Local analysis of the history dependence in tetrahedra packings

The mechanical properties of a granular sample depend frequently on the way the packing was prepared. However, is not well understood which properties of the packing store this information. Here we present an X-ray tomography study of three pairs of tetrahedra packings prepared with three different tapping protocols. The packings in each pair differs in the number of mechanical constraints $C$ imposed on the particles by their contacts, while their bulk volume fraction $\phi_{global}$ is approximately the same. We decompose $C$ into the contributions of the three different contact types possible between tetrahedra -- face-to-face (F2F), edge-to-face (E2F), and point contacts -- which each fix a different amount of constraints. We then perform a local analysis of the contact distribution by grouping the particles together according to their individual volume fraction $\phi_{local}$ computed from a Voronoi tessellation. We find that in samples which have been tapped sufficiently long the number of F2F contacts becomes an universal function of $\phi_{local}$. In contrast the number of E2F and point contacts varies with the applied tapping protocol. Moreover, we find that the anisotropy of the shape of the Voronoi cells depends on the tapping protocol. This behavior differs from spheres and ellipsoids and posses a significant constraint for any mean-field approach to tetrahedra packings.