnsr P$,
• second Piola-Kirchhoff stress $\tnsr S$, and
• Cauchy stress $\tnsr \sigma$,

based on the multiplicative decomposition of the deformation gradient $\tnsr F$ into elastic $\tnsr F_\text e$ and plastic part $\tnsr F_\text p$.

	$\tnsr P$	$\tnsr S$	$\tnsr\sigma$
$\tnsr P=$	$\tnsr P$	$\operatorname{det}(\tnsr F_\text p) \tnsr F_\text e \tnsr\sigma {\tnsr F_\text p}^{-\text T}$	$\operatorname{det}(\tnsr F) \tnsr\sigma {\tnsr F}^{-\text T}$
$\tnsr S=$	$\frac{1}{\operatorname{det}(\tnsr F_\text p)} {\tnsr F_\text e}^{-1} \tnsr P {\tnsr F_\text p}^{\text T}$	$\tnsr S$	$\operatorname{det}(\tnsr F_\text e) {\tnsr F_\text e}^{-1} \tnsr\sigma {\tnsr F_\text e}^{-\text T}$
$\tnsr\sigma=$	$\frac{1}{\operatorname{det}(\tnsr F)} \tnsr P {\tnsr F}^{\text T}$	$\frac{1}{\operatorname{det}(\tnsr F_\text e)} \tnsr F_\text e \tnsr S {\tnsr F_\text e}^{\text T}$	$\tnsr\sigma$