Strain in Granular Media: Probabilistic Approach to Dirichlet Tessellation
Publication: Journal of Engineering Mechanics
Volume 143, Issue 1
Abstract
Deformations in granular media are described by using a representation of the microkinematics of the underlying assembly through Dirichlet tessellation. Based on a probabilistic analysis of topological rearrangements induced by evolving microstructures in the assembly, homogenization is carried out within a multiscale approach—from deforming individual cells to cell network level—to eventually describe global strain in the granular ensemble. In contrast to other models in the literature, tessellation network properties are directly linked to physical microstructural characteristics of the granular assembly through local coordination number and fabric anisotropy. Because these microstructural variables dictate both strain and stress in a granular medium, this provides a route to establish a stress-strain relationship as an ultimate goal. In this paper, detailed attention is paid to the description of evolving fabric anisotropy and coordination number as a combination of dissipative microstructural rearrangements and nondissipative contact losses and gains. By introducing these two mechanisms, peak response of a dense assembly can be modeled as well as asymptotic behavior such as critical state as commonly known in soil mechanics. Model estimates of the response of granular assemblies compare very well with simulation results obtained from discrete element modeling (DEM) computations. Verification was conducted for a wide range of initial density for shearing under both constant mean stress and biaxial compression.
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Acknowledgments
This work is supported by the Natural Science and Engineering Research Council of Canada and Foundation Computer Modeling Group within the framework of a Government-Industry Partnership (NSERC-CRD) Grant toward the fundamental understanding of complex multiphasic granular media.
References
Antony, S., and Kruyt, N. (2009). “Role of interparticle friction and particle-scale elasticity in the shear-strength mechanism of three-dimensional granular media.” Phys. Rev. E, 79(3), 031308.
Azéma, E., Radjai, F., and Saussine, G. (2009). “Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles.” Mech. Mater., 41(6), 729–741.
Bagi, K. (1996). “Stress and strain in granular assemblies.” Mech. Mater., 22(3), 165–177.
Bagi, K. (2006). “Analysis of microstructural strain tensors for granular assemblies.” Int. J. Solids Struct., 43(10), 3166–3184.
Bathurst, R. J., and Rothenburg, L. (1990). “Observations on stress-force-fabric relationships in idealized granular materials.” Mech. Mater., 9(1), 65–80.
Cambou, B., Chaze, M., and Dedecker, F. (2000). “Change of scale in granular materials.” Eur. J. Mech. -A/Solids, 19(6), 999–1014.
Desrues, J., Besuelle, P., and Lewis, H. (2007). “Strain localization in geomaterials.” Geol. Soc. Spec. Publ., 289(1), 47–73.
El Shamy, U., and Denissen, C. (2012). “Microscale energy dissipation mechanisms in cyclically-loaded granular soils.” Geotech. Geol. Eng., 30(2), 343–361.
Goddard, J. (2008). “From granular matter to generalized continuum.” Mathematical models of granular matter, G. Capriz, P. M. Mariano, and P. Giovine, eds., Vol. 1937, Springer, Berlin, Heidelberg, 1–22.
Guo, N., and Zhao, J. (2014). “A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media.” Int. J. Numer. Methods Eng., 99(11), 789–818.
Kruyt, N. P. (2010). “Micromechanical study of plasticity of granular materials.” C. R. Mecanique, 338(10–11), 596–603.
Kruyt, N. P. (2012). “Micromechanical study of fabric evolution in quasi-static deformation of granular materials.” Mech. Mater., 44, 120–129.
Kruyt, N. P., and Rothenburg, L. (1996). “Micromechanical definition of the strain tensor for granular materials.” J. Appl. Mech., 63(3), 706–711.
Kuhn, M. R. (1997). “Deformation measures for granular materials.” Mechanics of Deformations and Flow of Particulate Materials, ASCE, New York, 91–104.
Kuhn, M. R. (2014). “Entropy model for granular materials at the critical state.” Engineering Mechanics Institute Conf., McMaster Univ., Hamilton, Canada.
Love, A. E. H. (1927). A treatise on the mathematical theory of elasticity, Cambridge University Press, New York.
Oda, M., and Iwashita, T. (1999). Mechanics of granular materials, an introduction, A.A. Balkema, Rotterdam, Netherlands.
Pouragha, M., Wan, R., and Hadda, N. (2014). “A microstructural plastic potential for granular materials.” Geomechanics from micro to macro, S. Kenichi, K. Kumar, G. Biscontin, and M. Kuo, eds., CRC, Boca Raton, FL, 661–665.
Powell, M. (1980). “Computer-simulated random packing of spheres.” Powder Technol., 25(1), 45–52.
Radjai, F., Delenne, J.-Y., Azéma, E., and Roux, S. (2012). “Fabric evolution and accessible geometrical states in granular materials.” Granul. Matter, 14(2), 259–264.
Rosato, A. D., and Yacoub, D. (2000). “Microstructure evolution in compacted granular beds.” Powder Technol., 109(1–3), 255–261.
Rothenburg, L., and Selvadurai, A. (1981). “A micromechanical definition of the Cauchy stress tensor for particulate media.” Proc., Int. Symp. on Mechanical Behaviour of Structured Media, A. Selvadurai, ed., Elsevier, Amsterdam, Netherlands, 469–486.
Satake, M. (1993). “New formulation of graph-theoretical approach in the mechanics of granular materials.” Mech. Mater., 16(1–2), 65–72.
Satake, M. (2004). “Tensorial form definitions of discrete-mechanical quantities for granular assemblies.” Int. J. Solids Struct., 41(21), 5775–5791.
Tordesillas, A., Lam, E., Metzger, P. T., Nakagawa, M., and Luding, S. (2009). “Hyperstaticity and loops in frictional granular packings.” Proc., 6th Int. Conf. on Micromechanics of Granular Media, M. Nakagawa and S. Luding, eds., American Institute of Physics, Melville, NY, 325–328.
Ueda, T., Matsushima, T., and Yamada, Y. (2012). “Micro structures of granular materials with various grain size distributions.” Powder Technol., 217, 533–539.
Wan, R., and Pouragha, M. (2015). “Fabric and connectivity as field descriptors for deformations in granular media.” Contin. Mech. Thermodyn., 27(1–2), 243–259.
Weber, J. (1966). “Recherches concernant les contraintes intergranulaires dans les milieux pulvérulents.” Bul. liaison P. et Ch, 2(20), 1–20 (in French).
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 1 • January 2017
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Apr 29, 2015
Accepted: Oct 12, 2015
Published online: Jan 5, 2016
Discussion open until: Jun 5, 2016
Published in print: Jan 1, 2017
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