Geometric structure and mechanical stability of disordered tetrahedra packings

An experimental X-ray computed tomography study

by Max Neudecker
Doctoral thesis
Date of Examination:2013-12-12
Date of issue:2013-12-18
Advisor:Dr. Matthias Schroeter
Referee:Prof. Dr. Annette Zippelius
Referee:Prof. Dr. Stephan Herminghaus
Persistent Address: http://dx.doi.org/10.53846/goediss-4288

 

 

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Abstract

English

In this study, the geometric structure of frictional, disordered tetrahedra packings is analysed in detail via X-ray Computed Tomography. The choice of the granulate is motivated by moving away from the "spherical cow" paradigm towards more realistic models of granulates. It is shown that different preparation protocols can be utilized to create packings with a wide range of packing fractions (0.47-0.62). Mechanical stability is discussed in the context of the Jamming paradigm: The generalized constraint number C, which depends on the contact geometries, reaches values between 12 and 18, substantially larger than the isostatic limit of 6 constraints per particle. Experimentally prepared, frictional tetrahedra packings are therefore hyperstatic, in contrast to previous studies claiming isostaticity. In general, mechanical stability is history dependent, that is, the constraint number depends not only on the packing fraction, but also on the preparation technique, particularly the shaking acceleration. Analysis of the geometric structure reveals that the number of face-face contacts per particle follows a Binomial distribution with a sample-dependent probability, which increases with higher packing fraction. This underlines the disordered, random structure of the packings. It is observed that a) dense local structures have a abundance of face-face contacts, b) face-face-connected clusters grow strongly with higher packing fraction, and c) the face-face contact number may serve as a global order parameter. The mapping between local packing fractions (via the Set Voronoi Diagram) and contact geometries reveals that globally denser packings are realised locally by an increasing number of edge-face or face-face contacts, at the cost of point contacts.
Keywords: Jamming; Tetrahedra; Granular matter; Computed Tomography; X-ray Computed Tomography
 
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