Skip to main content
Erschienen in: Acta Mechanica 9/2019

02.07.2019 | Original Paper

Coarse graining for granular materials: micro-polar balances

verfasst von: Riccardo Artoni, Patrick Richard

Erschienen in: Acta Mechanica | Ausgabe 9/2019

Einloggen, um Zugang zu erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this work, we extend a previously discussed averaging method for granular materials (Artoni and Richard in Phys Rev E 91:032202, 2015), by considering average balance equations related to particle rotations (the micro-inertia, the angular momentum and the rotational energy balances). The method is based on a fluctuation decomposition taking into account velocity gradients and on a local homogeneity assumption. After having developed the coarse-grained balances, we study the simplifications related to some classes of simple flows and particularly assess the relation between the micro-inertia balance and the average orientation of particles in a simple shear flow.
Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat Aranson, I.S., Tsimring, L.S.: Continuum description of avalanches in granular media. Phys. Rev. E 64, 020301 (2001)CrossRef Aranson, I.S., Tsimring, L.S.: Continuum description of avalanches in granular media. Phys. Rev. E 64, 020301 (2001)CrossRef
2.
Zurück zum Zitat Artoni, R., Richard, P.: Average balance equations, scale dependence, and energy cascade for granular materials. Phys. Rev. E 91, 032202 (2015)MathSciNetCrossRef Artoni, R., Richard, P.: Average balance equations, scale dependence, and energy cascade for granular materials. Phys. Rev. E 91, 032202 (2015)MathSciNetCrossRef
3.
Zurück zum Zitat Artoni, R., Richard, P.: Effective wall friction in wall-bounded 3D dense granular flows. Phys. Rev. Lett. 115, 158001 (2015)CrossRef Artoni, R., Richard, P.: Effective wall friction in wall-bounded 3D dense granular flows. Phys. Rev. Lett. 115, 158001 (2015)CrossRef
4.
Zurück zum Zitat Artoni, R., Richard, P.: Torsional shear flow of granular materials: shear localization and minimum energy principle. Comput. Part. Mech. 5(1), 3–12 (2018)CrossRef Artoni, R., Richard, P.: Torsional shear flow of granular materials: shear localization and minimum energy principle. Comput. Part. Mech. 5(1), 3–12 (2018)CrossRef
5.
Zurück zum Zitat Artoni, R., Santomaso, A., Canu, P.: Hysteresis in a hydrodynamic model of dense granular flows. Phys. Rev. E 83, 051304 (2011)CrossRefMATH Artoni, R., Santomaso, A., Canu, P.: Hysteresis in a hydrodynamic model of dense granular flows. Phys. Rev. E 83, 051304 (2011)CrossRefMATH
6.
Zurück zum Zitat Artoni, R., Soligo, A., Paul, J.M., Richard, P.: Shear localization and wall friction in confined dense granular flows. J. Fluid Mech. 849, 395–418 (2018)MathSciNetCrossRefMATH Artoni, R., Soligo, A., Paul, J.M., Richard, P.: Shear localization and wall friction in confined dense granular flows. J. Fluid Mech. 849, 395–418 (2018)MathSciNetCrossRefMATH
8.
Zurück zum Zitat Baran, O., Ertaş, D., Halsey, T.C., Grest, G.S., Lechman, J.B.: Velocity correlations in dense gravity-driven granular chute flow. Phys. Rev. E 74, 051302 (2006)CrossRef Baran, O., Ertaş, D., Halsey, T.C., Grest, G.S., Lechman, J.B.: Velocity correlations in dense gravity-driven granular chute flow. Phys. Rev. E 74, 051302 (2006)CrossRef
9.
Zurück zum Zitat Bonamy, D., Daviaud, F., Laurent, L., Bonetti, M., Bouchaud, J.P.: Multiscale clustering in granular surface flows. Phys. Rev. Lett. 89, 034301 (2002)CrossRef Bonamy, D., Daviaud, F., Laurent, L., Bonetti, M., Bouchaud, J.P.: Multiscale clustering in granular surface flows. Phys. Rev. Lett. 89, 034301 (2002)CrossRef
