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.

References

Related reading

• Aidan P. Thompson, Steven J. Plimpton, and William Mattson "General formulation of pressure and stress tensor for arbitrary many-body interaction potentials under periodic boundary conditions", Journal of Chemical Physics 131 154107 (2009)
• G. C. Rossi and M. Testa "The stress tensor in thermodynamics and statistical mechanics", Journal of Chemical Physics 132 074902 (2010)