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Taghizadeh K, Luding S, Basak R, Kondic L. Understanding slow compression of frictional granular particles by network analysis. SOFT MATTER 2024; 20:6440-6457. [PMID: 39091225 DOI: 10.1039/d4sm00560k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/04/2024]
Abstract
We consider frictional granular packings exposed to quasi-static compression rates, with a focus on systems above the jamming transition. For frictionless packings, earlier work (S. Luding et al., Soft Matter, 2022, 18(9), 1868-1884) has uncovered that the system evolution/response involves smooth evolution phases, interrupted by fast transitions (events). The general finding is that the force networks' static quantities correlate closely with the pressure, while their evolution resembles the kinetic energy for both frictionless and frictional packings. The former represents reversible (elastic) particle deformations with affine and non-affine components, whereas the latter also involves much stronger, irreversible (plastic) rearrangements of the packings. Events are associated with jumps in the overall kinetic energy as well as dramatic changes in the force networks describing the particle micro-structure. The frictional nature of particle interactions affects both their frequency and the relevant time scale magnitude. For intermediate friction, events are often followed by an unexpected slow-down during which the kinetic energy drops below its average value. We find that these slow-downs are associated with a significant decrease in the non-affine dynamics of the particles, and are strongly influenced by friction. Friction modifies the structure of the networks, both through the typical number of contacts of a particle, and by influencing topological features of the resulting networks. Furthermore, friction modifies the dynamics of the networks, with larger values of friction leading to smaller changes of the more stable networks.
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Affiliation(s)
- Kianoosh Taghizadeh
- MSM, TFE-ET, MESA+, University of Twente, PO Box 217, 7500AE Enschede, The Netherlands.
- Institute of Applied Mechanics (CE), SC SimTech, University of Stuttgart, Germany
| | - Stefan Luding
- MSM, TFE-ET, MESA+, University of Twente, PO Box 217, 7500AE Enschede, The Netherlands.
| | - Rituparna Basak
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA.
| | - Lou Kondic
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA.
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2
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Singh AP, Angelidakis V, Pöschel T, Roy S. Shear zones in granular mixtures of hard and soft particles with high and low friction. SOFT MATTER 2024; 20:3118-3130. [PMID: 38451109 DOI: 10.1039/d4sm00100a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/08/2024]
Abstract
Granular materials show inhomogeneous flows characterized by strain localization. When strain is localized in a sheared granular material, rigid regions of a nearly undeformed state are separated by shear bands, where the material yields and flows. The characteristics of the shear bands are determined by the geometry of the system, the micromechanical material properties, and the kinematics at the particle level. For a split-bottom shear cell, recent experimental work has shown that mixtures of hard, frictional and soft, nearly frictionless particles exhibit wider shear zones than samples with only one of the two components. To explain this finding, we investigate the shear zone properties and the stress response of granular mixtures using discrete element simulations. We show that both interparticle friction and elastic modulus determine the shear-band properties and packing density of granular mixtures of various mixing ratios, but their stress response depends strongly on the interparticle friction. Our study provides a fundamental understanding of the micromechanics of shear band formation in granular mixtures.
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Affiliation(s)
- Aditya Pratap Singh
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstrasse 3, 91058 Erlangen, Germany.
| | - Vasileios Angelidakis
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstrasse 3, 91058 Erlangen, Germany.
- School of Natural and Built Environment, Queen's University Belfast, David Keir Building, BT9 5AG Belfast, UK
| | - Thorsten Pöschel
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstrasse 3, 91058 Erlangen, Germany.
| | - Sudeshna Roy
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstrasse 3, 91058 Erlangen, Germany.
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3
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An Efficient Parallel Framework for the Discrete Element Method Using GPU. APPLIED SCIENCES-BASEL 2022. [DOI: 10.3390/app12063107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The discrete element method (DEM), a discontinuum-based method to simulate the interaction between neighbouring particles of granular materials, suffers from intensive computational workload caused by massive particle numbers, irregular particle shapes, and complicated interaction modes from the meso-scale representation of the macro information. To promote the efficiency of the DEM and enlarge the modelling scales with a higher realism of the particle shapes, parallel computing on the graphics processing unit (GPU) is developed in this paper. The potential data race between the computing cores in the parallelisation is tackled by establishing the contact pair list with a hybrid technique. All the computations in the DEM are made on the GPU cores. Three benchmark cases, a triaxial test of a sand specimen, cone penetration test and granular flow due to a dam break, are used to evaluate the performance of the GPU parallel strategy. Acceleration of the GPU parallel simulations over the conventional CPU sequential counterparts is quantified in terms of speedup. The average speedups with the GPU parallelisation are 84, 73, and 60 for the benchmark cases.
