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A collection of macro-sized particles resembling sand, which does not relax to thermal equilibrium, is known as a athermal particle system and is recognized for its unique behaviors. Additionally, as can be seen from the fact that the Earth's surface is covered by particulate matter, controlling such systems is extremely important. They have extensive applications in fields such as pharmacy, chemical engineering, mechanical engineering, and Earth sciences, and are also attracting attention as subjects of fundamental physics. This research meeting will be held on the occasion of Stefan Luding's visit, the managing editor of the specialized journal Granular Matter and president of the global community AEMMG, to conduct a one-day mini-workshop and facilitate information exchange.
Stefan Luding (Twente)
Haruku Ikeda（YITP）
Hisao Hayakawa (YITP)
Kuniyasu Saitoh（Kyoto Sangyo Univ.）
Michi Otsuki（Shimane Univ.）
Satoshi Takada（TUAT）
Takeshi Kawasaki（Osaka Univ.）
In this talk, I present a summary of studies on the impact of a projectile in dense suspensions, based on published papers that theoretically and experimentally [1-4].
In the first part, I focus on the early-stage dynamics of the impact, which the floating model can describe without consideration of the elastic force acting on a projectile [2,4].
In the second part, I discuss how the elastic force acting on the projectile appears after the impact [2,3].
[1] Pradipto and H. Hayakawa, Phys. Rev. Fluids, 3, 013187 (2021).
[2] Pradipto and H. Hayakawa, Phys. Fluids, 33, 093110 (2021).
[3] Pradipto and H. Hayakawa, Phys. Rev. E, 108, 024604 (2023).
[4] H. Maruoka and H. Hayakawa, arXiv:2406.19202.
The discrete element method (DEM) is commonly used to simulate granular flows and optimise processes involving particulate materials in various industries. DEM treats granular materials as individual particles, however the large number of particles present in industrial scales leads to high computational demands, making it less feasible for industrial scale simulations. Coarse graining (CG) presents a potential solution. CG replaces groups of small real particles with larger virtual particles, significantly reducing the number of simulated particles and computational load. However, applying CG to DEM simulations of mixing and segregation processes presents specific challenges, as the goal is to capture the effects associated with the original, fully resolved particle mixture. We investigate the effect of CG on mixing dynamics within a rotating drum across different operational regimes from rolling to cataracting. This approach allows us to observe flows with varying degrees of dynamic behaviour. We evaluate the mixing performance in each drum simulation using different mixing indices. We compare continuous fields, mixing characteristics and features between CG simulations and the original, unscaled simulations across different CG factors and operational regimes.
Several mean-field theories predict that the Hessian matrix of amorphous solids converges to the Wishart matrix in the limit of large spatial dimensions. Motivated by these results, we calculate here the density of states of random packing of harmonic spheres by mapping the Hessian of the original system to the Wishart matrix. We compare our result with that of previous numerical simulations of harmonic spheres in several spatial dimensions d=3, 5, and 9. For small pressure (near jamming), we find a good agreement even in d=3, and obtain better agreements in larger d, suggesting that the approximation becomes exact in the limit of large spatial dimension.
We performed a weakly nonlinear analysis of particle configurations that exhibit negative eigenvalues in the Hessian matrix. By expanding the potential energy in terms of particle displacements, we found that the linear term enhances the instability, whereas the cubic term suppresses its growth. A comparison between the derived nonlinear equation and numerical simulations revealed qualitative agreement in features such as the saturation amplitude and the growth dynamics of the oscillations. We also discussed the limitations of this analytical approach.
We formulate the kinetic theory of dry granular particles under a simple shear based on the Enskog and Grad approximations. We get a complete set of equations for the kinetic stress and the collisional contribution to the stress within this approximation. The steady solution under this approximation reproduces the quantitatively accurate results for the shear viscosity and kinetic temperature for the volume fraction $\varphi<0.5$ except for the case of nearly elastic situations. We also get qualitatively accurate results for the steady normal stress differences for $\varphi<0.5$. By using a protocol of reversing a shear rate satisfying Newton's equation of motion, we will also discuss the relaxation dynamics to reach the steady state.
We numerically investigate the shear modulus of jammed amorphous solids composed of cohesive grains. While repulsive grains exhibit critical scaling of the shear modulus as a function of the pressure or the excess coordination number, cohesive grains show pronounced hysteresis, which obscures the scaling behavior observed in repulsive systems. We relate this deviation to a possible breakdown of marginal stability, a condition believed to govern the mechanical properties of jammed packings of repulsive grains.
This study has been conducted in collaboration with Kiwamu Yoshii (Tokyo University of Science) and Hideyuki Mizuno (The University of Tokyo).
Many structures around us achieve mechanical stability against their
own weight through friction. Examples include arch bridges,
house-of-cards construction, and sandpile stabilized by their angle
of repose. In these systems, friction and geometry work together
to suppress sliding and enables mechanical equilibrium. But what
(if any) mechanism contributes to the strength of such
friction-stabilized configurations?
In this talk, we investigate a minimal model consisting of three
cylindrical particles stacked via side-to-side contact under gravity,
forming a triangular arrangement. A quasi-static compressive
force is applied from above via a wall. As the force increases,
the structure eventually collapses due to sliding at the contact
with the floor. We define the threshold force required to induce
this failure as the yield force, and study its dependence on the
floor friction coefficient and the stiffness of the cylinders.
Surprisingly, in the rigid-body case (i.e., no deformation), we find
a sharp transition: the yield force diverges at a critical friction
coefficient \mu_c ~ 0.268. To investigate more realistic conditions,
we employ the discrete element method (DEM) to analyze a pile
of elastic cylinders. We numerically observe a singular behavior
as the dimensionless effective elastic modulus becomes large.
