I'm also interested in shear (of solids), but I was applying it
via barostat, like:

fix 1 all npt temp .... x 0.0 0.0 \{d\} y 0\.0 0\.0 {d} z 0.0 0.0 \{d\} yz 0\.0 0\.0 {d} xz 0.0 0.0 \{d\} xy 0\.0 1000 {d} drage 2

and after that equilibrating it to get meaningful statistics.

I wonder if there will be difference between barostating and very slow shear strain rate NEMD?
Theoretically, if shear is infinitely slow compared to equilibration time, NEMD should give equilibrium solution,
right?

I guess in most cases if shear is applied experimentally on macro (solid) sample,
strain rate is much smaller than equilibration time of the system. Coming from macro scale,
applying shear pressure via barostat to me seems closer to experimental tests.

Is there any general consensus on how to model equilibrium shear of solids at non-zero temperature?

If you apply xy shear with the npt barostat,
then it will not be applied at a constant shear
rate. Rather you will get some odd oscillatory
behavior as the solid shears slightly to
attempt to equilibrate the xy pressure.

So using fix deform to shear at a constant
rate (as slow as you have patience for)
is a more typical way to monitor the
response of a liquid or solid.

What I was thinking of is, say, a comparison of the following:

1) well equilibrated (via barostat) RVE at shear stress Pxy and corresponding
shear strain Lxy.

2) 'very slow' fix deform (constant strain rate) and
the value of Pxy which corresponds
to the moment when its shear strain is Lxy.

Aren't these two the same theoretically ?
In quasi-static case, if I'm not interested in the complete loading 'curve',
but just a value of a shear strain at certain shear stress.

Or put it another way, should not barostat be preferable for quasi-static
loading study? Whereas fix deform has to have strain rates considerably
higher (orders of magnitude) compared to macro experiment?

If you just want a single stress/strain value then
I suppose you could use either method. Fix deform
(or box_displace) lets you set the strain and then
measure the stress. Fix npt would do the opposite.