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).
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