Furthermore, we derive a unified scaling function to describe
this singularity.
Granular materials are prevalent in both natural and industrial contexts, presenting complex physical behavior that arises from their discrete composition. This complexity is further amplified by thermal effects, which explain the current gaps in achieving a comprehensive understanding of the thermomechanics of granular matter. This talk will present a data-driven framework to efficiently simulate the thermomechanical behavior of granular materials following a continuum-discrete hierarchical multiscale approach. In particular, the focus is on thermal expansion of densely packed, confined granular media. The proposed methodology handles the macroscale using a continuous model, while the microscale response is obtained from Representative Volume Elements (RVEs) using the Discrete Element Method (DEM). To significantly reduce the computational cost, the DEM computations are not performed simultaneously with the macroscale solver; instead, they are performed in advance to create a database of RVE solutions under different conditions. This dataset is then used to train an artificial neural network, which serves as a surrogate model for the macroscale solver. The method is validated against pure DEM solutions of granular domains with distinct thermal conditions. It is concluded that the surrogate model can predict the evolution of the microstructure, effective conductivity, and Cauchy stress tensor of the granular assembly with satisfactory accuracy and at a drastically lower computational cost than the pure DEM approach.
How do soft granular materials (or dense amorphous systems) respond to
externally applied deformations at different rates – from fast to slow
to very slow – and for different system sizes? This long-standing
question was intensively studied for shear deformation modes, but only
more recently also for isotropic deformations, like
compression-decompression cycles [1,2]. For moderate strain rates, in
the solid-like state, above jamming [3,4,5], the system appears to
evolve more or less smoothly in time/strain, whereas for slow enough
deformations, the material flips intermittently between the elastic,
reversible base-state and plastic, dynamic “events”. Only during the
latter events the micro-structure changes, it re-arranges,
irreversibly. The reversible base state involves both affine and
non-affine deformations, while the events are purely non-affine.
Besides their phenomenology and statistical properties, in particular,
the system size and rate dependence [6] of the events is studied,
providing reference data, to be compared in future to experiments on
model materials
like hydrogel particles using modern techniques. Finally, perspectives
and relations to real materials in application are to be addressed.
Figure 1 displays the affine, non-affine, and total displacement
fields, where in the center of the event (much larger localized
displacements) the particles are highlighted.
Figure 2 displays the kinetic to potential energy ratio during
compression from below jamming to above, for various different system
sizes and strain-rates. The zoom-in in Fig. 2 (right) allows to
observe isolated events (for slow enough compression rate) and their
exponential decay of granular temperature (dynamic cooling) relaxing
towards the steady, smooth, elastic situation between events. The
larger the system size, the more events occur, overlapping in time
(strain) if the compression rate is too fast.
References
[1] K. Taghizadeh, S. Luding, R. Basak, L. Kondic, Understanding slow
compression of frictional
granular particles under slow compression by network analysis, Soft
Matter (submitted 2023)
[2] S. Luding, K. Taghizadeh, C. Cheng, L. Kondic, Understanding slow
compression and
decompression of frictionless soft granular matter by network
analysis, Soft Matter 18, 1868 (2022)
[3] S. Luding, Granular matter: so much for the jamming point, Nature
Physics 12, 531-532, 2016
[4] N. Kumar, S. Luding, Memory of jamming -- multiscale models for
soft and granular matter,
Granular Matter 18, 58, 2016
[5] S. Luding, Y. Jiang, and M. Liu, Un-jamming due to energetic
instability: statics to dynamics,
Granular Matter 23, 80, 2021
[6] S. Luding, How does static granular matter re-arrange for
different isotropic strain rate?, in
Powders & Grains 2021 – EPJ Web of Conferences (2021), Vol. 249, p. 10001
[7] S. Luding, Elastic-plastic intermittent re-arrangements of
frictionless, soft granular matter under
very slow isotropic deformations, Frontiers Physics 11, 1211394, 2023
When slowly sheared, jammed packings respond elastically before yielding. This linear elastic regime becomes progressively narrower as the jamming transition point is approached, and rich nonlinear rheologies such as shear softening and hardening emerge. However, the physical mechanism of these nonlinear rheologies remains elusive. To clarify this, we numerically study jammed packings of athermal frictionless soft particles under quasi-static shear $\gamma$. We find the universal scaling behavior for the ratio of the shear stress $\sigma$ and the pressure $P$, independent of the preparation protocol of the initial configurations. In particular, we reveal shear-softening $\sigma/P \sim \gamma^{1/2}$ over an unprecedentedly wide range of strain up to the yielding point, which a simple scaling argument can rationalize [1].
Ref:
[1] T. Kawasaki and K. Miyazaki, Phys. Rev. Lett. 132, 268201 (2024).
The jamming transition of soft athermal particles has long been explored by numerical models of undeformable spheres/circles and the researchers have extensively studied the critical behavior of the particles near jamming. It is now well known that the shear modulus of undeformable particles scales as the square root of the proximity to the jamming transition density. However, the square-root scaling of the shear modulus has never been validated experimentally and one questions whether ``deformability” of the particles alters the critical scaling. In this study, we numerically investigate the jamming transition of deformable foams to examine the influence of deformability. We show that the critical scaling of pressure, elastic energy, and excess coordination number is well established and the vibrational density of states (VDOS) exhibits a plateau above a characteristic frequency. We also examine the finite size scaling of shear modulus to clarify the effect of deformability.