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4
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Luding S, Taghizadeh K, Cheng C, Kondic L. Understanding slow compression and decompression of frictionless soft granular matter by network analysis. SOFT MATTER 2022; 18:1868-1884. [PMID: 35171180 DOI: 10.1039/d1sm01689j] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We consider dense granular systems in three spatial dimensions exposed to slow compression and decompression, below, during, above and well above jamming. The evolution of granular systems under slow deformation is non-trivial and involves smooth, continuous, reversible (de)compression periods, interrupted by fast, discontinuous, irreversible transition events. These events are often, but not always, associated with rearrangements of particles and of the contact network. How many particles are involved in these transitions between two states can range from few to almost all in the system. An analysis of the force network that is built on top of the contact network is carried out using the tools of persistent homology. Results involve the observation that kinetic energy is correlated with the intensity of rearrangements, while the evolution of global mechanical measures, such as pressure, is strongly correlated with the evolution of the topological measures quantifying loops in the force network. Surprisingly, some transitions are clearly detected by persistent homology even though motion/rearrangement of particles is much weaker, i.e., much harder to detect or, in some cases, not observed at all.
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Affiliation(s)
- Stefan Luding
- MSM, TFE-ET, MESA+, University of Twente, PO Box 217, 7500AE Enschede, The Netherlands.
| | - Kianoosh Taghizadeh
- MSM, TFE-ET, MESA+, University of Twente, PO Box 217, 7500AE Enschede, The Netherlands.
- Institute of Applied Mechanics (CE), SC SimTech, University of Stuttgart, Germany
| | - Chao Cheng
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
| | - Lou Kondic
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
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5
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Shaebani MR, Török J, Maleki M, Madani M, Harrington M, Rice A, Losert W. Gravity Governs Shear Localization in Confined Dense Granular Flows. PHYSICAL REVIEW LETTERS 2021; 127:278003. [PMID: 35061419 DOI: 10.1103/physrevlett.127.278003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2021] [Revised: 10/10/2021] [Accepted: 12/09/2021] [Indexed: 06/14/2023]
Abstract
The prediction of flow profiles of slowly sheared granular materials is a major geophysical and industrial challenge. Understanding the role of gravity is particularly important for future planetary exploration in varying gravitational environments. Using the principle of minimization of energy dissipation, and combining experiments and variational analysis, we disentangle the contributions of the gravitational acceleration, confining pressure, and layer thickness on shear strain localization induced by moving fault boundaries at the bottom of a granular layer. The flow profile is independent of the gravity for geometries with a free top surface. However, under a confining pressure or if the sheared layer withstands the weight of the upper layers, increasing gravity promotes the transition from closed shear zones buried in the bulk to open ones that intersect the top surface. We show that the center position and width of the shear zone and the axial angular velocity at the top surface follow universal scaling laws when properly scaled by the gravity, applied pressure, and layer thickness. Our finding that the flow profiles lie on a universal master curve opens the possibility to predict the quasistatic shear flow of granular materials in varying gravitational environments.
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Affiliation(s)
- M Reza Shaebani
- Department of Theoretical Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
| | - János Török
- MTA-BME Morphodynamics Research Group, Department of Theoretical Physics, Budapest University of Technology and Economics, Budapest H-1111, Hungary
| | - Maniya Maleki
- Department of Physics & Optics Research Center, Institute for Advanced Studies in Basic Sciences, Zanjan 45137-66731, Iran
| | - Mahnoush Madani
- Department of Physics & Optics Research Center, Institute for Advanced Studies in Basic Sciences, Zanjan 45137-66731, Iran
| | - Matt Harrington
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Allyson Rice
- Department of Biophysics Institute, UT Southwestern Medical Center, Dallas, Texas 75390, USA
| | - Wolfgang Losert
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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6
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Chattoraj J, Huy NH, Aggarwal S, Habibullah MS, Farbiz F. Shear-induced mixing of granular materials featuring broad granule size distributions. Phys Rev E 2021; 104:044910. [PMID: 34781494 DOI: 10.1103/physreve.104.044910] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2021] [Accepted: 10/13/2021] [Indexed: 11/07/2022]
Abstract
Granular flows during a shear-induced mixing process are studied using discrete element methods. The aim is to understand the underlying elementary mechanisms of transition from unmixed to mixed phases for a granular material featuring a broad distribution of particles, which we investigate systematically by varying the strain rate and system size. Here the strain rate varies over four orders of magnitude and the system size varies from ten thousand to more than a million granules. A strain rate-dependent transition from quasistatic to purely inertial flow is observed. At the macroscopic scale, the contact stresses drop due to the formation of shear-induced instabilities that serves as an onset of granular flows and initiates mixing between the granules. The stress-drop displays a profound system size dependence. At the granular scale, mixing dynamics are correlated with the formation of shear bands, which result in significantly different timescales of mixing, especially for those regions that are close to the system walls and the bulk. Overall, our results reveal that although the transient dynamics display a generic behavior, these have a significant finite-size effect. In contrast, macroscopic behaviors at steady states have negligible system size dependence.
