Barostating - Constante shear stress - Pure vs Simple shear

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Dear all LAMMPS users,

  I have been using LAMMPS for a while, and for 5-6 weeks now, I have been pursuing to enforce a constant shear stress via the npt command.
  There are two questions that I would like to make regarding this subject.

  The first one is the following: how is it that, when one applies a shear stress which induces a shear strain and a change in the box shape (thus, this question also applies to the "deform" fix or the "change_box" command), the atoms of the system do see that shear stress and remain in "their" place, and do not simply "flow" back to their position they had before the application of the shear stress? What is the barostat doing to make the atoms retain their "sheared" state? I have checked the Parrinello-Rahman barostat and the formulation developed by Shinoda et al., but I cannot see where that comes from.

The second question is also a general one. It is not mentioned anywhere in the LAMMPS manual, and, although I have my own idea, I prefer to ask and confirm, if that is the case. There are only 6 stress components to be affected by the npt thermostat-barostat, corresponding 3 of them to shear stresses. This is why there are only 3 tilt factors, whose meaning is clearly described in the manual. So, I guess that this implies symmetry of the shear stress components, this is, tau xz = tau zx and so on and so forth. Is this correct ? If that is the case, what type of shear is being applied when one fixes one shear stress component? Is it pure shear or simple shear ? I have got my own guess, as I said ... If it happened to be pure shear, wouldn't there be any chances to apply simple shear via the npt barostat (one could do it just imposing a displacement to some boundary layers of a non-periodic system ... but that would yield constant shear strain, not constant shear stress).

  Thanks in advance for your time !!

Aitor

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Some of your ideas seem confused. So I will try to answer some one by one. (I am assuming you’re simulating fluid, though most of what I’ll say still holds for solids)

The first one is the following: how is it that, when one applies a shear stress which induces a shear strain and a change in the box shape (thus, this question also applies to the “deform” fix or the “change_box” command), the atoms of the system do see that shear stress

Ok, atoms do not “see” shear. Shear stress arises from the diffusion of momentum, and thus is not an external potential. Shear is transmitted from pair-wise interactions. See the remapping section in fix deform to get a hold of how straining is achieved in your system.

and remain in “their” place, and do not simply “flow” back to their position they had before the application of the shear stress?

Newtons laws for fluids. The position remapping for solids(someone else might speak to this one, I am not clear exactly if the barostat does this).

What is the barostat doing to make the atoms retain their “sheared” state? I have checked the Parrinello-Rahman barostat and the formulation developed by Shinoda et al., but I cannot see where that comes from.

Barostat simply resizes the box to keep pressure/stress tensor constant. Its just application of control theory to achieve a constant pressure/stress ensemble, as opposed to constant volume/deformation. Again this is an indirect method, virial stresses arise from particle-particle/wall interactions.

The second question is also a general one. It is not mentioned anywhere in the LAMMPS manual, and, although I have my own idea, I prefer to ask and confirm, if that is the case. There are only 6 stress components to be affected by the npt thermostat-barostat, corresponding 3 of them to shear stresses. This is why there are only 3 tilt factors, whose meaning is clearly described in the manual. So, I guess that this implies symmetry of the shear stress components, this is, tau xz = tau zx and so on and so forth. Is this correct ?

Yes, but this is much deeper than just a LAMMPS command. The underlying assumption in a constitutive model is that solid rotations do not result in any stress. That means the constitutive law only works on the symmetrized part of the rate of deformation tensor. For solids the argument is much more simple, they are in static equilibrium.

If that is the case, what type of shear is being applied when one fixes one shear stress component? Is it pure shear or simple shear ? I have got my own guess, as I said … If it happened to be pure shear, wouldn’t there be any chances to apply simple shear via the npt barostat (one could do it just imposing a displacement to some boundary layers of a non-periodic system … but that would yield constant shear strain, not constant shear stress).

Look into my last comment and fix documentation, and you should find an answer.