Ericmock,Thanks for your

Bin Liu — Fri, 16 May 2008 04:36:12 -0400

Ericmock,
Thanks for your interest in our work. You are right that “the instantaneous stress in a body in 'equilibrium' need not be zero”. We’d like also point out that the absolute equilibrium can only be realized at 0K temperature, since the ordinary thermal movements of atoms imply the inequlibrium of the system. However, the example of atom chains used in our paper is actually assumed to be in statistical equilibrium or macroscopic equilibrium, which means the mechanical and thermal states would not evolve statistically. On the other hand, the Cauchy stress is the macroscopically meaningful stress definition, should be the average of the internal forces among atoms. Our point is that if this average is carried out in the Lagrangian way, no velocity appears in the definition. Virial stress corresponds to performing this average in Eulerian way, therefore, the velocity appears. But in Zhou’s work, neither these two frameworks is used completely in the averaging process to compute the stress, the kinetic part is then missed. The incorrectness of Zhou’s work has been numerically demonstrated by Subramaniyan (2007, see http://imechanica.org/node/871 and http://imechanica.org/node/3060). Another factor discussed in our paper is that the velocity is not an objective quantity, which depends on the choice of the reference frame. We therefore suggest adopting the Lagrangian atomic stress definition to avoid these probable velocity-related nonobjectivities.
In addition, we didn’t claim that “a perfectly elastic rod floating in space cannot have any stress in it”. If one computes the atomic stress locally, the stress due to the residual stress or waves propagating should not be zero. The spatial dimension to perform averaging internal forces depends on the specific problem: usually the smaller-sized averaging sample would lead to higher error, while the larger-sized sample may lose the resolution.

Is Zhou really 'incorrect'?

ericmock — Thu, 15 May 2008 16:34:02 -0400

It's not clear how you can say Zhou's expression is actually incorrect. It obviously depends on what you want to measure. Instantaneously, the stress in a body in 'equilibrium' need not be zero. Otherwise, what would be the mechanism of phase change, or residual stress? Your argument showing the incorrectness of Zhou's expression seems fundamentally flawed. You assume that the chain of atoms is in mechanical equilibrium but it clearly is not. It's like saying a perfectly elastic rod floating in space cannot have any stress in it. Surely there could be residual stress or waves propagating.

iMechanica - atomic stress - Comments

Ericmock,Thanks for your

Is Zhou really 'incorrect'?