Cooling after shearing: three possible fates for dense granular materials
Tóm tắt
We perform discrete element simulations of freely cooling, dense granular materials, previously sheared at a constant rate. Particles are identical, frictional spheres interacting via linear springs and dashpots and the solid volume fraction is constant and equal to 60% during both shearing and cooling. We measure the average and the distributions of contacts per particle and the anisotropy of the contact network. We observe that the granular material, at the beginning of cooling, can be shear-jammed, fragile or unjammed. The initial state determines the subsequent evolution of the dense assembly into either an anisotropic solid, an isotropic or an anisotropic fluid, respectively. While anisotropic solids and isotropic fluids rapidly reach an apparent final steady configuration, the microstructure continues to evolve for anisotropic fluids. We explain this with the presence of vortices in the flow field that counteract the randomizing and structure-annihilating effect of collisions. We notice, in accordance with previous findings, that the initial fraction of mechanically stable particles permits to distinguish between shear-jammed, fragile or unjammed states and, therefore, determine beforehand the fate of the freely evolving granular materials. We also find that the fraction of mechanically stable particles is in a one-to-one relation with the average number of contacts per particle. The latter is, therefore, a variable that must be incorporated in continuum models of granular materials, even in the case of unjammed states, where it was widely accepted that the solid volume fraction was sufficient to describe the geometry of the system.
Tài liệu tham khảo
Agnolin, I., Roux, J.N.: Internal states of model isotropic granular packings. III. Elastic properties. Phys. Rev. E 76(6 Pt 1), 061304 (2007), http://www.ncbi.nlm.nih.gov/pubmed/18233842
Behringer, R.P.: Jamming in granular materials. Comptes Rendus Physique 16(1), 10–25 (2015) https://doi.org/10.1016/j.crhy.2015.02.001, http://linkinghub.elsevier.com/retrieve/pii/S1631070515000158
Berzi, D., Buzzaccaro, S.: A heavy intruder in a locally-shaken granular solid. Soft Matter 16, 3921–3928 (2020)
Berzi, D., Jenkins, J.T.: Fluidity, anisotropy, and velocity correlations in frictionless, collisional grain flows. Phys. Rev. Fluids 3, 094303 (2018). https://doi.org/10.1103/PhysRevFluids.3.094303
Berzi, D., Thai-Quang, N., Guo, Y., Curtis, J.: Stresses and orientational order in shearing flows of granular liquid crystals. Phys. Rev. E 93(4), 040901 (2016) https://doi.org/10.1103/PhysRevE.93.040901, http://link.aps.org/doi/10.1103/PhysRevE.93.040901
Berzi, D., Thai-Quang, N., Guo, Y., Curtis, J.: Collisional dissipation rate in shearing flows of granular liquid crystals. Phys. Rev. E 95(5), 050901 (2017). https://doi.org/10.1103/PhysRevE.95.050901
Berzi, D., Jenkins, J.T., Richard, P.: Erodible, granular beds are fragile. Soft Matter 15, 7173–7178 (2019). https://doi.org/10.1039/c9sm01372e
Berzi, D., Jenkins, J.T., Richard, P.: Extended kinetic theory for granular flow over and within an inclined erodible bed. J. Fluid Mech. 885, A27 (2020). https://doi.org/10.1017/jfm.2019.1017
Bi, D., Zhang, J., Chakraborty, B., Behringer, R.P.: Jamming by shear. Nature 480, 355–358 (2011). https://doi.org/10.1038/nature10667
Campbell, C.S.: Granular shear flows at the elastic limit. J. Fluid Mech. 465, 261–291 (2002) https://doi.org/10.1017/S002211200200109X, http://www.journals.cambridge.org/abstract_S002211200200109X
Chacko, R., Mari, R., Fielding, S., Cates, M.: Shear reversal in dense suspensions: the challenge to fabric evolution models from simulation data. J. Fluid Mech. 847, 700–734 (2018)
