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Particle-scale origin of quadrupolar nonaffine displacement fields in granular solids
Evan P Willmarth1, Weiwei Jin1, Dong Wang1
1Yale University, Department of Mechanical Engineering, New Haven, Connecticut 06520, USA.
Physical Review. E
|December 23, 2025
Summary
Structural defects in jammed disk packings create nonaffine displacement fields. Breaking specific interparticle contacts, aligned with vibrational modes, leads to effective quadrupoles, explainable by Eshelby
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- Jammed disk packings exhibit complex nonaffine displacement fields under shear.
- Understanding these fields is crucial for predicting material behavior.
Purpose of the Study:
- Identify local structural defects controlling nonaffine displacements.
- Investigate the emergence of effective quadrupoles in shear-jammed disk systems.
Main Methods:
- Athermal, quasistatic simple shear simulations.
- Eshelby's equivalent inclusion method (EIM) adapted for discrete packings.
- Delaunay triangulation for local stiffness analysis.
Main Results:
- Isolated effective quadrupoles emerge with increasing pressure.
- Quadrupole formation linked to interparticle contact breaks aligned with low-frequency vibrational modes.
- Nonaffine fields reconstructed as sums of discrete Eshelby-like defects.
Conclusions:
- Local structural defects, specifically broken contacts, dictate nonaffine behavior.
- Eshelby-like defects provide a framework for understanding shear response in granular materials.
- Pressure influences the prevalence of quadrupolar defects.
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