Non-equilibrium thermodynamics in sheared hard-sphere materials

Abstract

We combine the shear-transformation-zone (STZ) theory of amorphous plasticity with Edwards' statistical theory of granular materials to describe shear flow in a disordered system of thermalized hard spheres. The equations of motion for this system are developed within a statistical thermodynamic framework analogous to that which has been used in the analysis of molecular glasses. For hard spheres, the system volume $V$ replaces the internal energy $U$ as a function of entropy $S$ in conventional statistical mechanics. In place of the effective temperature, the compactivity $X=\partial V/\partial S$ characterizes the internal state of disorder. We derive the STZ equations of motion for a granular material accordingly, and predict the strain rate as a function of the ratio of the shear stress to the pressure for different values of a dimensionless, temperature-like variable near a jamming transition. We use a simplified version of our theory to interpret numerical simulations by Haxton, Schmiedeberg and Liu, and in this way are able to obtain useful insights about internal rate factors and relations between jamming and glass transitions.

9 pages, 6 figures

References in corpus (9)

• Shear-transformation-zone theory of plastic deformation near the glass transition
• Strain localization in a shear transformation zone model for amorphous solids
• Topological persistence and dynamical heterogeneities near jamming
• Steady-state, effective-temperature dynamics in a glassy material
• Linear Response Theory for Hard and Soft Glassy Materials
• Shear-Transformation-Zone Theory of Linear Glassy Dynamics
• Universal Jamming Phase Diagram in the Hard-Sphere Limit
• Temperature-pressure scaling for air-fluidized grains on approaches to Point J
• Ratio of effective temperature to pressure controls the mobility of sheared hard spheres

Cited by in corpus (11)

• Memory of jamming - multiscale models for soft and granular matter
• Theories of Glass Formation and the Glass Transition
• Local and global avalanches in a 2D sheared granular medium
• The structural origin of the hard-sphere glass transition in granular packing
• Two-temperature continuum thermomechanics of deforming amorphous solids
• Stick-slip instabilities in sheared granular flow: the role of friction and acoustic vibrations
• Grain fragmentation in sheared granular flow: weakening effects, energy dissipation, and strain localization
• Shear flow of angular grains: acoustic effects and non-monotonic rate dependence of volume
• Glass Dynamics at High Strain Rates
• Localization and instability in sheared granular materials: Role of friction and vibration
• Hydrodynamics of fault gouges from constitutive modelling to the physics of friction