# Peridynamics for a material with cubic symmetry

Hello Users,

I am attempting to do some peridynamics simulations of an face centered cubic unit cell material. This material is a graphene structure of which I have calculated the stress strain curve (under tension and compression) along the pincipal directions and stiffness matrix, using molecolar dynamic simulations. https://arxiv.org/pdf/1606.05494v1.pdf First I would ask you about the possibility of simulating a material with cubic symmetry using peridynamics. I would like implement a pairwise force function that takes in to account the compressive (linear + plateau) and tensile (linear) behavior of the material. Is this possible in lammps implemetation of peridynamics?

Best regards
Andrea

Peridynamics (PD) is much more coarse-grained than

a typical all-atom model for graphene. What you

should find out (PD papers, email PD experts) is

whether are PD constitutive models for graphene-like

materials.

Steve

Thank you very much Steve,

I try to explain my idea in a better way.
I know that graphene is difficult to treat with peridynamics and I would like to avoid an explicit insertion of graphene in the model. My idea was essentially compute the stress strain curves along principal axis of the material [100][110][111] using molecular dynamics and then implement a pairwise force function or an influence function that takes into account the different behavior along different directions. Essentially I would like treat my 3D periodic graphene structure as a continuum. So I will increase my MD structures until the stress strain curves converge to a “macroscopic” trend. The peridynamics input would be the stress strain curves or, for small displacement, the bulk and the shear modulus. Starting from the second case, with bulk and shear modulus as input I would like to use peri/lps style. The problem here is that the model, as implemented in LAMMPS is isotropic, and I would instead take into account the anisotropy of my cubic material. My graphene structures also present negative Poisson ratio for large compression, so I’m bound to use lps model and not pmb, for which Poisson ratio is fixed. In the case of stress strain curves as input the problem is similar.
To semplify the problem:
I would know if there is a way for implement peridynamics for a material with cubic simmetry and high anisotropy, starting from the stress strain curves. And in this case what are the parameters to change in lammps code, influence function ecc.
Another, less useful, approach, valid only for small deformation, would be implement the cubic anisotropy. I imagine that in this case there must be the way to give as input the three constants of the stiffness matrix of a cubic material instead of the two of an isotropic material.
Graphene is not the important part, the important part is continuum highly anisotropic material with cubic symmetry.

Thank you very much,

Andrea