Two Approaches to Quantification of Force Networks in Particulate Systems
Publication: Journal of Engineering Mechanics
Volume 147, Issue 11
Abstract
The interactions between particles in dense particulate systems are organized in force networks, mesoscale features that influence the macroscopic response to applied stresses. The detailed structure of these networks is, however, difficult to extract from experiments that cannot resolve individual contact forces. In this study, we showed that certain persistent homology (PH) measures extracted from data accessible to experiment are strongly correlated with the same features extracted from the full contact force network. We performed simulations known to accurately model experiments on an intruder being pushed through a two-dimensional (2D) granular layer and compared PH properties of full contact force networks and networks constructed using only the sum of the normal forces on each grain. We found that the main features were highly correlated, suggesting that data commonly available in experiments are sufficient for quantifying the structure of force networks in evolving granular systems.
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Data Availability Statement
All the data used in this study are available from the authors upon request.
Acknowledgments
This study was supported by US Army Research Office Grant No. W911NF1810184. Authors L. A. P. and C. M. C. acknowledge support from Universidad Tecnológica Nacional through Grant Nos. PID-MAUTNLP0004415 and PID-MAIFIBA0004434TC and from Consejo Nacional de Investigaciones Científicas y Técnicas (Argentina) (CONICET) through Grant Nos. RES-1225-17 and PUE 2018 229 20180100010 CO.
References
Ardanza-Trevijano, S., I. Zuriguel, R. Arévalo, and D. Maza. 2014. “Topological analysis of tapped granular media using persistent homology.” Phys. Rev. E 89 (5): 052212. https://doi.org/10.1103/PhysRevE.89.052212.
Arévalo, R., L. A. Pugnaloni, I. Zuriguel, and D. Maza. 2013. “Contact network topology in tapped granular media.” Phys. Rev. E 87 (2): 022203. https://doi.org/10.1103/PhysRevE.87.022203.
Arévalo, R., I. Zuriguel, and D. Maza. 2010. “Topology of the force network in jamming transition of an isotropically compressed granular packing.” Phys. Rev. E 81 (4): 041302. https://doi.org/10.1103/PhysRevE.81.041302.
Azéma, E., and F. Radja. 2012. “Force chains and contact network topology in sheared packings of elongated particles.” Phys. Rev. E 85 (3): 031303. https://doi.org/10.1103/PhysRevE.85.031303.
Bassett, D. S., E. T. Owens, K. E. Daniels, and M. A. Porter. 2012. “Influence of network topology on sound propagation in granular materials.” Phys. Rev. E 86 (4): 041306. https://doi.org/10.1103/PhysRevE.86.041306.
Behringer, R. P., and B. Chakraborty. 2018. “The physics of jamming for granular materials: a review.” Rep. Progress Phys. 82 (1): 012601. https://doi.org/10.1088/1361-6633/aadc3c.
Bo, L., R. Mari, C. Song, and H. A. Makse. 2014. “Cavity method for force transmission in jammed disordered packings of hard particles.” Soft Matter 10 (37): 7379–7392. https://doi.org/10.1039/C4SM00667D.
Carlevaro, C., and L. Pugnaloni. 2011. “Steady state of tapped granular polygons.” J. Stat. Mech. 2011 (01): P01007. https://doi.org/10.1088/1742-5468/2011/01/P01007.
Carlevaro, C. M., R. Kozlowski, L. A. Pugnaloni, H. Zheng, J. E. S. Socolar, and L. Kondic. 2020. “Intruder in a two-dimensional granular system: Effects of dynamic and static basal friction on stick-slip and clogging dynamics.” Phys. Rev. E 101 (1): 012909. https://doi.org/10.1103/PhysRevE.101.012909.
Catto, E. 2005. “Iterative dynamics with temporal coherence.” Accessed March 15, 2017. https://box2d.org/downloads/.
Cheng, C., A. Zadeh, and L. Kondic. 2021. “Correlating the force network evolution and dynamics in slider experiments.” Preprint, submitted January 13, 2021. https://arxiv:2101:07218.
Daniels, K. E., J. E. Kollmer, and J. G. Puckett. 2017. “Photoelastic force measurements in granular materials.” Rev. Sci. Instrum. 88 (5): 051808. https://doi.org/10.1063/1.4983049.