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Affiliation(s)
- Joyjit Chattoraj
- Institute of High Performance Computing, Agency for Science Technology and Research, 138632 Singapore
| | - Nguyen Hoang Huy
- Institute of High Performance Computing, Agency for Science Technology and Research, 138632 Singapore
| | - Saurabh Aggarwal
- Institute of High Performance Computing, Agency for Science Technology and Research, 138632 Singapore
| | | | - Farzam Farbiz
- Institute of High Performance Computing, Agency for Science Technology and Research, 138632 Singapore
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Abstract
Cohesive granular materials such as wet sand, snow, and powders can flow like a viscous liquid. However, the elementary mechanisms of momentum transport in such athermal particulate fluids are elusive. As a result, existing models for cohesive granular viscosity remain phenomenological and debated. Here we use discrete element simulations of plane shear flows to measure the viscosity of cohesive granular materials, while tuning the intensity of inter-particle adhesion. We establish that two adhesion-related, dimensionless numbers control their viscosity. These numbers compare the force and energy required to break a bond to the characteristic stress and kinetic energy in the flow. This progresses the commonly accepted view that only one dimensionless number could control the effect of adhesion. The resulting scaling law captures strong, non-Newtonian variations in viscosity, unifying several existing viscosity models. We then directly link these variations in viscosity to adhesion-induced modifications in the flow micro-structure and contact network. This analysis reveals the existence of two modes of momentum transport, involving either grain micro-acceleration or balanced contact forces, and shows that adhesion only affects the latter. This advances our understanding of rheological models for granular materials and other soft materials such as emulsions and suspensions, which may also involve inter-particle adhesive forces.
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Affiliation(s)
- Matthew Macaulay
- School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia.
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Abstract
In this paper, a methodology of calculating the tortuosity in three-dimensional granular beds saved in a form of binary geometry with the application of the A-Star Algorithm and the Path Searching Algorithm is presented. The virtual beds serving as examples are prepared with the use of the Discrete Element Method based on data of real, existing samples. The obtained results are compared with the results described in other papers (obtained by the use of the Lattice Boltzmann Method and the Path Tracking Method) as well as with the selected empirical formulas found in the literature. It was stated in the paper that the A-Star Algorithm gives values similar (but always slightly underestimated) to the values obtained via approaches based on the Lattice Boltzmann Method or the Path Tracking Method. In turn, the Path Searching Algorithm gives results in the same value range as popular empirical formulas and additionally it is approximately two times faster than the A-Star Algorithm.
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10
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Saitoh K, Oyama N, Ogushi F, Luding S. Transition rates for slip-avalanches in soft athermal disks under quasi-static simple shear deformations. SOFT MATTER 2019; 15:3487-3492. [PMID: 30849152 DOI: 10.1039/c8sm01966e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We study slip-avalanches in two-dimensional soft athermal disks by quasi-static simulations of simple shear deformations. Sharp drops in shear stress, or slip-avalanches, are observed intermittently during steady state. Such stress drops are caused by restructuring of the contact networks, accompanied by drastic changes of the interaction forces, Δf. The changes of the forces happen heterogeneously in space, indicating that collective non-affine motions of the disks are most pronounced when slip-avalanches occur. We analyze and predict the statistics for the force changes, Δf, by transition rates of the contact forces and angles, where slip-avalanches are characterized by wide power-law tails. We find that the transition rates are described by a q-Gaussian distribution regardless of the area fraction of the disks. Because the transition rates quantify structural changes of the force-chains, our findings are an important step towards linking macroscopic observations to a microscopic theory of slip-avalanches in the experimentally accessible quasi-static regime.
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Affiliation(s)
- Kuniyasu Saitoh
- Research Alliance Center for Mathematical Sciences, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan.
