Lattice Boltzmann Model for Composites

So I was reading some articles on the LB method when I came across the following paper

Elastic property of multiphase composites with random microstructures

In the paper they use a variation on the LB method to model the displacements in a composite structure. Ive seen a similar method proposed by B. Chopard et al at the University of Geneva (although it doesn’t appear to have been applied to composites), however this one appears to be slightly different. My interest was tweeked so i started doing some searches online to see if I could find any more information about this model, however I was not able to find a single bit of literature relating to this method other than the article linked. The two articles which cite it are not concerned with the LB method used, and the article itself gives no references for the method, Has anyone here come across this method before?


Following the discovery of this paper I decided to implement the model described using matlab. I think I’ve done this correctly, however I now have to deal with the fact that the paper makes no mention of boundary conditions or initial conditions.

In the paper it can be seen that the sum of the populations for a particular lattice site is equal to the scalar value of displacement of a lattice site. That is the actual position of the lattice node (grain position) is not necesarily in the same location as the lattice location of the site (lattice position). Conceptually this can be tricky to understand first time, but if you read the paper it will become clearer. Based on this information I have taken the initial populations to be zero since in theory the system starts with zero displacement.

So on to boundary conditions. It seems to me that the boundary conditions for this method are likely to be very close to those used in the LBM for fluids. However, outside of palabos i haven’t personally implemented anything more complicated than bounce back nodes so im approaching the current limit of my understanding here. I’m currently working my way through this article:

Straight Velocity Boundaries in the Lattice Boltzmann Method

At the moment it seems to me that it may not be as straight forward as applying the fluid BC’s to this solid model. Anyone out there with any ideas?


PS I’ll give you a cookie if you figure it out before me.