It is interesting by the determination of the atomic pressure in solids.

I read some paper about the viral stress which was introduced by Lutsko (J. Appl. Phys. 64 (3), 1988) using the local momentum flux:

dp(r)/dt = - div s(r)

where p(r) is the momentum and s(r) the stress

Following the calculus, it is not clear for me if Lutsko uses the Lagrange of Euler description but I supposed a Lagrangien description. But in this case, I am not sure of the physical meaning of s(r). This point has been discussed by Zhou (Proc. R. Soc. Lond. A (2003) 459, 2347–2392) and in this website :

http://www.eng.fsu.edu/~dommelen/papers/virial/mosaic/index.html

In the absence of volumic forces, in continuum mechanics, the Newton's law is:

\rho d2u(r)/dt2 = - div s(r)

with u(r) and s(r) the displacement and the Cauchy stress. This equation is valid in the Euler description.

I am confused about the right way to get the atomic stress.

Does someone know about that point ? How can I determine the atomic stress properly ?

Thank you for your answers.