Dijksman, J. A., L. Kovalcinova, J. Ren, R. P. Behringer, M. Kramár, K. Mischaikow, and L. Kondic. 2018. “Characterizing granular networks using topological metrics.” Phys. Rev. E 97 (4): 042903. https://doi.org/10.1103/PhysRevE.97.042903.
Gameiro, M., A. Singh, L. Kondic, K. Mischaikow, and J. F. Morris. 2020. “Interaction network analysis in shear thickening suspensions.” Phys. Rev. Fluids 5 (3): 034307. https://doi.org/10.1103/PhysRevFluids.5.034307.
Giusti, C., L. Papadopoulos, E. T. Owens, K. E. Daniels, and D. S. Bassett. 2016. “Topological and geometric measurements of force-chain structure.” Phys. Rev. E 94 (3): 032909. https://doi.org/10.1103/PhysRevE.94.032909.
GUDHI. 2014. “Topological data analysis and geometric inference in higher dimension.” Accessed December 15, 2020. https://gudhi.inria.fr.
Howell, D., R. P. Behringer, and C. Veje. 1999. “Stress fluctuations in a 2D granular Couette experiment: A continuous transition.” Phys. Rev. Lett. 82 (26): 5241. https://doi.org/10.1103/PhysRevLett.82.5241.
Kawamoto, R., E. Andò, G. Viggiani, and J. E. Andrade. 2018. “All you need is shape: predicting shear banding in sand with LS-DEM.” J. Mech. Phys. Solids 111 (Feb): 375–392. https://doi.org/10.1016/j.jmps.2017.10.003.
Kondic, L., A. Goullet, C. O’Hern, M. Kramar, K. Mischaikow, and R. Behringer. 2012. “Topology of force networks in compressed granular media.” Europhys. Lett. 97 (5): 54001. https://doi.org/10.1209/0295-5075/97/54001.
Kondic, L., M. Kramár, L. A. Pugnaloni, C. M. Carlevaro, and K. Mischaikow. 2016. “Structure of force networks in tapped particulate systems of disks and pentagons. II. Persistence analysis.” Phys. Rev. E 93 (6): 062903. https://doi.org/10.1103/PhysRevE.93.062903.
Kozlowski, R., C. M. Carlevaro, K. E. Daniels, L. Kondic, L. A. Pugnaloni, J. E. S. Socolar, H. Zheng, and R. P. Behringer. 2019. “Dynamics of a grain-scale intruder in a two-dimensional granular medium with and without basal friction.” Phys. Rev. E 100 (3): 032905. https://doi.org/10.1103/PhysRevE.100.032905.
Kramár, M., A. Goullet, L. Kondic, and K. Mischaikow. 2013. “Persistence of force networks in compressed granular media.” Phys. Rev. E 87 (4): 042207. https://doi.org/10.1103/PhysRevE.87.042207.
Kramár, M., A. Goullet, L. Kondic, and K. Mischaikow. 2014a. “Evolution of force networks in dense particulate media.” Phys. Rev. E 90 (5): 052203. https://doi.org/10.1103/PhysRevE.90.052203.
Kramár, M., A. Goullet, L. Kondic, and K. Mischaikow. 2014b. “Quantifying force networks in particulate systems.” Phys. D 283 (Aug): 37–55. https://doi.org/10.1016/j.physd.2014.05.009.
Kramár, M., R. Levanger, J. Tithof, B. Suri, M. Xu, M. Paul, M. F. Schatz, and K. Mischaikow. 2016. “Analysis of Kolmogorov flow and Rayleigh–Bénard convection using persistent homology.” Phys. D 334 (Nov): 82–98. https://doi.org/10.1016/j.physd.2016.02.003.
Li, L., E. Marteau, and J. E. Andrade. 2019. “Capturing the inter-particle force distribution in granular material using LS-DEM.” Granular Matter 21 (43): 1–16.
Liu, J., A. Wautier, S. Bonelli, F. Nicot, and F. Darve. 2020. “Macroscopic softening in granular materials from a mesoscale perspective.” Int. J. Solids Struct. 193 (Jun): 222–238. https://doi.org/10.1016/j.ijsolstr.2020.02.022.
Mileyko, Y., S. Mukherjee, and J. Harer. 2011. “Probability measures on the space of persistence diagrams.” Inverse Prob. 27 (12): 124007. https://doi.org/10.1088/0266-5611/27/12/124007.
