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 calculationsDear 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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