Chialvo, S., Sun, J., Sundaresan, S.: Bridging the rheology of granular flows in three regimes. Phys. Rev. E 85(2), 021305 (2012) https://doi.org/10.1103/PhysRevE.85.021305, http://link.aps.org/doi/10.1103/PhysRevE.85.021305
Fischer, R., Gondret, P., Rabaud, M.: Transition by intermittency in granular matter: from discontinuous avalanches to continuous flow. Phys. Rev. Lett. 103(12), 128002 (2009) https://doi.org/10.1103/PhysRevLett.103.128002, http://link.aps.org/doi/10.1103/PhysRevLett.103.128002
Goldhirsch, I.: Rapid granular flows. Ann. Rev. Fluid Mech. 35, 267–293 (2003) https://doi.org/10.1146/annurev.fluid.35.101101.161114, http://www.annualreviews.org/doi/abs/10.1146/annurev.fluid.35.101101.161114
Göncü, F., Durán, O., Luding, S.: Constitutive relations for the isotropic deformation of frictionless packings of polydisperse spheres. Comptes Rendus Mécanique 338(10), 570–586 (2010) https://doi.org/10.1016/j.crme.2010.10.004, https://www.sciencedirect.com/science/article/pii/S1631072110001610, micromechanics of granular materials
Habdas, P., Schaar, D., Levitt, A.C., Weeks, E.R.: Forced motion of a probe particle near the colloidal glass transition. Europhys. Lett. 67(3), 477–483 (2004). https://doi.org/10.1209/epl/i2004-10075-y. (arXiv:0308622v2)
Hastings, M.B., Olson Reichhardt, C.J., Reichhardt, C.: Depinning by fracture in a glassy background. Phys. Rev. Lett. 90(9), 4 (2003). https://doi.org/10.1103/PhysRevLett.90.098302
Hatano, T.: Scaling properties of granular rheology near the jamming transition. J. Phys. Soc. Jpn. 77(12), 123002 (2008). https://doi.org/10.1143/JPSJ.77.123002
He, X., Wu, W., Wang, S.: A constitutive model for granular materials with evolving contact structure and contact forces-part i: framework. Granular Matter 21, 16 (2019)
Imole, O., Kumar, N., Magnanimo, V., Luding, S.: Hydrostatic and shear behavior of frictionless granular assemblies under different deformation conditions. KONA Powder Particle J. 30, 84–108 (2013). https://doi.org/10.14356/kona.2013011
Jenkins, J., Savage, S.: A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187–202 (1983) http://journals.cambridge.org/abstract_S0022112083001044
Kumar, N., Luding, S.: Memory of jamming—multiscale models for soft and granular matter. Granular Matter 18(3), 58 (2016). https://doi.org/10.1007/s10035-016-0624-2
Kumar, N., Imole, O.I., Magnanimo, V., Luding, S.: Effects of polydispersity on the micro-macro behavior of granular assemblies under different deformation paths. Particuology 12, 64–79 (2014) https://doi.org/10.1016/j.partic.2013.07.011, http://linkinghub.elsevier.com/retrieve/pii/S1674200113001971
Kumar, N., Luding, S., Magnanimo, V.: Macroscopic model with anisotropy based on micro-macro information. Acta Mech. 225, 2319–2343 (2014). https://doi.org/10.1007/s00707-014-1155-8
Lees, A., Edwards, S.: The computer study of transport processes under extreme conditions. J. Phys. C: Solid State Phys. 5(15), 1921–1929 (1972). https://doi.org/10.1088/0022-3719/5/15/006
Liu, A.J., Nagel, S.R.: Jamming is not just cool any more. Nature 396(6706), 21–22 (1998). https://doi.org/10.1038/23819
Luding, S.: Clustering instabilities, arching, and anomalous interaction probabilities as examples for cooperative phenomena in dry granular media. TASK Quart. Sci. Bull. Acad. Comput. Centre Tech. Univ. Gdansk 3, 417–443 (1998)
Luding, S.: Granular matter: so much for the jamming point. Nat. Phys. 12(6), 531–532 (2016). https://doi.org/10.1038/nphys3680
Majmudar, T., Sperl, M., Luding, S., Behringer, R.: The jamming transition in granular systems. Phys. Rev. Lett. 98(5), 058001 (2007). https://doi.org/10.1103/PhysRevLett.98.058001
Mitrano, P.P., Garzó, V., Hilger, A.M., Ewasko, C.J., Hrenya, C.M.: Assessing a hydrodynamic description for instabilities in highly dissipative, freely cooling granular gases. Phys. Rev. E 85(4), 5–9 (2012). https://doi.org/10.1103/PhysRevE.85.041303
