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Nonlocal Elasticity near Jamming in Frictionless Soft Spheres
Karsten Baumgarten1, Daniel Vågberg1, Brian P Tighe1
1Delft University of Technology, Process & Energy Laboratory, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands.
Physical Review Letters
|March 18, 2017
Summary
Simulations reveal new rules for elasticity in jammed materials, showing that conventional theories fail near the jamming transition. These findings apply to various soft solids like foams and emulsions.
Area of Science:
- Soft matter physics
- Materials science
- Statistical mechanics
Background:
- Conventional linear elasticity assumes local interactions.
- Jamming transition represents a critical point in disordered materials.
- Understanding elasticity in jammed systems is crucial for materials design.
Purpose of the Study:
- To identify novel constitutive relations for linear elasticity near the jamming transition.
- To investigate the role of characteristic length scales in jammed solids.
- To challenge the applicability of local elasticity theories in weakly jammed systems.
Main Methods:
- Simulations of frictionless soft sphere packings.
- Applying forces at varying wavelengths to probe material response.
- Analyzing transverse and longitudinal compliances.
Main Results:
- Discovered wavelength-dependent compliances, violating conventional local elasticity.
- Identified characteristic length scales associated with nonlocal effects.
- Observed divergence of length scales as pressure approaches zero, linking critical jamming effects to elasticity breakdown.
Conclusions:
- Developed nonlocal constitutive relations applicable to weakly jammed solids.
- Jamming criticality fundamentally alters elastic behavior, necessitating nonlocal descriptions.
- Findings are relevant for understanding and designing emulsions, foams, and granular materials.
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