Virial stress

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]


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Virial theorem — In mechanics, the virial theorem provides a general equation relating the average over time of the total kinetic energy, , of a stable system consisting of N particles, bound by potential forces, with that of the total potential energy, , where… …   Wikipedia

  • Stress (mechanics) — Continuum mechanics …   Wikipedia

  • virial — noun Half of the product of the stress of attraction or repulsion with the distance between two particles. The quantity 1/2 Rr, or half the product of the attraction into the distance across which the attraction is exerted, is defined by Clausis… …   Wiktionary

  • virial — ˈvirēəl noun ( s) Etymology: German, from Latin vires, plural, strength, power + German ial; akin to Latin vis strength, force, violence more at vim : half the product of the stress due to the attraction or repulsion between two particles in… …   Useful english dictionary

  • Polymer — Appearance of real linear polymer chains as recorded using an atomic force microscope on surface under liquid medium. Chain contour length for this polymer is 204 nm; thickness is 0.4 nm.[1] A polymer is a large molecule (macromolecule …   Wikipedia

  • Dioxygen — Eigenschaften …   Deutsch Wikipedia

  • Disauerstoff — Eigenschaften …   Deutsch Wikipedia

  • E948 — Eigenschaften …   Deutsch Wikipedia

  • E 948 — Eigenschaften …   Deutsch Wikipedia

  • Hyperoxid-Anion — Eigenschaften …   Deutsch Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”