O’Hern, C., Langer, S., Liu, A., Nagel, S.: Random packings of frictionless particles. Phys. Rev. Lett. 88(7), 075507 (2002). https://doi.org/10.1103/PhysRevLett.88.075507
Olsson, P.: Relaxation times and rheology in dense athermal suspensions. Phys. Rev. E 91, 062209 (2015). https://doi.org/10.1103/PhysRevE.91.062209
Olsson, P., Teitel, S.: Critical scaling of shear viscosity at the jamming transition. Phys. Rev. Lett. 99(17), 1–5 (2007). https://doi.org/10.1103/PhysRevLett.99.178001. (arXiv:0704.1806)
Otsuki, M., Hayakawa, H.: Critical behaviors of sheared frictionless granular materials near the jamming transition. Phys. Rev. E 80(1), 011308 (2009). https://doi.org/10.1103/PhysRevE.80.011308
Rintoul, M., Torquato, S.: Metastability and crystallization in hard-sphere systems. Phys. Rev. Lett. 77(20), 4198–4201 (1996) http://www.ncbi.nlm.nih.gov/pubmed/10062473
Rojas, E., Trulsson, M., Andreotti, B., Clément, E., Soto, R.: Relaxation processes after instantaneous shear-rate reversal in a dense granular flow. Epl (2015). https://doi.org/10.1209/0295-5075/109/64002
Luding, S.: Towards dense, realistic granular media in 2D. Nonlinearity 22(12), R101–R146 (2009). https://doi.org/10.1088/0951-7715/22/12/R01
Seto, R., Singh, A., Denn, C.M.B., Morris, J.: Shear jamming and fragility in dense suspensions. Granular Matter 21, 82 (2019). https://doi.org/10.1007/s10035-019-0931-5
Silbert, L.E.: Jamming of frictional spheres and random loose packing. Soft Matter 6(13), 2918 (2010) https://doi.org/10.1039/c001973a, http://xlink.rsc.org/?DOI=c001973a
Song, C., Wang, P., Makse, H.A.: A phase diagram for jammed matter: supplementary information. Nature pp. 1–27, (2008) https://doi.org/10.1038/nature06981
Sun, J., Sundaresan, S.: A constitutive model with microstructure evolution for flow of rate-independent granular materials. J. Fluid Mech. 682, 590–616 (2011) https://doi.org/10.1017/jfm.2011.251, http://www.journals.cambridge.org/abstract_S0022112011002515
Thornton, A., Weinhart, T., Luding, S., Bokhove, O.: Modeling of particle size segregation: calibration using the discrete particle method. Int. J. Mod. Phys. C 23(08), 1240014 (2012). https://doi.org/10.1142/S0129183112400141
To, K., Lai, P.Y., Pak, H.: Jamming of granular flow in a two-dimensional hopper. Phys. Rev. Lett. 86, 71–74 (2001)
Tordesillas, A., Muthuswamy, M., Walsh, S.D.C.: Mesoscale measures of nonaffine deformation in dense granualr assemblies. J. Eng. Mech. 134(12), 1095–1113 (2008). https://doi.org/10.1061/(ASCE)0733-9399(2008)134:12(1095)
Vescovi, D., Luding, S.: Merging fluid and solid granular behavior. Soft Matter 12, 8616–8628 (2016). https://doi.org/10.1039/c6sm01444e. (arXiv:1609.07414)
Vescovi, D., Berzi, D., di Prisco, C.: Fluid-solid transition in unsteady, homogeneous, granular shear flows. Granular Matter 20(2), 27 (2018). https://doi.org/10.1007/s10035-018-0797-y. (arXiv:1707.03322)
Vescovi, D., Redaelli, I., di Prisco, C.: Modelling phase transition in granular materials: from discontinuum to continuum. Int. J. Solids Struct. (2020 submitted)
Weinhart, T., Thornton, A.R., Luding, S., Bokhove, O.: From discrete particles to continuum fields near a boundary. Granular Matter 14(2), 289–294 (2012) https://doi.org/10.1007/s10035-012-0317-4, http://www.springerlink.com/index/10.1007/s10035-012-0317-4
Weinhart, T., Hartkamp, R., Thornton, A.R., Luding, S.: Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface. Phys. Fluids 25(7), 070605 (2013). https://doi.org/10.1063/1.4812809
Zhao, Y., Barés, J., Zheng, H., Socolar, J.E.S., Behringer, R.P.: Shear jammed, fragile, and steady states in homogeneously strained granular materials. Phys. Rev. Lett. 158001, 1–5 (2019). https://doi.org/10.1103/PhysRevLett.123.158001. (arXiv:1904.10051)
Zheng, H., Wang, D., Barés, J., Behringer, R.P.: Sinking in a bed of grains activated by shearing. Phys. Rev. E 98(1), 010191(R) (2018). https://doi.org/10.1103/PhysRevE.98.010901