Hi everyone, I am a simple question about stress. The concept of stress in a continuum body is well known, which is Cauchy stress, defined as the average amount of force exerted per unit area. In MD simulation virial stress is generally used as a equivalent of the continuum Cauchy stress. Of course we can get the stress tensor of per atom according to the Virial theory, but the problem is what is the meaning of the stress in the strain-stress curve of nanowire. How to calculate this stress? Is it still σ＝F/A? If yes, it is not so easy to do so, isnt it? Have anyone had such good experience? Any suggestion would be greatly appreciated. Thanks
Han
Han,
Unfortunately, your question is not as simple as you think. There has been a lot of articles written over the past several years that address the issue of stress in atomistic simulation. You might want to check out papers by Robert Hardy, Terry Delph, Youping Chen & James Lee, Min Zhou, Ian Murdoch, and myself (Jonathan Zimmerman) among others. In the meantime, here are some answers to your question:
1. You're correct that the individual atomic portion of the virial stress expression does not quite equal the thermo-mechanical stress from continuum theory. In particular, issues arise due to the presence of free surfaces (see my article from 2004 and the references therein). Nevertheless, it will give you some indication of the stress and include surface stresses.
2. One thing you can do to make it more accurate would be to calculate the individual atomic portion of the stress*volume tensor expression, then divide by an estimate of the current volume of the atom using the amount of deformation the atom has undergone.
3. The use of F/A is probably okay to use too. For this, you can measure force by summing up all the atoms at one end of the nanowire that have non-zero net force but have their motion constrained by whatever boundary condition you're using to induce loading. The area can be the nominal area of the nanowire (for an engineering stress type of value), or the current cross-sectional area value up to any localization behavior i.e. necking.
4. You should also check our articles by those who have done MD simulation of nanowire deformation to find out how they measured stress. Authors include Harold Park, Ken Gall, and Min Zhou.
Good luck!
Jon Zimmerman