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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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Gramlich JM, Zarif M, Bowles RK. Is there a granular potential? SOFT MATTER 2023; 19:1373-1383. [PMID: 36723165 DOI: 10.1039/d2sm01636b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Granular materials, such as sand or grain, exhibit many structural and dynamic characteristics similar to those observed in molecular systems, despite temperature playing no role in their properties. This has led to an effort to develop a statistical mechanics for granular materials that has focused on establishing an equivalent to the microcanonical ensemble and a temperature-like thermodynamic variable. Here, we expand on these ideas by introducing a granular potential into the Edwards ensemble, as an analogue to the chemical potential, and explore its properties using a simple model of a granular system. A simple kinetic Monte Carlo simulation of the model shows the effect of mass transport leading to equilibrium and how this is connected to the redistribution of volume in the system. An exact analytical treatment of the model shows that the compactivity and the ratio of the granular potential to the compactivity determine the equilibrium between two open systems that are able to exchange volume and particles, and that mass moves from high to low values of this ratio. Analysis of the granular potential shows that adding a particle to the system increases the entropy at high compactivity, but decreases the entropy at low compactivity. Finally, we demonstrate the use of a small system thermodynamics method for the measurement of granular potential differences.
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Affiliation(s)
- Josh M Gramlich
- Department of Chemistry, University of Saskatchewan, Saskatoon, SK, S7H 0H1, Canada.
| | - Mahdi Zarif
- Department of Physical and Computational Chemistry, Shahid Beheshti University, Tehran 19839-9411, Iran
| | - Richard K Bowles
- Department of Chemistry, University of Saskatchewan, Saskatoon, SK, S7H 0H1, Canada.
- Centre for Quantum Topology and its Applications (quanTA), University of Saskatchewan, SK S7N 5E6, Canada
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3
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Schaller FM, Punzmann H, Schröder-Turk GE, Saadatfar M. Mixing properties of bi-disperse ellipsoid assemblies: mean-field behaviour in a granular matter experiment. SOFT MATTER 2023; 19:951-958. [PMID: 36633168 DOI: 10.1039/d2sm00922f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The structure and spatial statistical properties of amorphous ellipsoid assemblies have profound scientific and industrial significance in many systems, from cell assays to granular materials. This paper uses a fundamental theoretical relationship for mixture distributions to explain the observations of an extensive X-ray computed tomography study of granular ellipsoidal packings. We study a size-bi-disperse mixture of two types of ellipsoids of revolutions that have the same aspect ratio of α ≈ 0.57 and differ in size, by about 10% in linear dimension, and compare these to mono-disperse systems of ellipsoids with the same aspect ratio. Jammed configurations with a range of packing densities are achieved by employing different tapping protocols. We numerically interrogate the final packing configurations by analyses of the local packing fraction distributions calculated from the Voronoi diagrams. Our main finding is that the bi-disperse ellipsoidal packings studied here can be interpreted as a mixture of two uncorrelated mono-disperse packings, insensitive to the compaction protocol. Our results are consolidated by showing that the local packing fraction shows no correlation beyond their first shell of neighbours in the binary mixtures. We propose a model of uncorrelated binary mixture distribution that describes the observed experimental data with high accuracy. This analysis framework will enable future studies to test whether the observed mean-field behaviour is specific to the particular granular system or the specific parameter values studied here or if it is observed more broadly in other bi-disperse non-spherical particle systems.
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Affiliation(s)
- F M Schaller
- Friedrich-Alexander Universität Erlangen-Nürnberg, Institut für Theoretische Physik, Staudtstr. 7B, 91058 Erlangen, Germany.
- Karlsruhe Institute of Technology (KIT), Institut für Stochastik, 76131 Karlsruhe, Germany
| | - H Punzmann
- The Australian National University, Research School of Physics, Canberra ACT 2601, Australia
| | - G E Schröder-Turk
- The Australian National University, Research School of Physics, Canberra ACT 2601, Australia
- Murdoch University, College of Science, Technology, Engineering and Mathematics, 90 South St, Murdoch WA 6150, Australia
| | - M Saadatfar
- The Australian National University, Research School of Physics, Canberra ACT 2601, Australia
- The University of Sydney, School of Civil Engineering, NSW 2006, Australia.
