First of all I have to apologise for repeating the topic of my post, but I am new with this posting system and I do not know how to reply to one thread.

Now my doubt:

I am trying to obtain the elasticity and rigidity tensors and looking to the example included on the LAMMPS package I do not know why stress/strain is used to obtain the Cs. I have been looking for some reference on the Internet to understand this better but I was not successful. I would appreciate if someone could send me some article’s reference where I can read more about this.

I used the source with some modifications for Cu at 300K with EAM and MEAM potentials and the results were the predicted ones by bibliography.

The example is the one where elasticity constant tensor is calculated for a silicon crystal. The one which has the init.mod, potential.mod, displace.mod and in.elastic files.

I don't have a reference. The validity of the method is based on the
definition of elastic constants as derivatives of stress w.r.t. strain,
which you can find in text books such as Kittel;

But there is a big danger measuring elastic constants at finite temperature. Due to thermal fluctuations you have to allow statistical variations and take account of them. Aiden’s method is clever in dealing with this, but I suggest you read a good MD book to understand what you are trying to achieve. These two are a start.

J.M. Haile. Molecular Dynamics Simulation. Wiley, 1997
D.C. Rapaport. The Art of Molecular Dynamics Simulation. Cambridge University
Press, second edition, 2004.