Local anisotropy in globally isotropic granular packings

Area of Science:

• Physics
• Materials Science
• Computational Science

Background:

• Granular materials exhibit complex behavior near the jamming transition.
• Understanding the relationship between stress, strain, and structure is crucial.

Purpose of the Study:

• Investigate the scaling of stress anisotropy and shear modulus in 2D frictionless granular packings.
• Determine the characteristic length scales and their behavior near the jamming point.

Main Methods:

• Performed two-dimensional computer simulations of frictionless granular packings.
• Analyzed stress anisotropy (ε(s)) and shear modulus (ε(m)) as functions of coarse-graining scale (R).
• Rescaled parameters to identify characteristic length scales (ξ) and anisotropy magnitudes (A).

Main Results:

• Stress anisotropy (ε(s)) collapses onto a master curve, with both A and ξ diverging as the jamming point (φ(c)) is approached.
• Shear modulus (ε(m)) exhibits a power-law dependence on R (ε(m)~R(-0.62)) without a characteristic length scale.
• Different scaling behaviors were observed for stress anisotropy and shear modulus.

Conclusions:

• The study suggests distinct physical mechanisms govern force chains and anomalous elastic response near jamming.
• Characteristic length scales associated with stress anisotropy diverge at the jamming point.
• The power-law behavior of shear modulus indicates scale-invariant properties over a wide range of scales.