A microscopic theory for discontinuous shear thickening of frictional granular materials

We extend a recent theory for the rheology of frictionless granular materials [K. Suzuki and H. Hayakawa, Phys. Rev. Lett. 2015, 115, 098001] to the case of frictional disks in two dimensions. Employing a frictional contact model for molecular dynamics simulations, we derive difference equations of the shear stress, the granular temperature, and the spin temperature from the generalized Green-Kubo formula, where all the terms are given by microscopic expressions. The numerical solutions of the difference equations not only describe the flow curve, but also reproduce the hysteresis of shear stress, which can be the signature of discontinuous shear thickening of frictional disks.Comment: 4 pages, 1 figure, the conference proceedings for Powders & Grains 201

Quantitative test of the time dependent Gintzburg-Landau equation for sheared granular flow in two dimension

We examine the validity of the time-dependent Ginzburg-Landau equation of granular fluids for a plane shear flow under the Lees-Edwards boundary condition derived from a weakly nonlinear analysis through the comparison with the result of discrete element method. We verify quantitative agreements in the time evolutions of the area fraction and the velocity fields, and also find qualitative agreement in the granular temperature.Comment: 10 pages, 4 figures. This paper is one of contributed papers to the proceedings of IUTAM symposium on "MOBILE PARTICULATE SYSTEMS: Kinematics, Rheology and Complex Phenomena" held at Bangalore in January 23-27, 201

Weakly nonlinear analysis of two dimensional sheared granular flow

Weakly nonlinear analysis of a two dimensional sheared granular flow is carried out under the Lees-Edwards boundary condition. We derive the time dependent Ginzburg-Landau (TDGL) equation of a disturbance amplitude starting from a set of granular hydrodynamic equations and discuss the bifurcation of the steady amplitude in the hydrodynamic limit.Comment: 24 pages, 6 figures. Section 3, 4 and 5 are changed. Figures 2-6 are update

Kinetic theory for dilute cohesive granular gases with a square well potential

We develop the kinetic theory of dilute cohesive granular gases in which the attractive part is described by a square well potential. We derive the hydrodynamic equations from the kinetic theory with the microscopic expressions for the dissipation rate and the transport coefficients. We check the validity of our theory by performing the direct simulation Monte Carlo.Comment: 22 pages, 11 figure

A master equation for force distributions in soft particle packings - Irreversible mechanical responses to isotropic compression and decompression

Mechanical responses of soft particle packings to quasi-static deformations are determined by the microscopic restructuring of force-chain networks, where complex non-affine displacements of constituent particles cause the irreversible macroscopic behavior. Recently, we have proposed a master equation for the probability distribution functions of contact forces and interparticle gaps [K. Saitoh et al., Soft Matter 11, 1253 (2015)], where mutual exchanges of contacts and interparticle gaps, i.e. opening and closing contacts, are also involved in the stochastic description with the aid of Delaunay triangulations. We describe full details of the master equation and numerically investigate irreversible mechanical responses of soft particle packings to cyclic loading. The irreversibility observed in molecular dynamics simulations is well reproduced by the master equation if the system undergoes quasi-static deformations. We also confirm that the degree of irreversible responses is a decreasing function of the area fraction and the number of cycles.Comment: 17 pages, 21 figures (6 figures are not displayed

A Master equation for force distributions in polydisperse frictional particles

An incremental evolution equation, i.e. a Master equation in statistical mechanics, is introduced for force distributions in polydisperse frictional particle packings. As basic ingredients of the Master equation, the conditional probability distributions of particle overlaps are determined by molecular dynamics simulations. Interestingly, tails of the distributions become much narrower in the case of frictional particles than frictionless particles, implying that correlations of overlaps are strongly reduced by microscopic friction. Comparing different size distributions, we find that the tails are wider for the wider distribution.Comment: 12 pages, 7 figures. Conference proceedings for PARTICLES 2015, 28-30 September, 2015, Barcelona, Spai

Master equation for the probability distribution functions of forces in soft particle packings

Employing molecular dynamics simulations of jammed soft particles, we study microscopic responses of force-chain networks to quasi-static isotropic (de)compressions. We show that not only contacts but also interparticle gaps between the nearest neighbors must be considered for the stochastic evolution of the probability distribution functions (PDFs) of forces, where the mutual exchange of contacts and interparticle gaps, i.e. opening and closing contacts, are also crucial to the incremental system behaviors. By numerically determining the transition rates for all changes of contacts and gaps, we formulate a Master equation for the PDFs of forces, where the insight one gets from the transition rates is striking: The mean change of forces reflects non-affine system response, while their fluctuations obey uncorrelated Gaussian statistics. In contrast, interparticle gaps are reacting mostly affine in average, but imply multi-scale correlations according to a wider stable distribution function.Comment: 5 pages, 4 figures, submitted to Soft Matte