arXiv subjects

Max Neudecker

Publications and source records attributed to Max Neudecker.

3 recordsLinked to original sources

arXiv2015

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.

cond-mat.soft↗

arXiv2013

Local origin of global contact numbers in frictional ellipsoid packings

In particulate soft matter systems the average number of contacts $Z$ of a particle is an important predictor of the mechanical properties of the system. Using X-ray tomography, we analyze packings of frictional, oblate ellipsoids of various aspect ratios $\alpha$, prepared at different global volume fractions $\phi_g$. We find that $Z$ is a monotonously increasing function of $\phi_g$ for all $\alpha$. We demonstrate that this functional dependence can be explained by a local analysis where each particle is described by its local volume fraction $\phi_l$ computed from a Voronoi tessellation. $Z$ can be expressed as an integral over all values of $\phi_l$: $Z(\phi_g, \alpha, X) = \int Z_l (\phi_l, \alpha, X) \; P(\phi_l | \phi_g) \; d\phi_l$. The local contact number function $ Z_l (\phi_l, \alpha, X)$ describes the relevant physics in term of locally defined variables only, including possible higher order terms $X$. The conditional probability $P(\phi_l | \phi_g)$ to find a specific value of $\phi_l$ given a global packing fraction $\phi_g$ is found to be independent of $\alpha$ and $X$. Our results demonstrate that for frictional particles a local approach is not only a theoretical requirement but also feasible.

cond-mat.soft↗

arXiv2012

Jammed frictional tetrahedra are hyperstatic

We prepare packings of frictional tetrahedra with volume fractions {\phi} ranging from 0.469 to 0.622 using three different experimental protocols under isobaric conditions. Analysis via X-ray micro-tomography reveals that the contact number Z grows with {\phi}, but does depend on the preparation protocol. While there exist four different types of contacts in tetrahedra packings, our analysis shows that the edge-to-face contacts contribute about 50% of the total increase in Z. The number of constraints per particle C increases also with {\phi} and even the loosest packings are strongly hyperstatic i.e. mechanically over-determined with C approximately twice the degrees of freedom each particle possesses.

cond-mat.soft↗