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Protocol dependence of the jamming transition.

Thibault Bertrand1, Robert P Behringer2, Bulbul Chakraborty3

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Summary

The protocol used to create jammed particle packings influences their properties, even for frictionless systems. Our framework predicts how shear strain affects jamming, showing good agreement with simulations.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • The jamming transition in granular materials is crucial for understanding their mechanical properties.
  • Previous studies often focused on specific protocols, limiting generalizability.
  • Frictionless spherical particles provide a simplified model system to probe fundamental jamming behaviors.

Purpose of the Study:

  • To develop a theoretical framework for predicting protocol dependence in frictionless jamming.
  • To investigate how isotropic compression and simple shear protocols affect jammed disk packings.
  • To quantify the relationship between packing properties and shear strain-induced jamming.

Main Methods:

  • Theoretical modeling of jamming transitions for frictionless particles.
  • Analysis of isostatic jammed disk packings generated via isotropic compression and simple shear.
  • Comparison of theoretical predictions with simulation results for shear strain-induced jamming.

Main Results:

  • All jammed packings are accessible via both isotropic compression and simple shear for frictionless systems.
  • The probability of obtaining a specific packing depends on the generation protocol.
  • Accurate prediction of average shear strain for jamming from packing density and basin properties.
  • Shear strain-induced jamming range diminishes in the large system limit for frictionless, overdamped dynamics.

Conclusions:

  • The packing generation protocol significantly impacts the probability distribution of jammed states.
  • The developed theoretical framework successfully predicts protocol-dependent jamming phenomena.
  • Understanding protocol dependence is key for controlling granular material properties.