Master curves for the stress tensor invariants in stationary states of static granular beds. Implications for the thermodynamic phase space

TL;DR

This study investigates static granular beds under gravity, demonstrating that a single invariant of the force moment tensor can characterize the macroscopic states, supported by simulations and experiments, with implications for thermodynamic phase space.

Contribution

It shows that the stress tensor invariants can be reduced to a single master curve, simplifying the description of granular states beyond previous variables.

Findings

Stress tensor invariants collapse onto a master curve when plotted against trace.

Granular assemblies share a common stress tensor shape, not hydrostatic.

Experimental results support simulation findings.

Abstract

We prepare static granular beds under gravity in different stationary states by tapping the system with pulsed excitations of controlled amplitude and duration. The macroscopic state---defined by the ensemble of static configurations explored by the system tap after tap---for a given tap intensity and duration is studied in terms of volume, V, and force moment tensor, \Sigma. In a previous paper [Pugnaloni et al., Phys. Rev. E 82, 050301(R) (2010)], we reported evidence supporting that such macroscopic states cannot be fully described by using only V or \Sigma, apart from the number of particles N. In this work, we present an analysis of the fluctuations of these variables that indicates that V and \Sigma may be sufficient to define the macroscopic states. Moreover, we show that only one of the invariants of \Sigma is necessary, since each component of \Sigma falls onto a master curve when plotted as a function of Tr(\Sigma). This implies that these granular assemblies have a common shape for the stress tensor, even though it does not correspond to the hydrostatic type. Although most results are obtained by molecular dynamics simulations, we present supporting experimental results.