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Dynamics of Granular Crystals with Elastic-Plastic Contacts


Burgoyne, Hayden Andrew (2016) Dynamics of Granular Crystals with Elastic-Plastic Contacts. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9J38QG6.


We study the behavior of granular crystals subjected to impact loading that creates plastic deformation at the contacts between constituent particles. Granular crystals are highly periodic arrangements of spherical particles, arranged into densely packed structures resembling crystals. This special class of granular materials has been shown to have unique dynamics with suggested applications in impact protection. However, previous work has focused on very low amplitude impacts where every contact point can be described using the Hertzian contact law, valid only for purely elastic deformation. In this thesis, we extend previous investigation of the dynamics of granular crystals to significantly higher impact energies more suitable for the majority of applications. Additionally, we demonstrate new properties specific to elastic-plastic granular crystals and discuss their potential applications as well. We first develop a new contact law to describe the interaction between particles for large amplitude compression of elastic-plastic spherical particles including a formulation for strain-rate dependent plasticity. We numerically and experimentally demonstrate the applicability of this contact law to a variety of materials typically used in granular crystals. We then extend our investigation to one-dimensional chains of elastic-plastic particles, including chains of alternating dissimilar materials. We show that, using the new elastic-plastic contact law, we can predict the speed at which impact waves with plastic dissipation propagate based on the material properties of the constituent particles. Finally, we experimentally and numerically investigate the dynamics of two-dimensional and three-dimensional granular crystals with elastic-plastic contacts. We first show that the predicted wave speeds for 1D granular crystals can be extended to 2D and 3D materials. We then investigate the behavior of waves propagating across oblique interfaces of dissimilar particles. We show that the character of the refracted wave can be predicted using an analog to Snell's law for elastic-plastic granular crystals and ultimately show how it can be used to design impact guiding "lenses" for mitigation applications.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:granular, granular crystal, impact, dynamic, waves, solitons, particle, high velocity impact
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Space Engineering
Awards:Ernest E. Sechler Memorial Award in Aeronautics, 2015. William F. Ballhaus Prize, 2016.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Daraio, Chiara
Thesis Committee:
  • Kochmann, Dennis M. (chair)
  • Ravichandran, Guruswami
  • Andrade, Jose E.
  • Newman, John A.
  • Daraio, Chiara
Defense Date:15 April 2016
Funding AgencyGrant Number
Air Force Office of Scientific ResearchFA9550-12-1-0091
NASA Space Technology Research FellowshipNNX13AL66H
Record Number:CaltechTHESIS:05182016-164150213
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapter 3 adapted for Chapter 4 adapted for Chapter 5
Burgoyne, Hayden Andrew0000-0003-0891-6411
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9729
Deposited By: Hayden Burgoyne
Deposited On:19 May 2016 21:24
Last Modified:08 Nov 2023 00:21

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