Many simulations or experiments in the field of granular materials are perform with two spatial dimensions, using cylinders instead of actual grains. This allows to simplify the problem and reduce the number of grains considered. However, there are some difference between two-dimensional grains and three-dimensional ones.
This project pushes the question forward: what would happened if higher dimensional grains were considered? Like a flow of four-dimensional or five dimensional (hyper)spheres. As this is not achievable experimentally (after all, we only have three dimensions of space), we developed a numerical simulation tool to study just this: NDDEM.
Here is for example an inlined plane flow of three-, four-, and five- dimensional monodisperse hyperspheres (all the grains are the same size, they appear different sizes on screen due to their distance in the non-visible dimensions):
More advance descriptions and videos explaining these concepts are available here.
NDDEM is actually a full-fleshed discrete element solver that works in any number of spatial dimensions. It includes
- Discrete element solver of hypersphere with translational and rotational degrees of freedom, elastic and frictional contact laws, polydisperse particles, periodic boundary conditions in any dimension, Lees-Edward boundary conditions.
- Coarse-graining solver with Lucy function in any number of spatial dimensions
- Texturing of rotating hyperspheres in any number of spatial dimensions.
This allowed to perform some mechanical tests in higher dimension frictional granular materials: