Carbon Nanotubes Static Bending

Dear LAMMPS users

I have been trying to examine the static bending of a clamped-clamped (10,10) carbon nanotube using molecular dynamics simulations and compare the results to nonlinear continuum models.
So I used fix addforce on two rings of carbon atoms located at the center of the nanotube. I used the total force on carbon atoms in a nonlinear Euler-Bernoulli model of the nanotube.

For short nanotubes (L=20-30 nm), the results obtained from molecular dynamics matches those obtained via continuum theories very well. However, for longer nanotubes (let’s say L=50 nm), the difference between the results increases significantly. As I increase the length even further (L=200 nm, for instance), the static bending predicted via Euler-Bernoulli model is almost 6 times that predicted via molecular dynamics simulations.
I have checked with both REBO and AIREBO potentials.

Could someone please explain the reason for this discrepancy, or suggest any possible solutions?

Many thanks,
Hamed

How did you do the “static bending”? How are the “total force” used in your calculation of Euler-Bernoulli model? Normalized? A longer tube may have larger fluctuations and non-neligible noises.

Anyhow, this is not a question about LAMMPS but about your model. Your advisor and colleagues are the best ones to discuss this with.

Ray

Thanks for the answer.
I used fix addforce to put force on the nanotube and fix viscous to damp the motion (so I could measure the total displacement).

Since fix addforce is applied on atoms, I multiplied the number of carbon atoms by the force magnitude to get the total force applied to the middle of the nanotube. I used this total force in the Euler-Bernoulli model of the nanotube, with a Delta Dirac function, of course (since it is a point force in the continuum model); as you mentioned, I use dimensionless values in the continuum model.

You mentioned that a longer tube may have larger fluctuations and noises. Are these fluctuations and noises due to molecular dynamics simulations error or limitations? Because, for instance, in NEMS applications, the length of the nanotube reaches to the order of micro-meter. But, if we examine such a long nanotube via MD simulations, I suppose that the noise and fluctuations increases substantially, so that a large portion of the force on the nanotube is wasted to overcome these noises. So, my last question is that could we trust the MD results for long nanotubes and consider them as benchmarks, or should we use continuum models for very long nanotubes?

Thanks again for taking the time to help me with this problem. I truly appreciate it.
Hamed

Sorry I don’t know. Like I said, None of your questions are related to LAMMPS as these are questions about your model. I suggest you talk to your advisor and/or experts in the field.

Ray