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4
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Francois N, Cruikshank R, Herring A, Kingston A, Webster S, Knackstedt M, Saadatfar M. A versatile microtomography system to study in situ the failure and fragmentation in geomaterials. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:083704. [PMID: 36050093 DOI: 10.1063/5.0093650] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Accepted: 07/04/2022] [Indexed: 06/15/2023]
Abstract
This article describes a microtomography experimental platform enabling in situ micro-mechanical study of failure and fragmentation in geomaterials. The system is based on an original high-pressure triaxial flow cell, which is fully integrated into a custom built microtomography scanner equipped with a laboratory x-ray source. The design of the high-precision mechanical apparatus was informed by the concurrent development of advanced tomographic reconstruction methods based on helical scanning and of algorithms correcting for hardware inaccuracies. This experimental system produces very high-quality 3D images of microstructural changes occurring in rocks undergoing mechanical failure and substantial fragmentation. We present the results of two experiments as case studies to demonstrate the capabilities and versatility of this instrumental platform. These experiments tackle various questions related to the onset of rock failure, the hydromechanical coupling and relaxation mechanisms in fractured rocks, or the fragmentation process in geomaterials such as copper ores.
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Affiliation(s)
- N Francois
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - R Cruikshank
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - A Herring
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - A Kingston
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - S Webster
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - M Knackstedt
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - M Saadatfar
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
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Osang G, Edelsbrunner H, Saadatfar M. Topological signatures and stability of hexagonal close packing and Barlow stackings. SOFT MATTER 2021; 17:9107-9115. [PMID: 34569592 DOI: 10.1039/d1sm00774b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Two common representations of close packings of identical spheres consisting of hexagonal layers, called Barlow stackings, appear abundantly in minerals and metals. These motifs, however, occupy an identical portion of space and bear identical first-order topological signatures as measured by persistent homology. Here we present a novel method based on k-fold covers that unambiguously distinguishes between these patterns. Moreover, our approach provides topological evidence that the FCC motif is the more stable of the two in the context of evolving experimental sphere packings during the transition from disordered to an ordered state. We conclude that our approach can be generalised to distinguish between various Barlow stackings manifested in minerals and metals.
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Affiliation(s)
- Georg Osang
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Herbert Edelsbrunner
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Mohammad Saadatfar
- School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia.
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6
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Peshkov A, Girvan M, Richardson DC, Losert W. Reversibility of granular rotations and translations. Phys Rev E 2019; 100:042905. [PMID: 31771010 DOI: 10.1103/physreve.100.042905] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2018] [Indexed: 06/10/2023]
Abstract
We analyze reversibility of displacements and rotations of spherical grains in three-dimensional compression experiments. Using transparent acrylic beads with cylindrical holes and index matching techniques, we are not only capable of tracking displacements but also analyzing reversibility of rotations. We observe that for moderate compression amplitudes, up to one bead diameter, the translational displacements of the beads after each cycle become mostly reversible after an initial transient. By contrast, granular rotations are largely irreversible. We find a weak correlation between translational and rotational displacements, indicating that rotational reversibility depends on more subtle changes in contact distributions and contact forces between grains compared with displacement reversibility. Three-dimensional rotations in dense granular systems are particularly important, since frictional losses associated with rotations are the dominant mechanism for energy dissipation. As such our work provides a first step toward a thorough study of rotations and tangential forces to understand the granular dynamics in dense systems.
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Affiliation(s)
- Anton Peshkov
- IREAP, University of Maryland, College Park, Maryland 20742, USA
| | - Michelle Girvan
- Department of Physics, IPST and IREAP, University of Maryland, College Park, Maryland 20742, USA
| | - Derek C Richardson
- Department of Astronomy, University of Maryland, College Park, Maryland 20742, USA
| | - Wolfgang Losert
- Department of Physics, IPST and IREAP, University of Maryland, College Park, Maryland 20742, USA
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8
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Pakpour M, Vandewalle N, Lumay G. Decompaction of wet granular materials under freeze-thaw cycling. Phys Rev E 2019; 99:012901. [PMID: 30780361 DOI: 10.1103/physreve.99.012901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2017] [Indexed: 11/07/2022]
Abstract
The packing fraction dynamics of a wet granular material submitted to freeze-thaw cycling is investigated experimentally. The dynamics is strongly influenced by the liquid volume fraction ω in the considered range of 0.03<ω<0.32. This range of liquid contents covers different regimes of wetness from the creation of the capillary network until the formation of large clusters and finally close to the saturated case. For the liquid contents ω≳0.15, the pile experiences a decompaction until a particular value of the packing fraction 0.56 corresponding to a random loose packing configuration for monosized spheres. Moreover, the decompaction starts after a cycling number that decreases exponentially with the liquid content. Finally, we show that the packing dynamics can be well modeled on the basis of a Landau potential with an asymmetric double-well structure. The onset of decompaction represents the tendency of the system to stay in a metastable state. After several cycles, the forces induced by the thermal cycling and local stochastic rearrangements of the grains can drive the system to overcome the energy barrier of the cohesive forces.
