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

CASE1

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]**

CASE2

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

Regards