Mean-field stability map of hard-sphere glasses

Area of Science:

• Physics
• Materials Science
• Statistical Mechanics

Background:

• Understanding the mechanical response of amorphous solids to shear deformation is crucial for both fundamental science and practical applications.
• Colloidal systems and granular matter are complex amorphous solids whose behavior under stress is challenging to model.
• Infinite-dimensional models offer a tractable approach to investigate the fundamental properties of these materials.

Purpose of the Study:

• To investigate the phase diagram of amorphous hard spheres under compression, decompression, and shear strain.
• To identify and characterize the boundaries of the solid phase, specifically shear jamming and shear yielding.
• To explore how glass preparation density influences these phase boundaries.

Main Methods:

• Utilizing a solvable model of hard spheres in infinite dimensions.
• Preparing the system above the dynamical glass transition density.
• Analyzing the phase diagram under various deformation conditions (compression, decompression, shear).

Main Results:

• The solid region is defined by a shear jamming line (close packing) and a shear yielding line (spinodal instability).
• The study characterizes the phase diagram, expanding on previous theoretical work.
• The evolution of shear jamming and yielding lines is mapped as a function of glass preparation density.

Conclusions:

• The research provides a comprehensive overview of yielding and jamming phenomena in hard-sphere systems.
• The findings contribute to a deeper understanding of the mechanical stability and failure of amorphous solids.
• The infinite-dimensional hard-sphere model serves as a valuable tool for studying complex material responses.