10.
Zurück zum Zitat Börzsönyi, T., Szabó, B., Törös, G., Wegner, S., Török, J., Somfai, E., Bien, T., Stannarius, R.: Orientational order and alignment of elongated particles induced by shear. Phys. Rev. Lett. 108, 228302 (2012)CrossRef Börzsönyi, T., Szabó, B., Törös, G., Wegner, S., Török, J., Somfai, E., Bien, T., Stannarius, R.: Orientational order and alignment of elongated particles induced by shear. Phys. Rev. Lett. 108, 228302 (2012)CrossRef
11.
Zurück zum Zitat Bouzid, M., Trulsson, M., Claudin, P., Clément, E., Andreotti, B.: Nonlocal rheology of granular flows across yield conditions. Phys. Rev. Lett. 111, 238301 (2013)CrossRef Bouzid, M., Trulsson, M., Claudin, P., Clément, E., Andreotti, B.: Nonlocal rheology of granular flows across yield conditions. Phys. Rev. Lett. 111, 238301 (2013)CrossRef
12.
Zurück zum Zitat Bouzid, M., Trulsson, M., Claudin, P., Clément, E., Andreotti, B.: Microrheology to probe non-local effects in dense granular flows. EPL (Europhys. Lett.) 109(2), 24002 (2015)CrossRef Bouzid, M., Trulsson, M., Claudin, P., Clément, E., Andreotti, B.: Microrheology to probe non-local effects in dense granular flows. EPL (Europhys. Lett.) 109(2), 24002 (2015)CrossRef
13.
Zurück zum Zitat Brodu, N., Delannay, R., Valance, A., Richard, P.: New patterns in high-speed granular flows. J. Fluid Mech. 769, 218–228 (2015)MathSciNetCrossRef Brodu, N., Delannay, R., Valance, A., Richard, P.: New patterns in high-speed granular flows. J. Fluid Mech. 769, 218–228 (2015)MathSciNetCrossRef
14.
Zurück zum Zitat Brodu, N., Richard, P., Delannay, R.: Shallow granular flows down flat frictional channels: steady flows and longitudinal vortices. Phys. Rev. E 87, 022202 (2013)CrossRef Brodu, N., Richard, P., Delannay, R.: Shallow granular flows down flat frictional channels: steady flows and longitudinal vortices. Phys. Rev. E 87, 022202 (2013)CrossRef
15.
Zurück zum Zitat Börzsönyi, T., Somfai, E., Szabó, B., Wegner, S., Mier, P., Rose, G., Stannarius, R.: Packing, alignment and flow of shape-anisotropic grains in a 3D silo experiment. New J. Phys. 18(9), 093017 (2016)CrossRef Börzsönyi, T., Somfai, E., Szabó, B., Wegner, S., Mier, P., Rose, G., Stannarius, R.: Packing, alignment and flow of shape-anisotropic grains in a 3D silo experiment. New J. Phys. 18(9), 093017 (2016)CrossRef
16.
Zurück zum Zitat Campbell, C.S.: Elastic granular flows of ellipsoidal particles. Phys. Fluids 23(1), 013306 (2011)CrossRef Campbell, C.S.: Elastic granular flows of ellipsoidal particles. Phys. Fluids 23(1), 013306 (2011)CrossRef
17.
Zurück zum Zitat Chen, K.C., Lan, J.Y.: Micromorphic modeling of granular dynamics. Int. J. Solids Struct. 46(6), 1554–1563 (2009)CrossRefMATH Chen, K.C., Lan, J.Y.: Micromorphic modeling of granular dynamics. Int. J. Solids Struct. 46(6), 1554–1563 (2009)CrossRefMATH
18.
Zurück zum Zitat Delannay, R., Louge, M., Richard, P., Taberlet, N., Valance, A.: Towards a theoretical picture of dense granular flows down inclines. Nat. Mater. 6, 99–108 (2007)CrossRef Delannay, R., Louge, M., Richard, P., Taberlet, N., Valance, A.: Towards a theoretical picture of dense granular flows down inclines. Nat. Mater. 6, 99–108 (2007)CrossRef
19.
Zurück zum Zitat Eringen, A.: Microcontinuum Field Theories: I. Foundations and Solids. Springer, New York (2012)MATH Eringen, A.: Microcontinuum Field Theories: I. Foundations and Solids. Springer, New York (2012)MATH
20.
Zurück zum Zitat Eringen, A.C.: Nonlocal Continuum Field Theories. Springer, Berlin (2002)MATH Eringen, A.C.: Nonlocal Continuum Field Theories. Springer, Berlin (2002)MATH
