- Virial stress
Virial stress is a measure of mechanical stress on an atomic scale. It is given by:au_{ij} = frac{1}{Omega} sum_{k in Omega} left(-m^{(k)} (u_i^{(k)}- ar{u}_i) (u_j^{(k)}- ar{u}_j) + frac{1}{2} sum_{ell in Omega} ( x_i^{(ell)} - x_i^{(k)}) f_j^{(kell)} ight)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",
* ar{u}_j 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]
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