Shift Vectors

Dear All


Here I want to know your opinions about mentioned below.
I am working with Graphene unit cell.

This is about shift vectors
Whenever I apply strain components E11 or E22 (one of them at a time),
In both of the case shift vector is always in direction 1, and shift is almost negligible in direction 2.

It seems me incorrect, what is your opinion ?

Thanks in advance.


Hi Sandeep,

It doesn't sound correct, but there is no way to say for sure unless you prove rather more details about exactly what you are doing. If you are using a common MD code like LAMMPS, can you provide the input and output you have obtained? Are you using a KIM potential for your calculations? How does this relate to the KIM project? If you want further help you will need to help us help you.


Ryan Elliott

Dear Prof Ryan

Many thanks for your mail. Details of the problem are as below. I will thankful if you can put your suggestion which will assist me to move further.

My current problem is Finite Deformation Static and Dynamics of Graphene Sheets using Cauchy - Born Rule.

(Using Tersoff Brenner 1990 generation potential)

Presently, I am working on Nonlinear Stretching of Graphene Sheets. For this following are the my base papers.

(1) Zhang et al (2002), The elastic modulus of single walled carbon nanotubes: a continuum analysis incorporating interatomic potential.
Int J Solids and Structures 39 (2002) 3893 - 3906
(2) Zhou and Huang (2008), Internal lattice relaxation of single layer graphene sheet under in-plane deformation
J Mech Phy Solids 56 (2008) 1609 - 1623
(3) Jiang et al (2003) The effect of nanotube radius o the constitutive modeling for carbon nanotube
Computational Mat Sci 28 (2003) 429 - 442

Among these paper 1st paper reports the elastic properties at zero stains, I have completely reproduced this paper.
But I have some problem for finding the shift vectors at finite deformation as in papers 2 and 3.

As we know, for finite deformation first we need to compute the shift vectors by solving dW/dx, which gives the system of nonlinear equations (refer paper (1))

Then I employed NR method for finding the components of shift vector.
I am bit surprised with these components of shift vectors.

If I give finite value of strain component E11 or E22 as input ( only one at a time).

for examples

when E11 is non zero

E11 = 0.03; E12 = E21 = 0; E22 = 0;
With this input for strain matrix my shift vector is [ -0.0016 ; 0.0000]


when E22 is non zero
E11 = 0; E12 = E21 = 0; E22 = 0.03;

in this case shift vector is [ 0.0017 ; 0.0000]

We can see that I flipped the strain components E11 and E22, but shifting is in the same direction for both the cases.
This seems me incorrect,
following these values of shift vectors it give incorrect elastic tangent modulus and energy at finite strains.

on the basis of your experience what is your opinion ? so that I can attack this problem further.

Thanks in advances


The only thing I can suggest is that the strain values you are using are quite large. Maybe you should try an "incremental" approach. Start with a very small value for E11 or E22, solve for the shift, then increment the strain and sovle for the updated shift. Continue in this way until you get to the value you want.

Other than this suggestion, I think you simply need to continue to investigate the problem. Poor over your code and check each aspect to make sure it is working correctly and it all makes sense to you. This sort of thing can sometimes take a lot of effort, but typically there is not much anyone can do to help you, without doing the code debugging for you...

I wish you the best of luck in finding your bugs.


Ryan Elliott