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Affiliation(s)
- Maryam Pakpour
- GRASP, Physics Department, University of Liège, B-4000 Liège, Belgium.,Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45195-1159, Iran.,Condensed Matter National Laboratory, Institute for Research in Fundamental Sciences (IPM), 19395-5531 Tehran, Iran
| | | | - Geoffroy Lumay
- GRASP, Physics Department, University of Liège, B-4000 Liège, Belgium
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Dhiman I, Kimber SAJ, Mehta A, Chatterji T. A neutron tomography study: probing the spontaneous crystallization of randomly packed granular assemblies. Sci Rep 2018; 8:17637. [PMID: 30518966 PMCID: PMC6281579 DOI: 10.1038/s41598-018-36331-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2018] [Accepted: 11/20/2018] [Indexed: 11/09/2022] Open
Abstract
We study the spontaneous crystallization of an assembly of highly monodisperse steel spheres under shaking, as it evolves from localized icosahedral ordering towards a packing reaching crystalline ordering. Towards this end, real space neutron tomography measurements on the granular assembly are carried out, as it is systematically subjected to a variation of frequency and amplitude. As expected, we see a presence of localized icosahedral ordering in the disordered initial state (packing fraction ≈ 0.62). As the frequency is increased for both the shaking amplitudes (0.2 and 0.6 mm) studied here, there is a rise in packing fraction, accompanied by an evolution to crystallinity. The extent of crystallinity is found to depend on both the amplitude and frequency of shaking. We find that the icosahedral ordering remains localized and its extent does not grow significantly, while the crystalline ordering grows rapidly as an ordering transition point is approached. In the ordered state, crystalline clusters of both face centered cubic (FCC) and hexagonal close packed (HCP) types are identified, the latter of which grows from stacking faults. Our study shows that an earlier domination of FCC gives way to HCP ordering at higher shaking frequencies, suggesting that despite their coexistence, there is a subtle dynamical competition at play. This competition depends on both shaking amplitude and frequency, as our results as well as those of earlier theoretical simulations demonstrate. It is likely that this involves the very small free energy difference between the two structures.
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Affiliation(s)
- Indu Dhiman
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831, USA.
| | - Simon A J Kimber
- Université Bourgogne-Franche Comté, Université de Bourgogne, ICB-Laboratoire Interdisciplinaire Carnot de Bourgogne, Bâtiment Sciences Mirande, 9 Avenue Alain Savary, B-P. 47870, 21078, Dijon Cedex, France
| | - Anita Mehta
- Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany
| | - Tapan Chatterji
- Institut Laue-Langevin, 71 Avenue des Martyrs, 38000, Grenoble, France.
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10
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Rietz F, Radin C, Swinney HL, Schröter M. Nucleation in Sheared Granular Matter. PHYSICAL REVIEW LETTERS 2018; 120:055701. [PMID: 29481202 DOI: 10.1103/physrevlett.120.055701] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2017] [Revised: 12/11/2017] [Indexed: 06/08/2023]
Abstract
We present an experiment on crystallization of packings of macroscopic granular spheres. This system is often considered to be a model for thermally driven atomic or colloidal systems. Cyclically shearing a packing of frictional spheres, we observe a first order phase transition from a disordered to an ordered state. The ordered state consists of crystallites of mixed fcc and hcp symmetry that coexist with the amorphous bulk. The transition, initiated by homogeneous nucleation, overcomes a barrier at 64.5% volume fraction. Nucleation consists predominantly of the dissolving of small nuclei and the growth of nuclei that have reached a critical size of about ten spheres.
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Affiliation(s)
- Frank Rietz
- Max-Planck-Institute for Dynamics and Self-Organization Göttingen, 37077 Göttingen, Germany
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91052 Erlangen, Germany
- Department of Nonlinear Phenomena, University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
- Department of Pattern Formation, University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
| | - Charles Radin
- Department of Mathematics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Harry L Swinney
- Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Matthias Schröter
- Max-Planck-Institute for Dynamics and Self-Organization Göttingen, 37077 Göttingen, Germany
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91052 Erlangen, Germany
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11
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Hurley RC, Hall SA, Wright JP. Multi-scale mechanics of granular solids from grain-resolved X-ray measurements. Proc Math Phys Eng Sci 2017; 473:20170491. [PMID: 29225500 PMCID: PMC5719631 DOI: 10.1098/rspa.2017.0491] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2017] [Accepted: 09/28/2017] [Indexed: 11/12/2022] Open
Abstract
This work discusses an experimental technique for studying the mechanics of three-dimensional (3D) granular solids. The approach combines 3D X-ray diffraction and X-ray computed tomography to measure grain-resolved strains, kinematics and contact fabric in the bulk of a granular solid, from which continuum strains, grain stresses, interparticle forces and coarse-grained elasto-plastic moduli can be determined. We demonstrate the experimental approach and analysis of selected results on a sample of 1099 stiff, frictional grains undergoing multiple uniaxial compression cycles. We investigate the inter-particle force network, elasto-plastic moduli and associated length scales, reversibility of mechanical responses during cyclic loading, the statistics of microscopic responses and microstructure-property relationships. This work serves to highlight both the fundamental insight into granular mechanics that is furnished by combined X-ray measurements and describes future directions in the field of granular materials that can be pursued with such approaches.