Nicot, F., H. Xiong, A. Wautier, J. Lerbet, and F. Darve. 2017. “Force chain collapse as grain column buckling in granular materials.” Granular Matter 19 (2): 18. https://doi.org/10.1007/s10035-017-0702-0.
Peters, J., M. Muthuswamy, J. Wibowo, and A. Tordesillas. 2005. “Characterization of force chains in granular material.” Phys. Rev. E 72 (4): 041307. https://doi.org/10.1103/PhysRevE.72.041307.
Pöschel, T., and T. Schwager. 2005. Computational granular dynamics: Models and algorithms. New York. Springer.
Pugnaloni, L., C. Carlevaro, M. Kramár, K. Mischaikow, and L. Kondic. 2016. “Structure of force networks in tapped particulate systems of disks and pentagons. I. Clusters and loops.” Phys. Rev. E 93 (6): 062902. https://doi.org/10.1103/PhysRevE.93.062902.
Pytlos, M., M. Gilbert, and C. C. Smith. 2015. “Modelling granular soil behaviour using a physics engine.” Geotech. Lett. 5 (4): 243–249. https://doi.org/10.1680/jgele.15.00067.
Radjai, F., M. Jean, J. J. Moreau, and S. Roux. 1996. “Force distribution in dense two-dimensional granular systems.” Phys. Rev. Lett. 77 (2): 274–277. https://doi.org/10.1103/PhysRevLett.77.274.
Sarkar, S., D. Bi, J. Zhang, R. P. Behringer, and B. Chakraborty. 2013. “Origin of rigidity in dry granular solids.” Phys. Rev. Lett. 111 (6): 068301. https://doi.org/10.1103/PhysRevLett.111.068301.
Shah, S., C. Cheng, P. Jalali, and L. Kondic. 2020. “Failure of confined granular media due to pullout of an intruder: from force networks to a system wide response.” Soft Matter 16 (33): 7685–7695. https://doi.org/10.1039/D0SM00911C.
Snoeijer, J. H., T. J. H. Vlugt, M. van Hecke, and W. van Saarloos. 2004. “Force network ensemble: A new approach to static granular matter.” Phys. Rev. Lett. 92 (5): 054302. https://doi.org/10.1103/PhysRevLett.92.054302.
Takahashi, T., A. H. Clark, T. Majmudar, and L. Kondic. 2018. “Granular response to impact: Topology of the force networks.” Phys. Rev. E 97 (1): 012906. https://doi.org/10.1103/PhysRevE.97.012906.
Tighe, B. P., J. H. Snoeijer, T. J. H. Vlugt, and M. van Hecke. 2010. “The force network ensemble for granular packings.” Soft Matter 6 (13): 2908–2917. https://doi.org/10.1039/b926592a.
Tordesillas, A., S. T. Tobin, M. Cil, K. Alshibli, and R. P. Behringer. 2015. “Network flow model of force transmission in unbonded and bonded granular media.” Phys. Rev. E 91 (6): 062204. https://doi.org/10.1103/PhysRevE.91.062204.
Tordesillas, A., D. M. Walker, G. Froyland, J. Zhang, and R. Behringer. 2012. “Transition dynamics of frictional granular clusters.” Phys. Rev. E 86 (1): 011306. https://doi.org/10.1103/PhysRevE.86.011306.
Tordesillas, A., D. M. Walker, and Q. Lin. 2010. “Force cycles and force chains.” Phys. Rev. E 81 (1): 011302. https://doi.org/10.1103/PhysRevE.81.011302.
Walker, D., and A. Tordesillas. 2012. “Taxonomy of granular rheology from grain property networks.” Phys. Rev. E 85 (1): 011304. https://doi.org/10.1103/PhysRevE.85.011304.
Zadeh, A. A., et al. 2019. “Enlightening force chains: A review of photoelasticimetry in granular matter.” Granular Matter 21 (4): 83. https://doi.org/10.1007/s10035-019-0942-2.
Zhao, Y., H. Zheng, D. Wang, M. Wang, and R. P. Behringer. 2019. “Particle scale force sensor based on intensity gradient method in granular photoelastic experiments.” New J. Phys. 21 (2): 023009. https://doi.org/10.1088/1367-2630/ab05e7.
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© 2021 American Society of Civil Engineers.
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Received: Feb 23, 2021
Accepted: Jun 26, 2021
Published online: Sep 11, 2021
Published in print: Nov 1, 2021
Discussion open until: Feb 11, 2022
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