Abstract
Particulate systems like powders, soil or granular matter are discrete, disordered systems displaying dynamic and static, fluid - and solid-like states. The transients between fluid - and solid-like behavior can be intermittent and sometimes both states coexist in steady-state. Bridging the gap between the particulate, microscopic picture (velocities, forces) on the particle scale and their continuum description (strain and stress) via a so-called micro-macro transition is the goal of this paper. The generalized local constitutive relation for the stress in critical state granular flows involves not only density and strain rate but also the jamming-density and the granular temperature.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Using either one of the correction terms alone, without the other, leads to slightly different coefficients in Eqs. (1) and (2), e.g., when the I-dependence is neglected for the case of very small gravity and thus very small confining stress, one observes a slightly different \( \mu_{0} = 0.17 \) due to the considerable inertial number at small p, see Eq. (14) and Fig. 5 in Ref. [5]. Thus, correction functions should always be applied together!
References
Luding, S.: The effect of friction on wide shear bands. Part. Sci. Tech. 26, 33–42 (2008)
Luding, S., Alonso-Marroquin, F.: The critical-state yield stress (termination locus) of adhesive powders from a single experiment. Granular Matter 13, 109–119 (2011)
Weinhart, T., Hartkamp, R., Thornton, A.R., Luding, S.: Coarse-grained local and objective continuum description of 3D granular flows down an inclined surface. Phys. Fluids 25, 070605 (2013)
Hartkamp, R., Todd, B., Luding, S.: A constitutive framework for the non-Newtonian pressure tensor of a simple fluid under planar flows. J. Chem. Phys. 138, 244508 (2013)
Singh, A., Saitoh, K., Magnanimo, V., Luding, S.: Role of gravity or confining pressure and contact stiffness in granular rheology. New J. Phys. 17, 043028 (2015)
Singh, A., Magnanimo, V., Saitoh, K., Luding, S.: Effect of cohesion on shear banding in quasi-static granular material. Phys. Rev. E 90(2), 022202 (2014)
Vescovi, D., Luding, S.: Merging fluid & solid granular behavior. Soft Matter 12, 8616 (2016)
Roy, S., Singh, A., Luding, S., Weinhart, T.: Micro-macro transition and simplified contact models for wet granular materials. Comp. Part. Mech. 3(4), 449–462 (2016)
Roy, S., Luding, S., Weinhart, T.: A general(ized) local rheology for wet granular materials. New J. Phys. 19, 043014 (2017)
Göncü, F., Luding, S.: Effect of particle friction and polydispersity on the macroscopic stress-strain relations of granular materials. Acta Geotech. 8, 629–643 (2013)
Kumar, N., Luding, S., Magnanimo, V.: Macroscopic model with anisotropy based on micro-macro informations. Acta Mech. 225(8), 2319–2343 (2014)
Goldhirsch, I.: Stress, stress asymmetry and couple stress: from discrete particles to continuous fields. Granular Matter 12, 239–252 (2010)
Weinhart, T., Thornton, A.R., Luding, S., Bokhove, O.: From discrete particles to continuum fields near a boundary. Granular Matter 14, 289–294 (2012)
Midi, G.D.R.: On dense granular flows. Eur. Phys. J. E 14, 367–371 (2004)
Ries, A., Wolf, D.E., Unger, T.: Shear zones in granular media: three-dimensional contact dynamics simulations. Phys. Rev. E 76, 051301 (2007)
Nguyen, V.B., Darnige, T., Bruand, A., Clément, E.: Creep and fluidity of a real granular packing near jamming. Phys. Rev. Lett. 107, 138303 (2011)
Kamrin, K., Koval, G.: Nonlocal constitutive relation for steady granular flow. Phys. Rev. Lett. 108, 178301 (2012)
Hennan, D.L., Kamrin, K.: A predictive, size-dependent continuum model for dense granular flows. Proc. Natl. Acad. Sci. USA 110, 6730–6735 (2013)
Shi, H., Luding, S., Magnanimo, V.: Limestone powders yielding and steady state resistance under shearing with different testers. In: Mallick, S.S. (ed.) Proceedings of PGBSIA 2016, 1–3 December 2016
Shi, H., et al.: Effect of particle size and cohesion on powder yielding and flow. KONA 2018014 (2017)
Göncü, F., Duran, O., Luding, S.: Constitutive relations for the isotropic deformation of frictionless packings of polydisperse spheres. C. R. Mecanique 338(10–11), 570–586 (2010)
Luding, S.: Granular matter: so much for the jamming point. Nat. Phys. 12, 531 (2016)
Kumar, N., Luding, S.: Memory of jamming – multiscale models for soft and granular matter. Granular Matter 18, 58 (2016)
Pons, A., Darnige, T., Crassous, J., Clement, E., Amon, A.: Spatial repartition of local plastic processes in different creep regimes in a granular material. EPL 113(2), 28001 (2016)
Koval, G., Roux, J.N., Corfdir, A., Chevoir, F.: Annular shear of cohesionless granular materials: from the inertial to quasistatic regime. Phys. Rev. E 79, 021306 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Luding, S. (2019). Constitutive Relations from Particle Simulations. In: Wu, W. (eds) Desiderata Geotechnica. Springer Series in Geomechanics and Geoengineering. Springer, Cham. https://doi.org/10.1007/978-3-030-14987-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-14987-1_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-14986-4
Online ISBN: 978-3-030-14987-1
eBook Packages: EngineeringEngineering (R0)