[lammps-users] local stress calculations

An initial draft of our paper laid out the details of obtaining an estimate
of local stress from the atom-stress, but that section is not in the JCP
version, because it is not rigorous. For pairwise potentials there are
rigorous methods for obtaining local stress based on IK, and LAMMPS has a
nice implementation of one of these (Hardy method) as part of the ATC
package. However, for many LAMMPS pair styles, IK-based don't work, in which
case I recommend using the the atom-stress. The Binder method seems
excessively complicated and somewha arbitrary. I expect that for volume
resolutions larger than the force cut-off, the differences between these
different methods are negligible. Also, it is not clear to me that trying to
resolve stress variations on the lengthscales of individual particles is a
meaningful exercise.

Aidan
  

From: Ajing Cao <[email protected]>
Date: Mon, 11 Jan 2010 16:48:03 -0700
To: Aidan Thompson <[email protected]>
Subject: Fwd: [lammps-users] local stress calculations

Dear Aidan,

Could you share with me the chapter of LAMMPS report as mentioned by steve?
Thanks and have a nice day.

Ajing Cao

Northwestern University

From: Steve Plimpton <[email protected]>
Date: Tue, Jan 5, 2010 at 9:15 AM
Subject: Re: [lammps-users] local stress calculations
To: chris forrey <[email protected]>
Cc: [email protected]

We have a recent paper on this, including how LAMMPS computes
per-atom and global virial/stress. See the LAMMPS citation
page and the JCP 2009 with Aidan Thompson as the 1st author.
Aidan (athomps at sandia.gov <http://sandia.gov> ) can give you chapter and
verse
on IK vs other methods.

Steve

Lammps community,

I am interested in calculating the state of stress in a diblock (A-B)
copolymer film. The films I am studying typically phase separate to produce
lamellar order (ie inhomogeneity is restricted to a single dimension). I am
interested in studying the components of the stress tensor along the
lamellar axis, ie crossing through A/B interfaces. Lammps allows for the
computation of a peratom stress (units of pressure-volume). Naively, I had
anticipated simply averaging peratom stresses in a region of space (much
like the "fixave spatial" lammps command) to get the local stress tensor for
that region of space. However, I have found a considerable body of
literature discussing atomisitic calculation of local stress tensors that
suggests that my naive approach is insufficient. Irving and Kirkwood first
proposed a method in the '50s and Pastor and more recently Binder have built
upon the Irving Kirkwood method. In all cases, an effort is made to prevent
pairwise (and larger N) interactions from being double counted, or in other
words the virial is "distributed" amongst the many arbitrary cubic volumes
of space upon which the mechanical definition of stress is based.
Typically, there is a weighting function of the contributions to the forces
felt across a given face, based upon the distance of separation of the 2 (or
more) particles. If anyone is really interested in this topic, I will be
glad to post relevent references.

What I am interested in is knowing whether anyone has thought about
calculating local stresses using lammps and has there been any initial
attempt to implement the Irving-Kirkwood, method of planes, or more recent
methods of calculating stress from atomistic simulations? I am aware of
current efforts to simply apply a cutoff to the peratom virial in
determining stress from MD. Does anyone have any opinions/expertise on this
topic that they would share? Thanks,

Chris

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