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Characterizing nonaffinity upon decompression of soft-sphere packings.

Stefan Kooij1, Edan Lerner2

  • 1Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands.

Physical Review. E
|November 28, 2019
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Summary
This summary is machine-generated.

Soft-sphere packings show universal scaling near unjamming. This study reveals differing contributions of affine and nonaffine forces to bulk modulus in various models, impacting the nonaffine to total bulk moduli ratio (Bna/B).

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Area of Science:

  • Physics of soft matter
  • Computational physics
  • Statistical mechanics

Background:

  • Athermal elastic moduli in soft-sphere packings exhibit universal scaling near the unjamming point.
  • The shear-to-bulk moduli ratio (G/B) vanishes upon decompression.
  • Nonaffinity of displacements differs significantly between shear and compressive strains.

Purpose of the Study:

  • To investigate how affine and nonaffine contributions to bulk modulus vary with proximity to the unjamming point.
  • To compare these contributions across different soft-sphere packing models.
  • To understand the differing scaling behaviors of the nonaffine to total bulk moduli ratio (Bna/B).

Main Methods:

  • Numerical simulations of soft-sphere packings.
  • Analysis of elastic moduli and displacement nonaffinity.
  • Theoretical scaling analysis based on interaction potentials.

Main Results:

  • Canonical unjamming models show Bna/B approaching a constant upon decompression.
  • Noncanonical models exhibit a vanishing Bna/B due to force invariance under compression.
  • A theoretical framework is developed to explain these distinct scaling behaviors.

Conclusions:

  • The dependence of Bna/B on proximity to unjamming is model-specific.
  • Emergent force invariance in noncanonical models dictates the vanishing Bna/B.
  • The study provides predictive power for Bna/B scaling based on interaction potentials.