# MM Simulations

Dear All,

Greetings.

This belongs to those guys who works in the area of molecular mechanics simulation.
I am working of MM simulation of graphene sheet. I have employed Tersoff-Brenner potential
to model C-C bond interactions. I am using Newton Raphson method to solve non-linear equations
and written a FORTRAN Code. It gives very good converged solution for in-plane load even for very high loads, But problem arises for the transverse load, in that case my solution diverges after few iterations. I have checked my code several times but couldn’t find the bug.

Boundary conditions used is the analysis all edge atoms are fixed in x,y and z direction.

Is it due to some numerical stability or related issues.

or anyone have dealt same kind of problem so that I can discuss to resolve this issue.

Hi Sandeep,

The only thing that really comes to mind, given the provided information, is that you might be encountering a turning point instability for the transverse loading. I'm guessing you are using an incremental NR type approach. Once you increment the BC's past the turning point in the equilibrium path, then there is no near-by equilibrium compatible with the boundary conditions and your initial guess is outside the radius of convergence for NR. You would need to use an arc-length path following method in order to eliminate this type of problem...

Cheers,

Ryan Elliott

Dear Prof Elliott

I want to extend the discussion with that I didn’t get your point "once you increment the BCs … "
and your guess is right I am using incremental approach, and increments are given to transverse load (load controlled method) and initial guess is taken as zero.

I will be thankful if your will comment further to resolve this problem.

Regards
Sandeep Singh

I guess you are fixing (in x,y,z) the boundary atoms and then applying out-of-plane forces to atoms on the interior of the sheet.

By "increment the BCs", I meant incrementing the out-of-plane force values.

Anyway, I think this issue is that the system is singular (has zero tangent stiffness) in the undeformed configuration with respect to out-of-plane forces. To first order no distances between atoms change for displacements out of plane...

So, you will probably have better luck if you use a non-zero initial guess. This will give you a non-singular stiffness (still ill-conditioned, but non-singular) matrix to use with the NR procedure.

Cheers,

Ryan

Dear Prof. Elliott

I am done with the problem. There was some bug.
Thanks for your help.

Will be in touch for further discussions.
Wish you a very very Happy New Year 2015.

Good Luck

Regards
Sandeep Singh