Oscillatory instabilities in three-dimensional frictional granular matter

The dynamics of amorphous granular matter with frictional interactions cannot be derived in general from a Hamiltonian and therefore displays oscillatory instabilities stemming from the onset of complex eigenvalues in the stability matrix. These instabilities were discovered in the context of one- a...

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Main Authors: Bonfanti, Silvia, Chattoraj, Joyjit, Guerra, Roberto, Procaccia, Itamar, Zapperi, Stefano
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2021
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Online Access:https://hdl.handle.net/10356/146574
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1465742023-02-28T19:55:40Z Oscillatory instabilities in three-dimensional frictional granular matter Bonfanti, Silvia Chattoraj, Joyjit Guerra, Roberto Procaccia, Itamar Zapperi, Stefano School of Physical and Mathematical Sciences Science::Physics Classical Statistical Mechanics Jamming The dynamics of amorphous granular matter with frictional interactions cannot be derived in general from a Hamiltonian and therefore displays oscillatory instabilities stemming from the onset of complex eigenvalues in the stability matrix. These instabilities were discovered in the context of one- and two-dimensional systems, while the three-dimensional case was never studied in detail. Here we fill this gap by deriving and demonstrating the presence of oscillatory instabilities in a three-dimensional granular packing. We study binary assemblies of spheres of two sizes interacting via classical Hertz and Mindlin force laws for the longitudinal and tangent interactions, respectively. We formulate analytically the stability matrix in three dimensions and observe that a couple of complex eigenvalues emerge at the onset of the instability as in the case of frictional disks in two dimensions. The dynamics then shows oscillatory exponential growth in the mean-square displacement, followed by a catastrophic event in which macroscopic portions of mechanical stress and energy are lost. The generality of these results for any choice of forces that break the symplectic Hamiltonian symmetry is discussed. Published version 2021-03-02T02:13:00Z 2021-03-02T02:13:00Z 2020 Journal Article Bonfanti, S., Chattoraj, J., Guerra, R., Procaccia, I., & Zapperi, S. (2020). Oscillatory instabilities in three-dimensional frictional granular matter. Physical Review E, 101(5), 052902-. doi:10.1103/physreve.101.052902 2470-0045 https://hdl.handle.net/10356/146574 10.1103/PhysRevE.101.052902 32575318 2-s2.0-85086306066 5 101 en Physical Review E © 2020 American Physical Society (APS). All rights reserved. This paper was published in Physical Review E and is made available with permission of American Physical Society (APS). application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Physics
Classical Statistical Mechanics
Jamming
spellingShingle Science::Physics
Classical Statistical Mechanics
Jamming
Bonfanti, Silvia
Chattoraj, Joyjit
Guerra, Roberto
Procaccia, Itamar
Zapperi, Stefano
Oscillatory instabilities in three-dimensional frictional granular matter
description The dynamics of amorphous granular matter with frictional interactions cannot be derived in general from a Hamiltonian and therefore displays oscillatory instabilities stemming from the onset of complex eigenvalues in the stability matrix. These instabilities were discovered in the context of one- and two-dimensional systems, while the three-dimensional case was never studied in detail. Here we fill this gap by deriving and demonstrating the presence of oscillatory instabilities in a three-dimensional granular packing. We study binary assemblies of spheres of two sizes interacting via classical Hertz and Mindlin force laws for the longitudinal and tangent interactions, respectively. We formulate analytically the stability matrix in three dimensions and observe that a couple of complex eigenvalues emerge at the onset of the instability as in the case of frictional disks in two dimensions. The dynamics then shows oscillatory exponential growth in the mean-square displacement, followed by a catastrophic event in which macroscopic portions of mechanical stress and energy are lost. The generality of these results for any choice of forces that break the symplectic Hamiltonian symmetry is discussed.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Bonfanti, Silvia
Chattoraj, Joyjit
Guerra, Roberto
Procaccia, Itamar
Zapperi, Stefano
format Article
author Bonfanti, Silvia
Chattoraj, Joyjit
Guerra, Roberto
Procaccia, Itamar
Zapperi, Stefano
author_sort Bonfanti, Silvia
title Oscillatory instabilities in three-dimensional frictional granular matter
title_short Oscillatory instabilities in three-dimensional frictional granular matter
title_full Oscillatory instabilities in three-dimensional frictional granular matter
title_fullStr Oscillatory instabilities in three-dimensional frictional granular matter
title_full_unstemmed Oscillatory instabilities in three-dimensional frictional granular matter
title_sort oscillatory instabilities in three-dimensional frictional granular matter
publishDate 2021
url https://hdl.handle.net/10356/146574
_version_ 1759858367458705408