The classical potential of carbon has limitations. The force field parameters are obtained at close-to-equilibrium situations. It is not surprising that you cannot obtain the far-from-equilibrium energies and forces correctly. You will need to use some special MD potentials or DFT instead.  

Dear Sayyed,

It'll be useful to compare the curve obtained by You and the experimental one (I'm not quite sure relying on your question, who did the experiment). Probably the experiment demonstrate different behavior at non-linear area. As I know, the theory often predicts values higher than expected because it's hard to model some defects in a sample or take into account some essential conditions of experiment. So the message is: pay double attention to the experiment details, including the graphene synthesis procedure.

Hope you'll find my answer useful. Good luck with your research!

The classical potential of carbon has limitations. The force field parameters are obtained at close-to-equilibrium situations. It is not surprising that you cannot obtain the far-from-equilibrium energies and forces correctly. You will need to use some special MD potentials or DFT instead.  

Dear Sayyed,

I think the simplest explanation is that MD practically forces you to use a strain rate that has nothing to do with reality. Thus, the system does not have enough time to relax to the physically appropriate state at a given strain rate, which could be a cracked crystal. Hence, the tensile strength and failure strain turn out much higher than the experimentally measured ones. As one possible solution, you might consider doing some sort of quasistatic simulation, where you incrementally increase the box size in the stretched direction and let the system relax for some time at each fixed box size. Essentially this means that you would be sampling the stretching and the particle dynamics with different time resolution.

Tersoff potentials are not to be trusted for 2D systems. Too many uncertainties and elastic and vibrational properties cannot be matched, hence elastic behaviour can be unrealistic in MD. I have looked at many force fields for graphene and then decided to make my own.....

Thanks to all friends.

Dear Max you made your own MD potential for graphene? 

Yes, it's called MMP. I have only published the version for Silicon.

The graphene one is under review.

http://m.iopscience.iop.org/1742-6596/367/1/012015

You can download from my profile.

The problem comes from the Tersoff potential. In general grounds classical potentials are not appropriate to correctly reproduce the experimental results at extreme strain conditions. I suggest you should use ab-initio methods for such calculations. Such calculations for graphene as well as some of its allotropes have been performed by our group and will be published soon.

Dear friends

Modification on Tersoff potential (increasing the minimum cutoff distance from 1.8 to 2.0 angstrom) could incredibly improve the results. Thanks to all. 

Dear Sayyed,

I can understand why by increasing the cutoff distance from 1.8 to 2.0 Ang the results are improved. In the original Tersoff potential the cutoff function takes nonzero values  in the range [1.80, 2.10]. For interatomic distances < 1.80, the cutoff function equals 1. Thus, for interatomic distances > 2.10, (i.e. for strains > 48%), there are no any interactions. For interatomic distances in the range [1.80, 2.10]  (i.e. for 27% < strain < 48%) the C atoms feel some extra forces of a type of "delta-function" derived from the derivative of the cutoff function. Those forces are not true forces, but they do exist in the frame of the Tersoff potential, and probably they are responsible for the tail you find in the stess-strain plot in the [0.3, 0.4] strain region.

By increasing the value of the cutoff distance to 2.0 Ang, what you really do is that you change the action of the cutoff function from the [1.80, 2.00] to the [2.00, 2.30] range. Thus, the extra cutoff function forces act for strains in the range [40%, 60%], the values of which correspond to stresses well beyond the ultimate strength limit and even beyond the fracture strain limit. Thus, by increasing the cutoff distance to 2.0 Ang, you avoid that tail in the stress-strain plot and probably you can find a value for the ultimate strength limit different from the fracture limit you found in your stress-strain plot using the original Tersoff potential. However, it is still under question if the values of ultimate strength and the fracture behaviour you find using the new cutoff distance are reliable.

(For the estimations of the above strain values I assumed that the equilibrium bond length ot graphene is 1.42 Ang.)

Stress-Strain curve after modification on Tersoff potential would be something like this:

Young modulus: 0.935 TPa

Tensile strength: 112 GPa

Dear Sayyed,

your results show that the ultimate tensile strength coincides with the fracture limit. According to DFT results, the fracture limit is beyond 30% of strain and there is a softening of grahene for strains >  20%. You can also check for the stress-strain plot for different orientations, for instance along zig-zag and along arm chair directions. According to DFT results the behaviour is different for those directions.

Dear colleagues

Did somebody try to use Reaxff force fields for investigation of stress-strain curve of graphene? what were the results?

Hi.

what is the difference between condition of your first and second graphs. because i have this problem like yours.

but in T=300K my answers are more better. 

Dear Amin,

I guess you use molecular dynamics to get your results. Your results are not surprising, but still they are not as expected according to DFT results. The problem comes form the potential, which can not reproduce the DFT results for high strain values.

Dear Zacharias

I know that problem  comes from the potential. but i want to fix this problem in referable way. Mr mahdizade have fixed this and i want the difference between the potential function parameters.

thank you. 

Following up on my previous answer, the new empirical potential for Graphene is now online in Carbon. You can download from my profile.

I should really try and include it in something like LAMMPS or similar, but it will be a while.

http://www.sciencedirect.com/science/article/pii/S0008622315003358

If you are interested in DFT results for graphene and its allotropes under extreme uniaxial strain, please have a look at our recent publication here

http://pubs.rsc.org/en/content/articlelanding/2015/cp/c5cp02412a#!divAbstract

Dear Mahdizadeh,

Could you please tell me how did you over come this issue? I have a problem like this but I don't know where I should change the cutoff  for Tersoff potential?

Can you clear this problem plz?

Regards

Amir

Dear all,

• As others mentioned, Tersoff empirical potential is more convenient for systems near the equilibrium and it fails out of equilibrium conditions, that's why the stress strain curve of graphene and other 2D nano materials calculated using Tersoff potential is off at high strain region specially near the failure point. One can fix the problem by enlongating the cutoff radious, R, slightly from 1.95 to 2.00. Also don't remember to set the cutoff switching parameter, D, to zero. These changes make the system to behave physically more reasonable at strains near the failure point.

Cheers

Jalil

Dear Amir,

You need to change the cutoff and switching cutoff parameters within the Tersoff potential manually.

Hi Seyyed,

• I will do it and share my results with you.
• Just one more question, in which direction the graphene model is strained and the results raised up? I mean zig-zag or armchair?

B. Regards

Amir

Dear Seyyed,

I run the simulation wirh R=2, D=0 and the strain value come back about 0.18 and the stress is about 88 GPa. It seems give a good results.

In your modified stress-strain curve the strain was 0.2 and the stress is around 115.

So, what is the difference here?

I forget to tell you my graphene dimension was 12x50 nm with 252 atoms. and in your simulation it was 50x50nm . ..... may the dimension is the source of this difference!!!!!

Regards

Amir

Definitely no, because I've evaluated the nano sheet size dependency and I've found no correlation there. I've applied the strain in armchair direction but as I've found, there was not a significant difference with zigzag direction. Difference between your result and mine may origins from two sources, the simulation code you are using and strain rate value. Also I've used the optimized Tersoff parameters rather than the original one.

@ Seyyed, Thanks for your helpful answers.

You welcome.