# compute local stress

Dear all
I need to calculate the local stress in a group during loading and I used the stress/atom and compute reduce commands.
to calculate the real stress I need to use the volume of group. I have searched the mailing list and find that there is not a direct command for do this.
1- is there a way to compute the real stress in group without compute the local volume, because I just need it to compute the stress?
2- is there a method to compute the volume of a group?
thanks

Dear all
I need to calculate the local stress in a group during loading and I used
the stress/atom and compute reduce commands.
to calculate the real stress I need to use the volume of group. I have
searched the mailing list and find that there is not a direct command for
do this.

...and there is a good reason for that: the volume of a single atom is
an ill-defined property. you can only infer an effective volume
indirectly, e.g. via density.

1- is there a way to compute the real stress in group without compute the
local volume, because I just need it to compute the stress?

if you want spatially resolved stress, you might find help in the
atoms-to-continuum (USER-ATC) package. other than that, you probably
will have to search the literature for a derivation (or come up with
one by yourself if there isn't any) and then program it.

2- is there a method to compute the volume of a group?

not really. it is not a well defined property. you could make some
assumptions, but they will all have flaws. if you'd assume an
effective volume per atom and sum over that, you cannot account for
volume changes due to changes in packing. if you use some kind of
tessellation, you have to make an assumption about the radius of an
atom, since the simulation itself uses point particles which have no
volume (and radius) at all. and so on...

axel.

While the volume of a single atom is not well defined, the volume of a
compact group (cluster) is (the larger the cluster more meaningful is
the volume). LAMMPS has a computer to calculate the voronoi volume per
atom. You can combine that with a "reduce sum" compute to obtain the
total voronoi volume of the group.

Daniel beat me to this response (and was too modest to mention
that he wrote the new compute voronoi/atom command).

This is a great use for the new command, and is probably the
best conceptual way to get the "volume" of a group of atoms for the
stress calculation you are doing.

Daniel - can't remember if you ever told me if it is possible
to use the Voro++ package (that the compute wraps) to get
voronoi areas for 2d systems?

Steve

Daniel - can't remember if you ever told me if it is possible
to use the Voro++ package (that the compute wraps) to get
voronoi areas for 2d systems?

I do not think so. But I could take a look at using a different
backend such as "Qhull" or "Viennagrid", which also do 2d.
Such a change would be transparent to the LAMMPS users.