21.
Zurück zum Zitat GDR-MiDi: On dense granular flows. Eur. Phys. J. E 14(4), 341–365 (2004)CrossRef GDR-MiDi: On dense granular flows. Eur. Phys. J. E 14(4), 341–365 (2004)CrossRef
22.
Zurück zum Zitat Henann, D.L., Kamrin, K.: Continuum modeling of secondary rheology in dense granular materials. Phys. Rev. Lett. 113, 178001 (2014)CrossRef Henann, D.L., Kamrin, K.: Continuum modeling of secondary rheology in dense granular materials. Phys. Rev. Lett. 113, 178001 (2014)CrossRef
23.
Zurück zum Zitat Hidalgo, R.C., Szabó, B., Gillemot, K., Börzsönyi, T., Weinhart, T.: Rheological response of nonspherical granular flows down an incline. Phys. Rev. Fluids 3, 074301 (2018)CrossRef Hidalgo, R.C., Szabó, B., Gillemot, K., Börzsönyi, T., Weinhart, T.: Rheological response of nonspherical granular flows down an incline. Phys. Rev. Fluids 3, 074301 (2018)CrossRef
25.
Zurück zum Zitat Jeffery, G.B.: The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 102(715), 161–179 (1922)CrossRefMATH Jeffery, G.B.: The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 102(715), 161–179 (1922)CrossRefMATH
26.
Zurück zum Zitat Jenkins, J., Berzi, D.: Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory. Granul. Matter 12, 151–158 (2010)CrossRefMATH Jenkins, J., Berzi, D.: Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory. Granul. Matter 12, 151–158 (2010)CrossRefMATH
27.
Zurück zum Zitat Kamrin, K., Henann, D.L.: Nonlocal modeling of granular flows down inclines. Soft Matter 11, 179–185 (2015)CrossRef Kamrin, K., Henann, D.L.: Nonlocal modeling of granular flows down inclines. Soft Matter 11, 179–185 (2015)CrossRef
28.
Zurück zum Zitat Kamrin, K., Koval, G.: Nonlocal constitutive relation for steady granular flow. Phys. Rev. Lett. 108, 178301 (2012)CrossRef Kamrin, K., Koval, G.: Nonlocal constitutive relation for steady granular flow. Phys. Rev. Lett. 108, 178301 (2012)CrossRef
29.
Zurück zum Zitat Lee, K.L., Yang, F.L.: Relaxation-type nonlocal inertial-number rheology for dry granular flows. Phys. Rev. E 96, 062909 (2017)CrossRef Lee, K.L., Yang, F.L.: Relaxation-type nonlocal inertial-number rheology for dry granular flows. Phys. Rev. E 96, 062909 (2017)CrossRef
30.
Zurück zum Zitat Lumay, G., Vandewalle, N.: Compaction of anisotropic granular materials: experiments and simulations. Phys. Rev. E 70, 051314 (2004)CrossRef Lumay, G., Vandewalle, N.: Compaction of anisotropic granular materials: experiments and simulations. Phys. Rev. E 70, 051314 (2004)CrossRef
31.
Zurück zum Zitat Mohan, L.S., Nott, P.R., Rao, K.K.: A frictional cosserat model for the flow of granular materials through a vertical channel. Acta Mech. 138(1), 75–96 (1999)CrossRefMATH Mohan, L.S., Nott, P.R., Rao, K.K.: A frictional cosserat model for the flow of granular materials through a vertical channel. Acta Mech. 138(1), 75–96 (1999)CrossRefMATH
32.
Zurück zum Zitat Moreau, J.J.: Unilateral Contact and Dry Friction in Finite Freedom Dynamics, pp. 1–82. Springer Vienna, Vienna (1988)MATH Moreau, J.J.: Unilateral Contact and Dry Friction in Finite Freedom Dynamics, pp. 1–82. Springer Vienna, Vienna (1988)MATH
33.
Zurück zum Zitat Nadler, B., Guillard, F., Einav, I.: Kinematic model of transient shape-induced anisotropy in dense granular flow. Phys. Rev. Lett. 120, 198003 (2018)CrossRef Nadler, B., Guillard, F., Einav, I.: Kinematic model of transient shape-induced anisotropy in dense granular flow. Phys. Rev. Lett. 120, 198003 (2018)CrossRef
34.
