You will have to choose a cubic Bravais lattice with a basis - the basis vectors specify the positions of the atoms in the unit cell with respect to some well-specified origin of the coordinate system (say, some point inside the unit cell). Changes in the basis vectors, or changes in the positions of the atoms in the unit cell corresponding to the adopted cubic Bravais lattice, will not affect the cubic symmetry of the system. For details, you may consult the book Solid State Physics, p. 75, by Ashcroft and Mermin.

Thanks.

However, the question is how implement a pairwise force function or an influence force function in LAMMPS peridynamics to properly describe an FCC material. More in detail, whether LPS model is suitable for this implementation and what are the parameters that I have to change in the LAMMPS peridynamics source code.

You are welcome Andrea.

I have no experience with LAMMPS, so am not in a position to comment. The basic principle related to the main question on this page is what I indicated in my previous comment. Essential is that the basis victors of a lattice with a basis indicate the positions of the atoms in the unit cell, so that whatever force function one uses, the relevant quantities are these very atomic positions. Of course the unit cell can also vary in the optimization process, however since you wish to preserve the cubic symmetry of your lattice, there is only one parameter to be varied, namely the lattice constant a.

Differential susceptibility begins as reversible susceptibility due to crystalline anisotropy and this is Xrev = Xi (1 - m^2) = Xi Xr where m = M/Ms is the fraction of saturation magnetization for cubic polycrystals and Xr is the texture. Irreversible suscetibility can be approximated as Xirr = DM Xr^2/2Hc which is the change in magnetization from a reversal times the texture squared divided by twice the coercive field.

Greetings Andrea,

Did you try asking this question in LAMMPS Mail list? It would be the right place to do so. http://lammps.sandia.gov/mail.html

I assume LAMMPS peridynamics package still supports lattice SC only. Otherwise you would be defining a lattice fcc command, and that's it.

Based on your manuscript, I guess you are trying to reproduce the FCC cell of the nanotruss. Am I right? Yet if I were you I would still try, at least as an exercise, to produce a SC lattice, where each lattice point would correspond to a whole fcc cell, and then perform the desired testing, trying to adjust the peridynamics LPS material model parameters to match the stress-strain curves of your MD manuscript. Do you follow my idea?

This approach will give information "at a larger scale" than if you were modelling the fullerene nanotube nano-truss network of your manuscript. 

If interested, drop me a private message and I can try to help you or at least explain myself better. Nice manuscript by the way!

Carlos

 Hi Carlos,

I ask the question in LAMMPS mail list, I got some answers but the question is very specific and the features that I search in peridinamics in LAMMPS are still lacking.

There is confusion about the sc lattice in peridinamics: the lattice geometry and the material geometry are not bound. You can simulate also a fcc or bcc solid with sc lattice. The results have to be independent from the peridinamics point lattice.

Yes I'm trying to reproduce the fcc grapheme structures at larger scale. The advice is good but my interest will be in the behavior at high strain. Essentially I would like implement or the stress strain curves using some influence function or non linear pairwise potential. The main points are: non isotropic (and LAMMPS implementation is still isotropic), the nonlinearity (LAMMPS implementations are linear). 

In general at the moment is not possible do this in LAMMPS without coding some model implementations. 

After all, some test with current LPS model can be done but making the approximation of isotropicity and linearity. 

My opinion is that the more interesting thing will be however implement the entire model to take into account the nonlinearity, mainly under compression, and the anisotropy. 

If you want try I can send you the bulk modulus and the shear modulus of the four structures. In this case I think that the results  will be reliable only for small (local) strain.

I think that I have to contact the developers of peridinamics to find a final solution.

Anyway, thanks for your appropriate answer!

Andrea

Ah, now I can grasp the challenge of your problem. Truly interesting and challenging.

I agree with you on the usefulness of an implementation in LAMMPS, the way you describe it.

Are you aware of Peridigm? Is a peridynamics code developed by SANDIA LABS

http://chrislammi.org/research/peridigm-the-open-source-peridynamics-solver/

It might be useful for your needs. I did not try myself yet.

If you still want to share the bulk and shear modulus for the structures I will give it a try once I finish teaching this quarter.

Good luck and I look forward to the publication of your research!

Carlos