Jammed frictional tetrahedra are hyperstatic

TL;DR

This study investigates the mechanical properties of packings of frictional tetrahedra, revealing they are hyperstatic and that contact types influence the contact number growth with packing density.

Contribution

It demonstrates that frictional tetrahedra packings are hyperstatic across a range of densities and highlights the significant role of edge-to-face contacts in contact number increase.

Findings

Contact number Z increases with volume fraction {}

Packings are strongly hyperstatic with constraints roughly twice degrees of freedom

Edge-to-face contacts account for about 50% of contact number growth

Abstract

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.