Open Conference Systems, StatPhys 27 Main Conference

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Mechanical rigidity and the duality of networks in jammed granular packings
Deshpreet Singh Bedi, Bulbul Chakraborty

##manager.scheduler.building##: Edificio San Jose
##manager.scheduler.room##: Aula 110/111
Date: 2019-07-11 03:00 PM – 03:15 PM
Last modified: 2019-06-10

Abstract


A phenomenon that remains of widespread interest is the manifestation of mechanical rigidity in dry, athermal, amorphous materials, such as foams and granular matter, when subjected to external stresses, despite the lack of the stabilizing presence of cohesive interactions between constituent particles. Analogously, the loss of rigidity in a jammed packing is also the subject of significant inquiry: it is crucial to understand the onset of yielding and plastic rearrangements of particles in such materials in response to perturbations.

 

To this end, it is useful to analyze jammed granular systems as a set of distinct networks. Typically, this entails mapping the jammed configuration of grains to a contact network of springs connecting nodes in mechanical equilibrium. This by itself is problematic, since the use of two-sided springs in place of purely repulsive contacts can lead to non-trivial changes in the mechanical response and physical properties of a system. It is additionally possible, however, to use the contact forces to represent the system as a separate network of edges that form a space-filling tiling in a dual force space. This force tiling paradigm has been found to be particularly valuable in the characterization of stress-induced transitions in granular materials. As a generic network itself, the force network can be studied with techniques used in the investigation of more conventional networks.

 

Using jammed granular packings obtained from simulations, we explore the duality between the resultant real-space contact networks and force tilings. We analyze the relationship between zero modes and states of self-stress in these dual networks, and connect it to physical properties of jammed packings and to unjamming. In particular, we use this duality to allow for the more expedient investigation of states with only repulsive interactions. Furthermore, this analysis can also provide improved understanding of the stability of granular systems against the effect of external perturbations.