Abstract
Multiscale modeling and computation of confined granular media opens a novel way of simulating and understanding the complicated behavior of granular structures. Phenomenological continuum approaches are often not capable of reproducing distinguishing features of granular media, like, e.g., the breaking and forming of particle contacts. Alternatively, a multiscale homogenization procedure, based on a discrete element method, allows to capture such distinguishing features. The present manuscript deals with the variationally based computational homogenization and simulation of granular media, whereby the macroscopic impact of inter-particle friction defines the overall focal point. To bridge the gap between both scales, we apply the concept of a representative volume element, essentially linking both scales through variational considerations. As the beneficial outcome of the variational approach, the Piola stress is derived from the overall macroscopic energy density.
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
Comi, C. and Perego, U., A unified approach for variationally consistent finite elements in elastoplasticity. Comput. Meth. Appl. Mech. Eng 121, 1995, 323–344.
Cundall, P.A. and Strack, O.D.L., The distinct element method as a tool for research in granular media. Tech. Rep., Report to the National Science Foundation Concerning NSF Grant ENG76-20711, Parts I, II, 1978.
Cundall, P.A. and Strack, O.D.L., A discrete numerical model for granular assemblies. Géotechnique 29(1), 1979, 47–65.
Duran, J., Sands, Powders, and Grains. Springer, 1999.
Meier, H.A., Kuhl, E. and Steinmann, P., A note on the generation of periodic granular microstructures based on grain size distributions. Int. J. Numer. Anal. Meth. Geomech 32(5), 2008, 509–522.
Meier, H.A., Steinmann, P. and Kuhl, E., Towards multiscale computation of confined granular media – Contact forces, stresses and tangent operators. Tech. Mech 28, 2008, 32–42.
Miehe, C., Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation. Int. J. Numer. Meth. Eng 55(11), 2002, 1285–1322.
Miehe, C., Schotte, J. and Lambrecht, M., Homogenization of inelastic solid materials at finite strains based on incremental minimization principles. Application to the texture analysis of polycrystals. J. Mech. Phys. Solid 50(10), 2002, 2123–2167.
Mindlin, D., Compliance of elastic bodies in contact. ASME J. Appl. Mech 16(3), 1949, 259–268.
Ortiz, M. and Pandolfi, A., A variational Cam-clay theory of plasticity. Comput. Meth. Appl. Mech. Eng 193, 2004, 2645–2666.
Ortiz, M. and Stainier, L., The variational formulation of viscoplastic constitutive updates. Comput. Meth. Appl. Mech. Eng 171, 1999, 419–444.
Schröder, J., Homogenisierungsmethoden der nichtlinearen Kontinuumsmechanik unter Beachtung von Stabilitätsproblemen. Habilitation, Bericht Nr. I-7 des Instituts für Mechanik (Bauwesen) Lehrstuhl I, Universität Stuttgart, 2000.
Simo, J.C. and Hughes, T.J.R., Computational Inelasticity Springer-Verlag, 2000.
Taylor, G.I., Plastic strain in metals. J. Inst. Met 62, 1938, 307–324.
Vu-Quoc, L. and Zhang, X., An accurate and efficient tangential force-displacement model for elastic frictional contact in particle-flow simulations. Mech. Mater 31, 1999, 235–269.
Vu-Quoc, L., Zhang, X. and Walton, O.R., A 3-d discrete-element method for dry granular flows of ellipsoidal particles. Mech. Mater 31, 2000, 483–528.
Walton, O.R., Numerical simulation of inclined chute flows of monodisperse inelastic, frictional spheres. Mech. Mater 16, 1993, 239–247.
Walton, O.R. and Braun, R.L., Viscosity granular-temperature and stress calculations for shearing assemblies of inelastic frictional disks. J. Rheol 30, 1986, 949–980.
Zohdi, T.I., Homogenization methods and multiscale modeling: Linear problems. In Encyclopedia of Computational Mechanics E. Stein, R. de Borst and T. Hughes (Eds.), Wiley, 2004.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this paper
Cite this paper
Meier, H.A., Steinmann, P., Kuhl, E. (2010). Computational Homogenization of Confined Frictional Granular Matter. In: Hackl, K. (eds) IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials. IUTAM Bookseries, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9195-6_12
Download citation
DOI: https://doi.org/10.1007/978-90-481-9195-6_12
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-9194-9
Online ISBN: 978-90-481-9195-6
eBook Packages: EngineeringEngineering (R0)