Agglomerations of granules are described as continuous complex bodies in which the generic material element is an open system made of a family of granules. Inertia is neglected while migration of granules is allowed: an evolution equation for the local numerosity of granules is derived in the present setting. In a reduced framework in which the generic material element coincides with a single granule, the balance of interactions governing the motion of a single granule during segregation is also discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aronson, I.S., Tsimring, L.S.: Patterns and collective behavior in granular media: theoretical concepts. Rev. Modern Phys., 78, 641–692 (2006)
Bobylev, A.V., Carrillo, J.A., Gamba, I.M.: On some properties of kinetic and hydrodynamic equations for inelastic interactions. J. Stat. Phys., 98, 743–773 (2000)
Bobylev, A., Cercignani, C., Toscani, G.: Proof of an asymptotic property of the Boltzmann for granular materials. J. Stat. Phys., 111, 403–416 (2003)
Capriz, G.: Continua with latent microstructure. Arch. Rational Mech. Anal., 90, 43–56 (1985)
Capriz, G.: Continua with Microstructure. Springer Tracts in Natural Philosophy. Springer-Verlag, Berlin Heidelberg New York, 35 (1989)
Capriz, G.: Elementary preamble to a theory of granular gases. Rend. Sem. Mat. Univ. Padova, 110, 179–198 (2003)
Capriz, G.: Pseudofluids. In: Capriz, G., Mariano, P.M. (eds) Material Substructures in Complex Bodies: from Atomic Level to Continuum. Elsevier Science B.V., Amsterdam, 238–261 (2007)
Cercignani, C.: Microscopic foundations of the mechanics of gases and granular materials. In: Capriz, G., Mariano, P.M. (eds) Material Substructures in Complex Bodies: from Atomic Level to Continuum. Elsevier Science B.V., Amsterdam, 63–79 (2007)
Edwards, S.F., Grinev, D.V.: The statistical–mechanical theory of stress transmission in granular matter. Physica A, 263, 545–553 (1999)
Ericksen, J.L.: Kinematics of macromolecules. Arch. Rational Mech. Anal., 9, 1–8 (1962)
Gamba, I.M., Panferov, V., Villani, C.: On the Boltzmann equation for diffusively excited granular media. Comm. Math. Phys., 246, 503–541 (2004)
Goddard, J.D.: Material instability in comlex fluids. Ann. Rev. Fluid Mech., 35, 113–133 (2003)
Gurtin, M.E.: Generalized Ginzburg–Landau and Cahn–Hilliard equations based on a microforce balance. Physica D, 92, 178–192 (1996)
Jaeger, H.M., Nagel, S.R., Behringer, R.P.: Granular solids, liquid and gases. Rev. Modern Phys., 68, 1259–1273 (1996)
Kadanoff, L.P.: Built upon sand: Theoretical ideas inspired by granular flows. Rev. Modern Phys., 71, 435–444 (1999)
Krimer, D.O., Pfitzener, M., Bräuer, K., Jiang, Y., Liu, M.: Granular elasticity: General considerations and the stress dip in sand piles. Phys. Rev. E, 74, 061310-1-10 (2006)
Mariano, P.M.: Multifield theories in mechanics of solids. Adv. Appl. Mech., 38, 1–93 (2002)
Mariano, P.M.: Migration of substructures in complex fluids. J. Phys. A, 38, 6823–6839 (2005)
Mariano, P.M.: Continua with spin structure. In: Capriz, G., Mariano, P.M. (eds) Material Substructures in Complex Bodies: from Atomic Level to Continuum. Elsevier Science B.V., Amsterdam, 314–334 (2007)
Mariano, P.M., Stazi, F.L.: Computational aspects of the mechanics of complex bodies. Arch. Comp. Meth. Eng., 12, 391–478 (2005)
Mitarai, N., Hayakawa, H., Nakanishi, H.: Collisional granular flow as a micropolar fluid. Phys. Rev. Lett., 88, 174301-1-4 (2002)
Šilhavý, M.: The Mechanics and Thermodynamics of Continuous Media. Springer–Verlag, Berlin (1997)
Truesdell, C.A., Noll, W.: The Non-Linear Field Theories of Mechanics. Third edition, Springer–Verlag, Berlin (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mariano, P.M. (2008). Slow Motion in Granular Matter. In: Capriz, G., Mariano, P.M., Giovine, P. (eds) Mathematical Models of Granular Matter. Lecture Notes in Mathematics, vol 1937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78277-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-78277-3_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78276-6
Online ISBN: 978-3-540-78277-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)