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Rigidity loss in disordered systems: three scenarios.

Wouter G Ellenbroek1, Varda F Hagh2, Avishek Kumar2

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|April 18, 2015
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Disordered network materials exhibit distinct rigidity transitions. Jammed and stress-relieved networks self-organize globally, unlike randomly diluted networks, impacting their mechanical properties.

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Area of Science:

  • Materials Science
  • Network Physics
  • Statistical Mechanics

Background:

  • Disordered network materials are crucial in various scientific fields.
  • Understanding their rigidity transition is key to predicting material properties.
  • Existing models often simplify the complex behavior of these networks.

Purpose of the Study:

  • To investigate and compare the rigidity transition in three distinct types of disordered network materials.
  • To elucidate the role of global self-organization in the mechanical behavior of these networks.
  • To identify qualitative differences in their responses to perturbations.

Main Methods:

  • Analysis of randomly diluted spring networks.
  • Simulation of jammed sphere packings.
  • Study of stress-relieved networks avoiding floppy regions.
  • Examination of isostaticity and network responses to bond addition/removal.

Main Results:

  • Significant qualitative differences were observed in the rigidity transition of the three network types.
  • Jammed and stress-relieved networks exhibit global isostaticity at the marginal state.
  • Randomly diluted networks display heterogeneous overconstrained and underconstrained regions.
  • Perturbations to isostatic jammed networks lead to global over- or under-constraint, while stress-relieved networks show localized effects.

Conclusions:

  • Global self-organization plays a critical and unusual role in the mechanical properties of jammed sphere packings.
  • The distinct behaviors highlight the importance of network preparation protocols and inherent structural organization.
  • Findings advance the understanding of mechanical stability in disordered materials.