- WPI-Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
| | - Norihiro Oyama
- Mathematics for Advanced Materials-OIL, AIST, Sendai 980-8577, Japan
| | - Fumiko Ogushi
- Center for Materials Research by Information Integration, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
- Kyoto University Institute for Advanced Study, Kyoto University, Yoshida Ushinomiya-cho, Sakyo-ku, Kyoto, Japan
| | - Stefan Luding
- Faculty of Engineering Technology, MESA+, University of Twente, Drienerlolaan 5, Enschede, The Netherlands
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11
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Roy S, Scheper BJ, Polman H, Thornton AR, Tunuguntla DR, Luding S, Weinhart T. Surface flow profiles for dry and wet granular materials by Particle Tracking Velocimetry; the effect of wall roughness. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:14. [PMID: 30756195 DOI: 10.1140/epje/i2019-11778-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2018] [Accepted: 01/04/2019] [Indexed: 06/09/2023]
Abstract
Two-dimensional Particle Tracking Velocimetry (PTV) is a promising technique to study the behaviour of granular flows. The aim is to experimentally determine the free surface width and position of the shear band from the velocity profile to validate simulations in a split-bottom shear cell geometry. The position and velocities of scattered tracer particles are tracked as they move with the bulk flow by analyzing images. We then use a new technique to extract the continuum velocity field, applying coarse-graining with the postprocessing toolbox MercuryCG on the discrete experimental PTV data. For intermediate filling heights, the dependence of the shear (or angular) velocity on the radial coordinate at the free surface is well fitted by an error function. From the error function, we get the width and the centre position of the shear band. We investigate the dependence of these shear band properties on filling height and rotation frequencies of the shear cell for dry glass beads for rough and smooth wall surfaces. For rough surfaces, the data agrees with the existing experimental results and theoretical scaling predictions. For smooth surfaces, particle-wall slippage is significant and the data deviates from the predictions. We further study the effect of cohesion on the shear band properties by using small amount of silicon oil and glycerol as interstitial liquids with the glass beads. While silicon oil does not lead to big changes, glycerol changes the shear band properties considerably. The shear band gets wider and is situated further inward with increasing liquid saturation, due to the correspondingly increasing trend of particles to stick together.
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Affiliation(s)
- Sudeshna Roy
- Multi-Scale Mechanics, Engineering Technology (ET) and MESA + University of Twente, 7500, AE Enschede, The Netherlands.
| | - Bert J Scheper
- Multi-Scale Mechanics, Engineering Technology (ET) and MESA + University of Twente, 7500, AE Enschede, The Netherlands
| | - Harmen Polman
- Multi-Scale Mechanics, Engineering Technology (ET) and MESA + University of Twente, 7500, AE Enschede, The Netherlands
| | - Anthony R Thornton
- Multi-Scale Mechanics, Engineering Technology (ET) and MESA + University of Twente, 7500, AE Enschede, The Netherlands
| | - Deepak R Tunuguntla
- Multi-Scale Mechanics, Engineering Technology (ET) and MESA + University of Twente, 7500, AE Enschede, The Netherlands
| | - Stefan Luding
- Multi-Scale Mechanics, Engineering Technology (ET) and MESA + University of Twente, 7500, AE Enschede, The Netherlands
| | - Thomas Weinhart
- Multi-Scale Mechanics, Engineering Technology (ET) and MESA + University of Twente, 7500, AE Enschede, The Netherlands
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12
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Saitoh K, Shrivastava RK, Luding S. Rotational sound in disordered granular materials. Phys Rev E 2019; 99:012906. [PMID: 30780228 DOI: 10.1103/physreve.99.012906] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2018] [Indexed: 06/09/2023]
Abstract
We numerically study the evolution of elastic standing waves in disordered disk systems with a focus on the dispersion relations of rotational sound. As on a lattice, the rotational mode exhibits an optical-like dispersion relation in the high frequency regime, representing a shoulder in the vibrational density of states and fast oscillations of the autocorrelations of rotational velocities. If tangential stiffness between the disks is large enough, a lattice-based model perfectly describes the dispersion relation of the rotational mode. If it is comparable to or smaller than the normal stiffness, the model fails for short wavelengths. However, the dispersion relation then follows the model prediction for the transverse mode, implying that the fast oscillations of disks' rotations switch to acousticlike behavior. We evidence such a transition from rotational to transverse modes by analyzing their respective participation of different degrees of freedom to the eigenvectors.
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Affiliation(s)
- Kuniyasu Saitoh
- Research Alliance Center for Mathematical Sciences, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
- WPI-Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
| | - Rohit K Shrivastava
- Faculty of Engineering Technology, MESA+, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Stefan Luding
- Faculty of Engineering Technology, MESA+, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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13
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Koeze DJ, Tighe BP. Sticky Matters: Jamming and Rigid Cluster Statistics with Attractive Particle Interactions. PHYSICAL REVIEW LETTERS 2018; 121:188002. [PMID: 30444395 DOI: 10.1103/physrevlett.121.188002] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2018] [Indexed: 06/09/2023]
Abstract
While the large majority of theoretical and numerical studies of the jamming transition consider athermal packings of purely repulsive spheres, real complex fluids and soft solids generically display attraction between particles. By studying the statistics of rigid clusters in simulations of soft particles with an attractive shell, we present evidence for two distinct jamming scenarios. Strongly attractive systems undergo a continuous transition in which rigid clusters grow and ultimately diverge in size at a critical packing fraction. Purely repulsive and weakly attractive systems jam via a first-order transition, with no growing cluster size. We further show that the weakly attractive scenario is a finite size effect, so that for any nonzero attraction strength, a sufficiently large system will fall in the strongly attractive universality class. We therefore expect attractive jamming to be generic in the laboratory and in nature.
