1. The Kirchhoff stress ({displaystyle {boldsymbol {tau }}}).

2. The Nominal stress ({displaystyle {boldsymbol {N}}}).

3. The first Piola-Kirchhoff stress ({displaystyle {boldsymbol {P}}}). This stress tensor is the transpose of the nominal stress ({displaystyle {boldsymbol {P}}={boldsymbol {N}}^{T}}).

4. The second Piola-Kirchhoff stress or PK2 stress ({displaystyle {boldsymbol {S}}}).

5. The Biot stress ({displaystyle {boldsymbol {T}}})

https://en.wikipedia.org/wiki/Stress_measures#Cauchy_stress