Variable-cell method for stress-controlled jamming of athermal, frictionless grains

Area of Science:

• Physics
• Materials Science
• Computational Science

Background:

• Understanding granular materials and jamming phenomena is crucial in various scientific fields.
• Previous models often simplified grain shapes and lacked detailed stress-strain analysis.

Purpose of the Study:

• To develop a novel simulation method for jamming of polyhedral grains under controlled stress.
• To precisely define the ideal jamming point under hydrostatic and athermal conditions.
• To investigate the structural and contact properties of jammed grains with varying symmetries.

Main Methods:

• Simulation of polyhedral grain jamming using a method incorporating global degrees of freedom via the metric tensor.
• Application of hydrostatic (isotropic) stress and athermal conditions.
• Utilizing the variable-cell method to analyze responses to shear-stress perturbation.

Main Results:

• Defined the ideal jamming point at zero shear stress for hydrostatically jammed systems.
• Observed that hydrostatically jammed tetrahedra exhibit less translational order and lower density than previously modeled.
• Found that cubes jam with negligible nematic order, while octahedral grains (s>0.5) form abundant face-face contacts.
• Identified the formation of percolating clusters in systems with high face-face contact numbers.

Conclusions:

• The developed method provides a precise framework for studying granular jamming under controlled stress.
• Grain shape symmetry significantly influences jamming behavior, contact types, and emergent structures like percolating clusters.
• The study offers new insights into the mechanical response of jammed granular systems to shear stress.