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Affiliation(s)
- Dion J Koeze
- Delft University of Technology, Process & Energy Laboratory, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
| | - Brian P Tighe
- Delft University of Technology, Process & Energy Laboratory, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
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14
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Ye F, Li Y, Hu J, Chen K. Investigation of Particle Dynamics in a Disc Rotating Device by Means of Experiments and Numerical Simulations Using DEM. JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 2018. [DOI: 10.1252/jcej.17we404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Fangping Ye
- School of Logistics Engineering, Wuhan University of Technology
| | - Yu Li
- School of Logistics Engineering, Wuhan University of Technology
| | - Jiquan Hu
- School of Logistics Engineering, Wuhan University of Technology
| | - Kaikai Chen
- School of Logistics Engineering, Wuhan University of Technology
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15
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Murphy E, Sundararajan S, Subramaniam S. Rheological transition in simple shear of moderately dense assemblies of dry cohesive granules. Phys Rev E 2018; 97:062902. [PMID: 30011438 DOI: 10.1103/physreve.97.062902] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2018] [Indexed: 11/07/2022]
Abstract
The rheology of homogeneous cohesive granular assemblies under shear at moderate volume fractions is investigated using the discrete element method for both frictionless and frictional granules. A transition in rheology from inertial to quasistatic scaling is observed at volume fractions below the jamming point of noncohesive systems, which is a function of the granular temperature, energy dissipation, and cohesive potential. The transition is found to be the result of growing clusters, which eventually percolate the domain, and change the mode of momentum transport in the system. Differences in the behavior of the shear stress normalized by the pressure are observed when frictionless and frictional cases are compared. These differences are explained through contact anisotropy after percolation occurs. Both frictionless and frictional systems are found to be vulnerable to instabilities after full system percolation has occurred, where the former becomes thermodynamically unstable and the latter may form shear bands. Finally, implications for constitutive modeling are discussed.
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Affiliation(s)
- Eric Murphy
- Center for Multiphase Flow Research and Education, Department of Mechanical Engineering, Iowa State University, Ames, Iowa 50011, USA
| | - Sriram Sundararajan
- Department of Mechanical Engineering, Iowa State University, Ames, Iowa 50011, USA
| | - Shankar Subramaniam
- Center for Multiphase Flow Research and Education, Department of Mechanical Engineering, Iowa State University, Ames, Iowa 50011, USA
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16
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Abstract
Rheology of a dilute cohesive granular gas is theoretically and numerically studied. The flow curve between the shear viscosity and the shear rate is derived from the inelastic Boltzmann equation for particles having square-well potentials in a simple shear flow. It is found that (i) the stable uniformly sheared state only exists above a critical shear rate and (ii) the viscosity in the uniformly sheared flow is almost identical to that for uniformly sheared flow of hard core granular particles. Below the critical shear rate, clusters grow with time, in which the viscosity can be approximated by that for the hard-core fluids if we replace the diameter of the particle by the mean diameter of clusters.
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Affiliation(s)
- Satoshi Takada
- Earthquake Research Institute, The University of Tokyo, 1-1-1, Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan.,Department of Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
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17
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Kang W, Feng Y, Liu C, Blumenfeld R. Archimedes' law explains penetration of solids into granular media. Nat Commun 2018; 9:1101. [PMID: 29549250 PMCID: PMC5856792 DOI: 10.1038/s41467-018-03344-3] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2017] [Accepted: 02/06/2018] [Indexed: 11/25/2022] Open
Abstract
Understanding the response of granular matter to intrusion of solid objects is key to modelling many aspects of behaviour of granular matter, including plastic flow. Here we report a general model for such a quasistatic process. Using a range of experiments, we first show that the relation between the penetration depth and the force resisting it, transiently nonlinear and then linear, is scalable to a universal form. We show that the gradient of the steady-state part, K ϕ , depends only on the medium's internal friction angle, ϕ, and that it is nonlinear in μ = tan ϕ, in contrast to an existing conjecture. We further show that the intrusion of any convex solid shape satisfies a modified Archimedes' law and use this to: relate the zero-depth intercept of the linear part to K ϕ and the intruder's cross-section; explain the curve's nonlinear part in terms of the stagnant zone's development.
