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

${\sigma }_{ij}\equiv [\begin{array}{ccc}{\sigma }_x& {\tau }_{xy}& {\tau }_{xz}\\ {\tau }_{yx}& {\sigma }_y& {\tau }_{yz}\\ {\tau }_{zx}& {\tau }_{zy}& {\sigma }_z\\ \end{array}]$

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.