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Affiliation(s)
- R. C. Hurley
- Physical and Life Sciences, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - S. A. Hall
- Division of Solid Mechanics, Lund University, Lund 22818, Sweden
| | - J. P. Wright
- European Synchrotron Radiation Facility, Grenoble 38000, France
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12
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Pore configuration landscape of granular crystallization. Nat Commun 2017; 8:15082. [PMID: 28497794 PMCID: PMC5437301 DOI: 10.1038/ncomms15082] [Citation(s) in RCA: 50] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2016] [Accepted: 02/23/2017] [Indexed: 11/08/2022] Open
Abstract
Uncovering grain-scale mechanisms that underlie the disorder–order transition in assemblies of dissipative, athermal particles is a fundamental problem with technological relevance. To date, the study of granular crystallization has mainly focussed on the symmetry of crystalline patterns while their emergence and growth from irregular clusters of grains remains largely unexplored. Here crystallization of three-dimensional packings of frictional spheres is studied at the grain-scale using X-ray tomography and persistent homology. The latter produces a map of the topological configurations of grains within static partially crystallized packings. Using numerical simulations, we show that similar maps are measured dynamically during the melting of a perfect crystal. This map encodes new information on the formation process of tetrahedral and octahedral pores, the building blocks of perfect crystals. Four key formation mechanisms of these pores reproduce the main changes of the map during crystallization and provide continuous deformation pathways representative of the crystallization dynamics. Emergence and growth of crystalline domains in granular media remains under-explored. Here, the authors analyse tomographic snapshots from partially recrystallized packings of spheres using persistent homology and find agreement with proposed transitions based on continuous deformation of octahedral and tetrahedral voids.
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Weis S, Schröter M. Analyzing X-ray tomographies of granular packings. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2017; 88:051809. [PMID: 28571396 DOI: 10.1063/1.4983051] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Starting from three-dimensional volume data of a granular packing, as, e.g., obtained by X-ray Computed Tomography, we discuss methods to first detect the individual particles in the sample and then analyze their properties. This analysis includes the pair correlation function, the volume and shape of the Voronoi cells, and the number and type of contacts formed between individual particles. We mainly focus on packings of monodisperse spheres, but we will also comment on other monoschematic particles such as ellipsoids and tetrahedra. This paper is accompanied by a package of free software containing all programs (including source code) and an example three-dimensional dataset which allows the reader to reproduce and modify all examples given.
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Affiliation(s)
- Simon Weis
- Institut für Theoretische Physik I, Friedrich-Alexander-Universität, 91058 Erlangen, Germany
| | - Matthias Schröter
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität, 91052 Erlangen, Germany
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Evans ME, Schröder-Turk GE, Kraynik AM. A geometric exploration of stress in deformed liquid foams. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:124004. [PMID: 28067638 DOI: 10.1088/1361-648x/aa57c7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We explore an alternate way of looking at the rheological response of a yield stress fluid: using discrete geometry to probe the heterogeneous distribution of stress in soap froth. We present quasi-static, uniaxial, isochoric compression and extension of three-dimensional random monodisperse soap froth in periodic boundary conditions and examine the stress and geometry that result. The stress and shape anisotropy of individual cells is quantified by Q, a scalar measure derived from the interface tensor that gauges each cell's contribution to the global stress. Cumulatively, the spatial distribution of highly deformed cells allows us to examine how stress is internally distributed. The topology of highly deformed cells, how they arrange relative to one another in space, gives insight into the heterogeneous distribution of stress.
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Affiliation(s)
- Myfanwy E Evans
- Institute for Mathematics, Technical University of Berlin, Germany
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15
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Saadatfar M, Takeuchi H, Hanifpour M, Robins V, Francois N, Hiraoka Y. Granular compaction and the topology of pore deformation. EPJ WEB OF CONFERENCES 2017. [DOI: 10.1051/epjconf/201714016009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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