arXiv subjects

Kuniyasu Saitoh

Publications and source records attributed to Kuniyasu Saitoh.

At least 37 records · Page 2Linked to original sources

arXiv2018

Elastic wave propagation in dry granular media: effects of probing characteristics and stress history

Elastic wave propagation provides a noninvasive way to probe granular materials. The discrete element method using particle configuration as input, allows a micromechanical interpretation on the acoustic response of a given granular system. This paper compares static and dynamic numerical probing methods, from which wave velocities are either deduced from elastic moduli or extracted from the time/frequency-domain signals. The dependence of wave velocities on key characteristics, i.e., perturbation magnitude and direction for static probing, and maximum travel distance and inserted signals for dynamic probing, is investigated. It is found that processing the frequency-domain signals obtained from dynamic probing leads to reproducible wave velocities at all wavenumbers, irrespective of the perturbation characteristics, whereas the maximum travel distance and input signals for the time domain analysis have to be carefully chosen, so as to obtain the same long-wavelength limits as from the frequency domain. Static and dynamic probes are applied to calibrated representative volumes of glass beads, subjected to cyclic oedometric compression. Although the perturbation magnitudes are selected to reveal only the elastic moduli, the deduced wave velocities are consistently lower than the long-wavelength limits at various stress states, and thus sensitive to sample size. While the static probes investigate the influence of stress history on modulus degradation, dynamic probing offers insights about how dispersion relations evolve during cyclic compression. Interestingly, immediately after each load reversal the incremental behavior is reversibly elastoplastic, until it becomes truly elastic with further unload/reload. With repeating unload/reload, the P- or S-wave dispersion relations become increasingly scalable with respect to their long-wavelength limits.

physics.geo-ph↗

arXiv2018

Rotational sound in disordered granular materials

We employ numerical simulations to understand the evolution of elastic standing waves in disordered frictional disk systems, where the dispersion relations of rotational sound modes are analyzed in detail. As in the case of frictional particles on a lattice, the rotational modes exhibit an "optical-like" dispersion relation in the high frequency regime, representing a shoulder of the vibrational density of states and fast oscillations of the autocorrelations of rotational velocities. A lattice-based model describes the dispersion relations of the rotational modes for small wave numbers. The rotational modes are perfectly explained by the model if tangential elastic forces between the disks in contact are large enough. If the tangential forces are comparable with or smaller than normal forces, the model fails for short wave lengths. However, the dispersion relation of the rotational modes then follows the model prediction for transverse modes, implying that the fast oscillations of disks' rotations switch to acoustic sound behavior. We evidence such a transition of the rotational modes by analyzing the eigen vectors of disordered frictional disks and identify upper and lower limits of the frequency-bands. We find that those are not reversed over the whole range of tangential stiffness as a remarkable difference from the rotational sound in frictional particles on a lattice.

cond-mat.soft↗

arXiv2018

Non-local effects in inhomogeneous flows of soft athermal disks

We numerically investigate non-local effects on inhomogeneous flows of soft athermal disks close to but below their jamming transition. We employ molecular dynamics to simulate Kolmogorov flows, in which a sinusoidal flow profile with fixed wave number is externally imposed, resulting in a spatially inhomogeneous shear rate. We find that the resulting rheology is strongly wave number-dependent, and that particle migration, while present, is not sufficient to describe the resulting stress profiles within a conventional local model. We show that, instead, stress profiles can be captured with non-local constitutive relations that account for gradients to fourth order. Unlike nonlocal flow in yield stress fluids, we find no evidence of a diverging length scale.

cond-mat.soft↗

arXiv2017

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.

cond-mat.soft↗

arXiv2016

Elastic Moduli and Vibrational Modes in Jammed Particulate Packings

When we elastically impose a homogeneous, affine deformation on amorphous solids, they also undergo an inhomogeneous, non-affine deformation, which can have a crucial impact on the overall elastic response. To correctly understand the elastic modulus $M$, it is therefore necessary to take into account not only the affine modulus $M_A$, but also the non-affine modulus $M_N$ that arises from the non-affine deformation. In the present work, we study the bulk ($M=K$) and shear ($M=G$) moduli in static jammed particulate packings over a range of packing fractions $φ$. One novelty of this work is to elucidate the contribution of each vibrational mode to the non-affine $M_N$ through a modal decomposition of the displacement and force fields. In the vicinity of the (un)jamming transition, $φ_{c}$, the vibrational density of states, $g(ω)$, shows a plateau in the intermediate frequency regime above a characteristic frequency $ω^\ast$. We illustrate that this unusual feature apparent in $g(ω)$ is reflected in the behavior of $M_N$: As $φ\rightarrow φ_c$, where $ω^\ast \rightarrow 0$, those modes for $ω< ω^\ast$ contribute less and less, while contributions from those for $ω> ω^\ast$ approach a constant value which results in $M_N$ to approach a critical value $M_{Nc}$, as $M_N-M_{Nc} \sim ω^\ast$. At $φ_c$ itself, the bulk modulus attains a finite value $K_c=K_{Ac}-K_{Nc} > 0$, such that $K_{Nc}$ has a value that remains below $K_{Ac}$. In contrast, for the critical shear modulus $G_c$, $G_{Nc}$ and $G_{Ac}$ approach the same value so that the total value becomes exactly zero, $G_c = G_{Ac}-G_{Nc} =0$. We explore what features of the configurational and vibrational properties cause such the distinction between $K$ and $G$, allowing us to validate analytical expressions for their critical values.