Zurück zum Zitat Nagy, D.B., Claudin, P., Börzsönyi, T., Somfai, E.: Rheology of dense granular flows for elongated particles. Phys. Rev. E 96(6), 062903 (2017)CrossRef Nagy, D.B., Claudin, P., Börzsönyi, T., Somfai, E.: Rheology of dense granular flows for elongated particles. Phys. Rev. E 96(6), 062903 (2017)CrossRef
35.
Zurück zum Zitat Pouliquen, O.: Velocity correlations in dense granular flows. Phys. Rev. Lett. 93, 248001 (2004)CrossRef Pouliquen, O.: Velocity correlations in dense granular flows. Phys. Rev. Lett. 93, 248001 (2004)CrossRef
36.
Zurück zum Zitat Pouliquen, O., Forterre, Y.: A non-local rheology for dense granular flows. Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 367(1909), 5091–5107 (2009)CrossRefMATH Pouliquen, O., Forterre, Y.: A non-local rheology for dense granular flows. Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 367(1909), 5091–5107 (2009)CrossRefMATH
37.
Zurück zum Zitat Radjai, F., Jean, M., Moreau, J.J., Roux, S.: Force distributions in dense two-dimensional granular systems. Phys. Rev. Lett. 77, 274–277 (1996)CrossRef Radjai, F., Jean, M., Moreau, J.J., Roux, S.: Force distributions in dense two-dimensional granular systems. Phys. Rev. Lett. 77, 274–277 (1996)CrossRef
38.
Zurück zum Zitat Renouf, M., Dubois, F., Alart, P.: A parallel version of the non smooth contact dynamics algorithm applied to the simulation of granular media. J. Comput. Appl. Math. 168(1–2), 375–382 (2004). Selected Papers from the Second International Conference on Advanced Computational Methods in Engineering (ACOMEN 2002)MathSciNetCrossRefMATH Renouf, M., Dubois, F., Alart, P.: A parallel version of the non smooth contact dynamics algorithm applied to the simulation of granular media. J. Comput. Appl. Math. 168(1–2), 375–382 (2004). Selected Papers from the Second International Conference on Advanced Computational Methods in Engineering (ACOMEN 2002)MathSciNetCrossRefMATH
39.
Zurück zum Zitat Ribière, P., Richard, P., Bideau, D., Delannay, R.: Experimental compaction of anisotropic granular media. Eur. Phys. J. E 16(4), 415–420 (2005)CrossRef Ribière, P., Richard, P., Bideau, D., Delannay, R.: Experimental compaction of anisotropic granular media. Eur. Phys. J. E 16(4), 415–420 (2005)CrossRef
40.
Zurück zum Zitat Ribière, P., Richard, P., Delannay, R., Bideau, D.: Importance of convection in the compaction mechanisms of anisotropic granular media. Phys. Rev. E 71, 011304 (2005)CrossRef Ribière, P., Richard, P., Delannay, R., Bideau, D.: Importance of convection in the compaction mechanisms of anisotropic granular media. Phys. Rev. E 71, 011304 (2005)CrossRef
41.
Zurück zum Zitat Staron, L.: Correlated motion in the bulk of dense granular flows. Phys. Rev. E 77, 051304 (2008)CrossRef Staron, L.: Correlated motion in the bulk of dense granular flows. Phys. Rev. E 77, 051304 (2008)CrossRef
42.
Zurück zum Zitat Villarruel, F.X., Lauderdale, B.E., Mueth, D.M., Jaeger, H.M.: Compaction of rods: relaxation and ordering in vibrated, anisotropic granular material. Phys. Rev. E 61, 6914–6921 (2000)CrossRef Villarruel, F.X., Lauderdale, B.E., Mueth, D.M., Jaeger, H.M.: Compaction of rods: relaxation and ordering in vibrated, anisotropic granular material. Phys. Rev. E 61, 6914–6921 (2000)CrossRef
Metadaten
Titel
Coarse graining for granular materials: micro-polar balances
verfasst von
Riccardo Artoni
Patrick Richard
Publikationsdatum
02.07.2019
Verlag
Springer Vienna
Erschienen in
Acta Mechanica / Ausgabe 9/2019
Print ISSN: 0001-5970
Elektronische ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-019-02440-9

Weitere Artikel der Ausgabe 9/2019

Acta Mechanica 9/2019 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.