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Affiliation(s)
- Wenting Kang
- State Key Laboratory of Turbulence and Complex System, College of Engineering, Peking University, 100871, Beijing, China
| | - Yajie Feng
- State Key Laboratory of Turbulence and Complex System, College of Engineering, Peking University, 100871, Beijing, China
| | - Caishan Liu
- State Key Laboratory of Turbulence and Complex System, College of Engineering, Peking University, 100871, Beijing, China.
| | - Raphael Blumenfeld
- Imperial College London, London SW7 2AZ, UK
- University of Cambridge, Cambridge CB3 0HE, UK
- National University of Defence Technology, Changsha, Hunan 410073, China
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18
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Jones MA, Ness C. Linking attractive interactions and confinement to the rheological response of suspended particles close to jamming. GRANULAR MATTER 2017; 20:3. [PMID: 31983891 PMCID: PMC6954019 DOI: 10.1007/s10035-017-0770-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/28/2017] [Indexed: 06/10/2023]
Abstract
We study the response to simple shear start-up of an overdamped, athermal assembly of particles with tuneable attractive interactions. We focus on volume fractions close to the jamming point, where such systems can become disordered elastoplastic solids. By systematically varying the strength of the particle-particle attraction and the volume fraction, we demonstrate how cohesion and confinement individually contribute to the shear modulus and yield strain of the material. The results provide evidence for the influence of binding agents on the rheology of dense, athermal suspensions and describe a set of handles with which the macroscopic properties of such materials can be engineered.
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Affiliation(s)
- Michael A. Jones
- Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE UK
| | - Christopher Ness
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge, CB3 0AS UK
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Handl L, Torbahn L, Spettl A, Schmidt V, Kwade A. Structural analysis and tracking of micron-sized glass particles during shear deformation: A study based on time-resolved tomographic data. ADV POWDER TECHNOL 2017. [DOI: 10.1016/j.apt.2017.05.002] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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20
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Shi H, Luding S, Magnanimo V. Steady state rheology from homogeneous and locally averaged simple shear simulations. EPJ WEB OF CONFERENCES 2017. [DOI: 10.1051/epjconf/201714003070] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Luo Q, Zheng Q, Yu A. Finite element investigation of granular dynamics in a split-bottom shear cell. POWDER TECHNOL 2017. [DOI: 10.1016/j.powtec.2016.09.069] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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22
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Kievitsbosch R, Smit H, Magnanimo V, Luding S, Taghizadeh K. Influence of dry cohesion on the micro- and macro-mechanical properties of dense polydisperse powders & grains. EPJ WEB OF CONFERENCES 2017. [DOI: 10.1051/epjconf/201714008016] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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23
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Cheng H, Shuku T, Thoeni K, Yamamoto H. Calibration of micromechanical parameters for DEM simulations by using the particle filter. EPJ WEB OF CONFERENCES 2017. [DOI: 10.1051/epjconf/201714012011] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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25
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Liu W, Li S, Chen S. Computer simulation of random loose packings of micro-particles in presence of adhesion and friction. POWDER TECHNOL 2016. [DOI: 10.1016/j.powtec.2016.08.068] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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26
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Irani E, Chaudhuri P, Heussinger C. Athermal rheology of weakly attractive soft particles. Phys Rev E 2016; 94:052608. [PMID: 27967137 DOI: 10.1103/physreve.94.052608] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2016] [Indexed: 06/06/2023]
Abstract
We study the rheology of a soft particulate system where the interparticle interactions are weakly attractive. Using extensive molecular dynamics simulations, we scan across a wide range of packing fractions (ϕ), attraction strengths (u), and imposed shear rates (γ[over ̇]). In striking contrast to repulsive systems, we find that at small shear rates generically a fragile isostatic solid is formed even if we go to ϕ≪ϕ_{J}. Further, with increasing shear rates, even at these low ϕ, nonmonotonic flow curves occur which lead to the formation of persistent shear bands in large enough systems. By tuning the damping parameter, we also show that inertia plays an important role in this process. Furthermore, we observe enhanced particle dynamics in the attraction-dominated regime as well as a pronounced anisotropy of velocity and diffusion constant, which we take as precursors to the formation of shear bands. At low enough ϕ, we also observe structural changes via the interplay of low shear rates and attraction with the formation of microclusters and voids. Finally, we characterize the properties of the emergent shear bands, and thereby, we find surprisingly small mobility of these bands, leading to prohibitively long time scales and extensive history effects in ramping experiments.
