ABSTRACT
Numerical simulations of assemblies of grains under cyclic loading exhibit "granular ratcheting:" a small net deformation occurs with each cycle, leading to a linear accumulation of deformation with cycle number. We show that this is due to a curious property of the most frequently used models of the particle-particle interaction: namely, that the potential energy stored in contacts is path dependent. There exist closed paths that change the stored energy, even if the particles remain in contact and do not slide. An alternative method for calculating the tangential force removes granular ratcheting.
ABSTRACT
The existence of a very special ratcheting regime has recently been reported in a granular packing subjected to cyclic loading. In this state, the system accumulates a small permanent deformation after each cycle. The value of this permanent strain accumulation becomes independent of the number of cycles after a short transient regime. We show in this paper that a characterization of the material response in this peculiar state is possible in terms of three simple macroscopic variables. The definition of these variables is such that they can be easily measured both in the experiments and in the simulations. A thorough investigation of the micro- and macromechanical factors affecting these variables has been carried out by means of molecular-dynamics simulations of a polydisperse disk packing, as a simple model system for granular material. Biaxial test boundary conditions with periodically varying load were implemented. The effect on the plastic response of the confining pressure, the deviatoric stress, and the number of cycles has been investigated. The stiffness of the contacts and friction has been shown to play an important role in the overall response of the system. Especially illustrative is the influence of the peculiar hysteretical behavior in the stress-strain space on the accumulation of permanent strain and the energy dissipation.
ABSTRACT
The spontaneous symmetry breaking taking place in the direction perpendicular to the energy flux in a dilute vibrofluidized granular system is investigated, using both a hydrodynamic description and simulation methods. The latter include molecular dynamics and direct Monte Carlo simulation of the Boltzmann equation. A marginal stability analysis of the hydrodynamic equations, carried out in the WKB approximation, is shown to be in good agreement with the simulation results. The shape of the hydrodynamic profiles beyond the bifurcation is discussed.
ABSTRACT
Spontaneous symmetry breaking in a vibrated system confined into two connected compartments in the absence of external fields is reported. For a small number of particles, the grains are equipartitioned, but if it is increased beyond a critical value, the number of particles in each of the compartments becomes different in the steady state, and the number of particles in one of the compartments decreases monotonically tending to a given value. This phase transition is accurately described by the hydrodynamic equations for a granular gas. The relationship with previous phenomena of phase separation in vibrofluidized granular materials is discussed.
ABSTRACT
The dynamics of a heavy particle in a gas of much lighter particles is studied via the Boltzmann-Lorentz equation with inelastic collisions among all particles. A formal expansion in the ratio of gas to tagged particle mass transforms the Boltzmann-Lorentz equation into a Fokker Planck equation. The predictions of the latter are tested here using direct Monte Carlo simulation of the Boltzmann-Lorentz equation. Excellent agreement is obtained for the approach to a homogeneous cooling state, the temperature of that state, approach to diffusion, and the dependence of the diffusion constant on dissipation parameters. Some results from molecular-dynamics simulations are also presented and shown to agree with the theoretical predictions.
