Virial Stress and Mechanical Stress

Hi Ibrahim,

Allow me to set the record straight: to obtain the full Cauchy stress from
the Virial (the stress/atom compute), one DOES need to include the kinetic
contribution. If you¹d like a definitive discussion about this, check out
this reference:

Jonathan A. Zimmerman, Reese E. Jones and Jeremy A. Templeton, ³A Material
Frame Approach for Evaluating Continuum Variables in Atomistic
Simulations², Journal of Computational Physics, 229 (2010) 2364-2389

Moreover, the individual per-atom contribution to the virial stress is not
truly mechanical (Cauchy) stress, even with the kinetic term. Rather, one
needs to average the per-atom contribution over a reasonably sized
sub-volume of material in order for them to be equivalent. More discussion
on this can be found in the reference above, and references therein.
Certainly the system-averaged virial does correspond to the average Cauchy
stress for the system.

Regarding your questions:

When periodic boundary conditions is employed but atoms don't cross any
of the sides of the simulation box, does that mean that Lagrangian frame
of reference is employed implicitly in lammps or there's another way to
activate that reference?

For LAMMPS simulations, the atoms are always in the Eulerian/Spatial
configuration. Just because the atoms don¹t cross PBCs doesn¹t make them
any less so, or change the reference frame of the simulation.

When temperature increases and LJ potential is used, how does that
affect the virial stress and LJ potential is temperature independent?

Your question is non-sensical. The LJ potential has nothing to do with
either temperature or stress, other than it depends on instantaneous
positions of atoms, which in-turn depend on those quantities. As
temperature increases, the kinetic contribution to stress increases (as
does the system energy).

Jon Zimmerman