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Affiliation(s)
- Ehsan Irani
- Institute for Theoretical Physics, Georg-August University of Göttingen, Friedrich-Hund Platz 1, 37077 Göttingen, Germany
| | - Pinaki Chaudhuri
- Institute of Mathematical Sciences, Taramani, Chennai 600 113, Tamil Nadu, India
| | - Claus Heussinger
- Institute for Theoretical Physics, Georg-August University of Göttingen, Friedrich-Hund Platz 1, 37077 Göttingen, Germany
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Kumar N, Magnanimo V, Ramaioli M, Luding S. Tuning the bulk properties of bidisperse granular mixtures by small amount of fines. POWDER TECHNOL 2016. [DOI: 10.1016/j.powtec.2015.11.042] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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28
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Thakur SC, Ooi JY, Ahmadian H. Scaling of discrete element model parameters for cohesionless and cohesive solid. POWDER TECHNOL 2016. [DOI: 10.1016/j.powtec.2015.05.051] [Citation(s) in RCA: 66] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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29
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Reprint of "Experiments and discrete element simulation of the dosing of cohesive powders in a simplified geometry". POWDER TECHNOL 2016. [DOI: 10.1016/j.powtec.2015.07.052] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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31
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Saitoh K, Mizuno H. Anomalous energy cascades in dense granular materials yielding under simple shear deformations. SOFT MATTER 2016; 12:1360-1367. [PMID: 26701740 DOI: 10.1039/c5sm02760h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
By using molecular dynamics (MD) simulations of dense granular particles in two dimensions, we study turbulent-like structures of their non-affine velocities under simple shear deformations. We find that the spectrum of non-affine velocities, introduced as an analog of the energy spectrum for turbulent flows, exhibits the power-law decay if the system is yielding in a quasi-static regime, where large-scale collective motions and inelastic interactions of granular particles are crucial for the anomalous cascade of kinetic energy. Based on hydrodynamic equations of dense granular materials, which include both kinetic and contact contributions in constitutive relations, we derive a theoretical expression for the spectrum, where a good agreement between the result of MD simulations and theoretical prediction is established over a wide range of length scales.
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Affiliation(s)
- Kuniyasu Saitoh
- Faculty of Engineering Technology, MESA+, University of Twente, Drienerlolaan 5, 7522 NB, Enschede, The Netherlands.
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32
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Experiments and discrete element simulation of the dosing of cohesive powders in a simplified geometry. POWDER TECHNOL 2016. [DOI: 10.1016/j.powtec.2015.07.051] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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33
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Saitoh K, Takada S, Hayakawa H. Hydrodynamic instabilities in shear flows of dry cohesive granular particles. SOFT MATTER 2015; 11:6371-6385. [PMID: 26133497 DOI: 10.1039/c5sm01160d] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We extend the dynamic van der Waals model introduced by A. Onuki [Phys. Rev. Lett., 2005, 94, 054501] to the description of cohesive granular flows under a plane shear to study their hydrodynamic instabilities. By numerically solving the dynamic van der Waals model, we observed various heterogeneous structures of density fields in steady states, where the viscous heating is balanced with the energy dissipation caused by inelastic collisions. Based on the linear stability analysis, we found 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 ∂p/∂ϕ < 0.
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Affiliation(s)
- Kuniyasu Saitoh
- Faculty of Engineering Technology, MESA+, University of Twente, Drienerlolaan 5, 7522 NB, Enschede, The Netherlands.
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34
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Khamseh S, Roux JN, Chevoir F. Flow of wet granular materials: A numerical study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022201. [PMID: 26382388 DOI: 10.1103/physreve.92.022201] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2015] [Indexed: 06/05/2023]
Abstract
We simulate dense assemblies of frictional spherical grains in steady shear flow under controlled normal stress P in the presence of a small amount of an interstitial liquid, which gives rise to capillary menisci, assumed isolated (pendular regime), and attractive forces, which are hysteretic: Menisci form at contact, but do not break until grains are separated by a finite rupture distance. The system behavior depends on two dimensionless control parameters, inertial number I and reduced pressure P*=aP/(πΓ), comparing confining forces ∼a2P to meniscus tensile strength F0=πΓa, for grains of diameter a joined by menisci with surface tension Γ. We pay special attention to the quasistatic limit of slow flow and observe systematic, enduring strain localization in some of the cohesion-dominated (P*∼0.1) systems. Homogeneous steady flows are characterized by the dependence of internal friction coefficient μ* and solid fraction Φ on I and P*. We also record normal stress differences, fairly small but not negligible and increasing for decreasing P*. The system rheology is moderately sensitive to saturation within the pendular regime, but would be different in the absence of capillary hysteresis. Capillary forces have a significant effect on the macroscopic behavior of the system, up to P* values of several units, especially for longer force ranges associated with larger menisci. The concept of effective pressure may be used to predict an order of magnitude for the strong increase of μ* as P* decreases but such a crude approach is unable to account for the complex structural changes induced by capillary cohesion, with a significant decrease of Φ and different agglomeration states and anisotropic fabric. Likewise, the Mohr-Coulomb criterion for pressure-dependent critical states is, at best, an approximation valid within a restricted range of pressures, with P*≥1. At small enough P*, large clusters of interacting grains form in slow flows, in which liquid bonds survive shear strains of several units. This affects the anisotropies associated with different interactions and the shape of function μ*(I), which departs more slowly from its quasistatic limit than in cohesionless systems (possibly explaining the shear banding tendency).
