Virial stress

Virial stress is a measure of mechanical stress on an atomic scale. It is given by:where
* $k$ and $ell$ are atoms in the volume,
* $Omega$,
* $m^\{(k)\}$ is the mass of atom "k",
* $u\_i^\{(k)\}$ is the "i"^th component of the velocity of atom "k",
* is the "j"^th component of the average velocity of atoms in the volume,
* $x\_i^\{(k)\}$ is the "i"^th component of the position of atom "k", and
* $f\_i^\{(kell)\}$ is the "i"^th component of the force between atom $k$ and $ell$.

At zero kelvin, all velocities are zero so we have:$au\_\{ij\}\; =\; frac\{1\}\{2Omega\}\; sum\_\{k,ell\; in\; Omega\}\; (\; x\_i^\{(ell)\}\; -\; x\_i^\{(k)\})\; f\_j^\{(kell)\}$.

This can be thought of as follows. The τ₁₁ component of stress is the force in the 1 direction divided by the area of a plane perpendicular to that direction. Consider two adjacent volumes separated by such a plane. The 11-component of stress on that interface is the sum of all pairwise forces between atoms on the two sides....

ee also

* Virial theorem

External links

* [http://www.eng.fsu.edu/~dommelen/papers/virial/mosaic/index.html Physical Interpretation of the Virial Stress]
* [http://adsabs.harvard.edu/abs/2003RSPSA.459.2347Z A new look at the atomic level virial stress: on continuum-molecular system equivalence]