cond-mat.soft↗

arXiv2016

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.

cond-mat.stat-mech↗

arXiv2015

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.

cond-mat.soft↗

arXiv2015

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.

cond-mat.soft↗

arXiv2015

Hydrodynamic instabilities in shear flows of cohesive granular particles

We extend the dynamic van der Waals model introduced by A. Onuki [Phys. Rev. Lett. 94, 054501 (2005)] to the description of cohesive granular flows under a plane shear to study their hydrodynamic instabilities. Numerically solving the dynamic van der Waals model, we observe various heterogeneous structures of the density in steady states, where the viscous heating is balanced with the energy dissipation caused by inelastic collisions. Based on the linear stability analysis, we find that the spatial structures are determined by the mean volume fraction, the applied shear rate, and the inelasticity, where the instability is triggered if the system is thermodynamically unstable, i.e. the pressure, $p$, and the volume fraction, $ϕ$, satisfy $\partial p/\partialϕ<0$.

cond-mat.soft↗

arXiv2014

Simulation of cohesive fine powders under a plane shear

Three dimensional molecular dynamics simulations of cohesive dissipative powders under a plane shear are performed. We find the various phases depending on the dimensionless shear rate and the dissipation rate as well as the density. We also find that the shape of clusters depends on the initial condition of velocities of particles when the dissipation is large. Our simple stochastic model reproduces the non-Gaussian velocity distribution function appearing in the coexistence phase of a gas and a plate.

cond-mat.soft↗

arXiv2014

Role of gravity or confining pressure and contact stiffness in granular rheology

The steady shear rheology of granular materials is investigated in slow quasi-static states and inertial flows. The effect of the gravity field and contact stiffness, which are conventionally trivialized is the focus of this study. Series of Discrete Element Method simulations are performed on a weakly frictional granular assembly in a split-bottom geometry considering various gravity fields and contact stiffnesses. While traditionally the inertial number, i.e., the ratio of stress to strain-rate timescales describes the flow rheology, we find that a second dimensionless number, the ratio of softness and stress timescales, must also be included to characterize the bulk flow behavior. For slow, quasi-static flows, the density increases while the macroscopic friction decreases with respective increase in particle softness and gravity. This trend is added to the $μ(I)$ rheology and can be traced back to the anisotropy in the contact network, displaying a linear correlation between macroscopic friction and deviatoric fabric in the steady state. Interestingly, the linear relation holds when the external rotation rate is increased for a given gravity field and contact stiffness.

cond-mat.soft↗

arXiv2014

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.

cond-mat.soft↗

arXiv2014

Effect of cohesion on shear banding in quasi-static granular material

It is widely recognized in particle technology that adhesive powders show a wide range of different bulk behavior due to the peculiarity of the particle interaction. We use Discrete Element simulations to investigate the effect of contact cohesion on the steady state of dense powders in a slowly sheared split-bottom Couette cell, which imposes a wide stable shear band. The intensity of cohesive forces can be quantified by the {\em granular Bond number} ($Bo$), namely the ratio between maximum attractive force and average force due to external compression. We find that the shear banding phenomenon is almost independent of cohesion for Bond numbers $Bo<1$, but for $Bo \ge 1$ cohesive forces start to play an important role, as both width and center position of the band increase for $Bo > 1$. Inside the shear band, the mean normal contact force is always independent of cohesion and depends only on the confining stress. In contrast, when the behavior is analyzed focusing on the eigen-directions of the local strain rate tensor, a dependence on cohesion shows up. Forces carried by contacts along the compressive and tensile directions are symmetric about the mean force (larger and smaller respectively), while the force along the third, neutral direction follows the mean force. This anisotropy of the force network increases with cohesion, just like the heterogeneity in all (compressive, tensile and neutral) directions.

cond-mat.soft↗

arXiv2014

Collective motion of macroscopic spheres floating on capillary ripples: Dynamic heterogeneity and dynamic criticality

When a dense monolayer of macroscopic slightly polydisperse spheres floats on chaotic capillary Faraday waves, a coexistence of large scale convective motion and caging dynamics typical for jammed systems is observed. We subtract the convective mean flow using a coarse graining and reveal subdiffusion for the caging time scales followed by a diffusive regime at later times. To test the system in the light of dynamic criticality, we apply the methods of dynamic heterogeneity to obtain the power-law divergent time and length scales as the floater concentration approaches the jamming point. We find that these are independent of the application of the coarse graining procedure. The critical exponents are consistent with those found in dense suspensions of colloids indicating universal stochastic dynamics.

cond-mat.soft↗

arXiv2012

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.

cond-mat.soft↗

arXiv2012

Time Dependent Ginzburg-Landau Equation for Sheared Granular Flow

The time dependent Ginzburg-Landau equation for a two-dimensional granular shear flow is numerically solved, where we study both the transient dynamics and the steady state of the order parameter. The structural changes of the numerical solutions are qualitatively similar to the shear bands observed in the discrete element method (DEM) simulation of the two-dimensional granular shear flow.

cond-mat.soft↗

arXiv2012

Slow Dynamics Near Jamming

Static and dynamic properties of two-dimensional bidisperse dissipative particles are numerically studied near the jamming transition. We investigate the dependency of the critical scaling on the ratio of the different diameters and find a new scaling of the maximum overlap (not consistent with the scaling of the mean overlap). The ratio of kinetic and potential energies drastically slows down near the jamming transition, i.e. the relaxation time diverges at the jamming point.

cond-mat.soft↗

arXiv2011

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.

cond-mat.soft↗