Abstract
Mesoscopic structures form in dense granular materials due to the self-organisation of the constituent particles. These structures have internal structural degrees of freedom in addition to the translational degree of freedom. The resultant granular elasticity, which exhibits intrinsic variations and inevitable relaxation, is a key quantity that accounts for macroscopic solid- or fluid-like properties and the transitions between them. In this work, we propose a potential energy landscape (PEL) with local stable basins and low elastic energy barriers to analyse the nature of granular elasticity. A function for the elastic energy density is proposed for stable states and is further calibrated with ultrasonic measurements. Fluctuations in the elastic energy due to the evolution of internal structures are proposed to describe a so-called configuration temperature Tc as a counterpart of the classical kinetic granular temperature Tk that is attributed to the translational degrees of freedom. The two granular temperatures are chosen as the state variables, and a fundamental equation is established to develop non-equilibrium thermodynamics for granular materials. Due to the relatively low elastic energy barrier in the PEL, granular elasticity relaxes more under common mechanical loadings, and a simple model based on mean-field theory is developed to account for this behaviour.
Highlights
Mesoscopic structures form in dense granular materials due to the self-organisation of the constituent particles
We propose a potential energy landscape (PEL) with local stable basins and low elastic energy barriers to analyse the nature of granular elasticity
Granular elasticity originates from enduring interparticle contacts, whereas the emergent force network structures generate a greater variety of stable states, significant fluctuations and clear relaxations than in molecular systems
Summary
Mesoscopic structures form in dense granular materials due to the self-organisation of the constituent particles. D ense granular materials are collections of distinct macroscopic particles and are widely encountered in engineering and natural hazards[1,2] Due to their discrete and dissipative nature, particles self-organise into various types of coherent structures, such as vortices, even at small Reynolds numbers[3,4] and force networks[5], which indicates that these particles have a pronounced short range order but no long-range structural order, as represented by the pair correlation function[6]. Several ensemble theories for static states have been proposed to explore the influence of granular configurations on the statistical properties of the free volume or contact stress This was first studied by Edwards and co-workers by proposing a temperature-like parameter compactivity x 12, and measurements of x for binary disc packing were recently reported[13]. To describe the transition between neighbouring stable states in the PEL, we propose a simple model for granular elasticity relaxation that is based on mean-field theory
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