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

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

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

Eigenvalue analysis of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain

The stress-strain curve of two-dimensional frictional dispersed grains interacting with a harmonic potential without considering the dynamical slip under a finite strain is determined by using eigenvalue analysis of the Hessian matrix. After the configuration of grains is obtained, the stress-strain curve based on the eigenvalue analysis is in almost perfect agreement with that obtained by the simulation, even if there are plastic deformations caused by stress avalanches. Unlike the naive expectation, the eigenvalues in our model do not indicate any precursors to the stress-drop events.Comment: 22 pages, 16 figures. arXiv admin note: text overlap with arXiv:2207.0663

Theory of rigidity and density of states of two-dimensional amorphous solids of dispersed frictional grains in the linear response regime

Using the Jacobian matrix, we theoretically determine the rigidity of two-dimensional amorphous solids consisting of frictional grains in the linear response to an infinitesimal strain, in which we ignore the dynamical friction caused by the slip processes of contact points. The theoretical rigidity agrees with that obtained by molecular dynamics simulations. We confirm that the rigidity is smoothly connected to the value in the frictionless limit. We find that there are two modes in the density of states for sufficiently small $k_{T}/k_{N}$, which is the ratio of the tangential to normal stiffness. Rotational modes exist at low frequencies or small eigenvalues, whereas translational modes exist at high frequencies or large eigenvalues. The location of the rotational band shifts to the high-frequency region with an increase in $k_{T}/k_{N}$ and becomes indistinguishable from the translational band for large $k_{T}/k_{N}$. The rigidity determined by the translational modes agrees with that obtained by the molecular dynamics simulations, whereas the contribution of the rotational modes is almost zero for small $k_{T}/k_{N}$.Comment: 10 pages, 15 figure