Alternative stress measures

In continuum mechanics, the most commonly used measure of stress is the Cauchy stress tensor, often called simply the stress tensor or "true stress". However, several alternative measures of stress can be defined:

1. The Kirchhoff stress (${\displaystyle {\boldsymbol {\tau }}}$).
2. The nominal stress (${\displaystyle {\boldsymbol {N}}}$).
3. The Piola–Kirchhoff stress tensors
   1. The first Piola–Kirchhoff stress (${\displaystyle {\boldsymbol {P}}}$). This stress tensor is the transpose of the nominal stress (${\displaystyle {\boldsymbol {P}}={\boldsymbol {N}}^{T}}$).
   2. The second Piola–Kirchhoff stress or PK2 stress (${\displaystyle {\boldsymbol {S}}}$).
4. The Biot stress (${\displaystyle {\boldsymbol {T}}}$)