Stress

The stress is given by

${\mathbf {F} }=\sigma _{ij}{\mathbf {A} }$

where ${\mathbf {F} }$ is the force, ${\mathbf {A} }$ is the area, and $\sigma _{ij}$ is the stress tensor, given by

$\sigma _{ij}\equiv \left[{\begin{matrix}\sigma _{x}&\tau _{xy}&\tau _{xz}\\\tau _{yx}&\sigma _{y}&\tau _{yz}\\\tau _{zx}&\tau _{zy}&\sigma _{z}\\\end{matrix}}\right]$

where where $\ \sigma _{x}$, $\ \sigma _{y}$, and $\ \sigma _{z}$ are normal stresses, and $\ \tau _{xy}$, $\ \tau _{xz}$, $\ \tau _{yx}$, $\ \tau _{yz}$, $\ \tau _{zx}$, and $\ \tau _{zy}$ are shear stresess.