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Affiliation(s)
- Saeed Khamseh
- Université Paris-Est, Laboratoire Navier, 2 Allée Kepler, 77420 Champs-sur-Marne, France
| | - Jean-Noël Roux
- Université Paris-Est, Laboratoire Navier, 2 Allée Kepler, 77420 Champs-sur-Marne, France
| | - François Chevoir
- Université Paris-Est, Laboratoire Navier, 2 Allée Kepler, 77420 Champs-sur-Marne, France
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35
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Szabó B, Török J, Somfai E, Wegner S, Stannarius R, Böse A, Rose G, Angenstein F, Börzsönyi T. Evolution of shear zones in granular materials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032205. [PMID: 25314435 DOI: 10.1103/physreve.90.032205] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2014] [Indexed: 06/04/2023]
Abstract
The evolution of wide shear zones or shear bands was investigated experimentally and numerically for quasistatic dry granular flows in split bottom shear cells. We compare the behavior of materials consisting of beads, irregular grains, such as sand, and elongated particles. Shearing an initially random sample, the zone width was found to significantly decrease in the first stage of the process. The characteristic shear strain associated with this decrease is about unity and it is systematically increasing with shape anisotropy, i.e., when the grain shape changes from spherical to irregular (e.g., sand) and becomes elongated (pegs). The strongly decreasing tendency of the zone width is followed by a slight increase which is more pronounced for rodlike particles than for grains with smaller shape anisotropy (beads or irregular particles). The evolution of the zone width is connected to shear-induced packing density change and for nonspherical particles it also involves grain reorientation effects. The final zone width is significantly smaller for irregular grains than for spherical beads.
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Affiliation(s)
- Balázs Szabó
- Institute for Solid State Physics and Optics, Wigner Research Center for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
| | - János Török
- Institute of Physics, Budapest University of Technology and Economics, H-1111 Budapest, Hungary
| | - Ellák Somfai
- Institute for Solid State Physics and Optics, Wigner Research Center for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
| | - Sandra Wegner
- Otto-von-Guericke University, D-39106 Magdeburg, Germany
| | | | - Axel Böse
- Otto-von-Guericke University, D-39106 Magdeburg, Germany
| | - Georg Rose
- Otto-von-Guericke University, D-39106 Magdeburg, Germany
| | | | - Tamás Börzsönyi
- Institute for Solid State Physics and Optics, Wigner Research Center for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
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Gu Y, Chialvo S, Sundaresan S. Rheology of cohesive granular materials across multiple dense-flow regimes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032206. [PMID: 25314436 DOI: 10.1103/physreve.90.032206] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2014] [Indexed: 06/04/2023]
Abstract
We investigate the dense-flow rheology of cohesive granular materials through discrete element simulations of homogeneous, simple shear flows of frictional, cohesive, spherical particles. Dense shear flows of noncohesive granular materials exhibit three regimes: quasistatic, inertial, and intermediate, which persist for cohesive materials as well. It is found that cohesion results in bifurcation of the inertial regime into two regimes: (a) a new rate-independent regime and (b) an inertial regime. Transition from rate-independent cohesive regime to inertial regime occurs when the kinetic energy supplied by shearing is sufficient to overcome the cohesive energy. Simulations reveal that inhomogeneous shear band forms in the vicinity of this transition, which is more pronounced at lower particle volume fractions. We propose a rheological model for cohesive systems that captures the simulation results across all four regimes.
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Affiliation(s)
- Yile Gu
- Chemical and Biological Engineering Department, Princeton University, Princeton, New Jersey 08540, USA
| | - Sebastian Chialvo
- Chemical and Biological Engineering Department, Princeton University, Princeton, New Jersey 08540, USA
| | - Sankaran Sundaresan
- Chemical and Biological Engineering Department, Princeton University, Princeton, New Jersey 08540, USA
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