Low-frequency behavior of beads constrained on a lattice

Area of Science:

• Physics
• Materials Science
• Acoustics

Background:

• Sound propagation in granular materials is complex due to inter-particle contact dynamics.
• Real granular systems exhibit disorder, deviating from idealized models.
• Hertz contact theory describes elastic contact but may not fully capture disordered systems.

Purpose of the Study:

• To investigate sound velocity and correlations in a disordered triangular lattice of spherical beads under isotropic stress.
• To understand the relationship between stress, lattice regularity, and sound propagation characteristics.
• To explore the underlying mechanisms responsible for non-Hertzian behavior in granular acoustics.

Main Methods:

• Simulating sound propagation through a triangular lattice of spherical beads with controlled polydispersity and isotropic stress.
• Analyzing sound velocity and signal correlations as a function of applied stress.
• Comparing experimental observations with theoretical predictions, including Hertz contact law.

Main Results:

• Sound velocity exhibits a crossover from non-Hertzian to Hertzian behavior with increasing stress.
• The observed stress evolution of sound velocity is reversible upon increasing or decreasing stress.
• Correlations are highly sensitive to disorder and increase with stress, indicating improved lattice regularity.
• Non-Hertzian behavior is attributed to the progressive activation of contacts.

Conclusions:

• The study provides a new interpretation of non-Hertzian acoustic behavior in granular media.
• Progressive contact activation, rather than force chain buckling, explains deviations from Hertzian theory.
• The findings highlight the critical role of disorder and stress in governing wave propagation in granular systems.