Abstract
Soft-grain materials such as clays and other colloidal pastes share the common feature of being composed of grains that can undergo large deformations without rupture. For the simulation of such materials, we present two alternative methods: (1) an implicit formulation of the material point method (MPM), in which each grain is discretized as a collection of material points, and (2) the bonded particle model (BPM), in which each soft grain is modeled as an aggregate of rigid particles using the contact dynamics method. In the MPM, a linear elastic behavior is used for the grains. In order to allow the aggregates in the BPM to deform without breaking, we use long-range center-to-center attraction forces between the primary particles belonging to each grain together with steric repulsion at their contact points. We show that these interactions lead to a plastic behavior of the grains. Using both methods, we analyze the uniaxial compaction of 2D soft granular packings. This process is nonlinear and involves both grain rearrangements and large deformations. High packing fractions beyond the jamming state are reached as a result of grain shape change for both methods. We discuss the stress-strain and volume change behavior as well as the evolution of the connectivity of the grains. Similar textures are observed at large deformations although the BPM requires higher stress than the MPM to reach the same level of packing fraction.
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References
Agnolin, I., Roux, J.N.: Internal states of model isotropic granular packings. III. Elastic properties. Phys. Rev.E (Stat. Nonlinear Soft Matter Phys.) 76, 061304 (2007)
Antonyuk, S., Khanal, M., Tomas, J., Heinrich, S., Mörl, L.: Impact breakage of spherical granules: experimental study and dem simulations. Chem. Eng. Process. 45, 838–856 (2006)
Azéma, E., Radjai, F.: Stress-strain behavior and geometrical properties of packings of elongated particles. Phys. Rev. E 81, 051304 (2010)
Azéma, E., Radjai, F., Peyroux, R., Saussine, G.: Force transmission in a packing of pentagonal particles. Phys. Rev. E (Stat. Nonlinear Soft Matter Phys.) 76, 011301 (2007)
Bardenhagen, S., Brackbill, J., Sulsky, D.: The material-point method for granular materials. Comput. Methods Appl. Mech. Eng. 187, 529–541 (2000)
Bolton, M.D., N, Y., Cheng, P.: Micro- and macro-mechanical behaviour of dem crushable materials. Géotechnique 58, 471–480 (2008)
Bonnecaze, R., Cloitre, M.: Micromechanics of soft particle glasses. Adv. Polym. Sci. 236, 117–161 (2010)
Bratberg, I., Radjai, F., Hansen, A.: Dynamic rearrangements and packing regimes in randomly deposited two-dimensional granular beds. Phys. Rev. E 66(031), 031303 (2002)
Brogliato, B.: Nonsmooth Mechanics. Springer, London (1999)
Cummins, S., Brackbill, J.: An implicit particle-in-cell method for granular materials. J. Comput. Phys. 180, 506–548 (2002)
Estrada, N., Taboada, A., Radjai, F.: Shear strength and force transmission in granular media with rolling resistance. Phys. Rev. E 78, 021301 (2008)
Guilkey, J., Weiss, J.: Implicit time integration for the material point method: quantitative and algorithmic comparisons with the finite element method. Int. J. Numer. Methods Eng. 57, 1323–1338 (2003)
Huang, P., Zhang, X., Ma, S., Huang, X.: Contact algorithms for the material point method in impact and penetration simulation. Int. J. Numer. Methods Eng. 85, 498–517 (2011)
Ioannidou, K., Pellenq, R., Gado, E.D.: Controlling local packing and growth in calcium-silicate-hydrate gels. Soft Matter 10, 1121 (2014)
Israelachvili, J.N.: Intermolecular and Surface Forces. Academic Press, London (1993)
Jean, M.: Frictional contact in rigid or deformable bodies: numerical simulation of geomaterials. In: Salvadurai, A., Boulon, J. (eds.) Mechanics of Geomaterial Interfaces, pp. 463–486. Elsevier Science Publisher, Amsterdam (1995)
Kabla, A.: Collective cell migration: leadership, invasion and segregation. J. R. Soc. Interface 9, 3268–3278 (2012)
Lepesanta, P., Bohera, C., Berthierb, Y., Rézai-Ariaa, F.: A phenomenological model of the third body particles circulation in a high temperature contact. Wear 298–299, 66–79 (2013)
Liu, L., Kafui, K., Thornton, C.: Impact breakage of spherical, cuboidal and cylindrical agglomerates. Powder Technol. 199, 189–196 (2010)
Lorenzo, G., Zartizky, N., Califano, A.: Rheological analysis of emulsion-filled gels based on high acyl gellan gum. Food Hydrocoll. 30, 672–680 (2013)
Ma, G., Zhou, W., Chang, X.L.: Modeling the particle breakage of rockfill materials with the cohesive crack model. Comput. Geotech. 61, 132–143 (2014)
Makse, H.A., Johnson, D., Schwartz, L.: Packing of compressible granular materials. Phys. Rev. Lett. 84, 4160–4163 (2000)
Menut, P., Seiffert, S., Sprakelae, J., Weitz, D.: Does size matter? elasticity of compressed suspensions of colloidal- and granular-scale microgels. Soft Matter 8, 156–164 (2012)
Moreau, J.: Some numerical methods in multibody dynamics: application to granular materials. Eur. J. Mech. A. Solids 13, 93–114 (1994)
Moreau, J.J.: Evolution problem associated with a moving convex set in a hilbert space. J. Differ. Equ. 26, 347–374 (1977)
Moreau, J.J.: Bounded variation in time. In: Panagiotopoulos, P., Strang, G. (eds.) Topics in Nonsmooth Mechanics, pp. 1–74. Bikhäuser, Basel (1988)
Moreno, R., Ghadiri, M., Antony, S.: Effect of the impact angle on the breakage of agglomerates: a numerical study using dem. Powder Technol. 130, 132–137 (2003)
Nezamabadi, S., Radjai, F., Averseng, J., Delenne, J.Y.: Implicit frictional-contact model for soft particle systems. J. Mech. Phys. Solids 83, 72–87 (2015)
Nguyen, D.H., Azéma, E., Sornay, P., Radjai, F.: Bonded-cell model for particle fracture. Phys. Rev. E 91, 022203 (2015)
Peyneau, P.E., Roux, J.N.: Frictionless bead packs have macroscopic friction, but no dilatancy. Phys. Rev. E 78, 011307 (2008)
Quezada, J.C., Breul, P., Saussine, G., Radjai, F.: Stability, deformation, and variability of granular fills composed of polyhedral particles. Phys. Rev. E 86, 031308 (2012)
Radjai, F., Dubois, F.: Discrete Numerical Modelling of Granular Materials. Wiley-ISTE, Berlin (2011)
Radjai, F., Jean, M., Moreau, J., Roux, S.: Force distributions in dense two-dimensional granular systems. Phys. Rev. Lett. 77, 274 (1996)
Radjai, F., Richefeu, V.: Contact dynamics as a nonsmooth discrete element method. Mech. Mater. 41, 6715–728 (2009)
Radjai, F., Roux, S.: Turbulentlike fluctuations in quasistatic flow of granular media. Phys. Rev. Lett. 89, 064302 (2002)
Radjai, F., Wolf, D.E., Jean, M., Moreau, J.: Bimodal character of stress transmission in granular packings. Phys. Rev. Lett. 80, 61–64 (1998)
Saint-Cyr, B., Delenne, J.Y., Voivret, C., Radjai, F., Sornay, P.: Rheology of granular materials composed of nonconvex particles. Phys. Rev. E 84, 041302 (2011)
Sator, N., Mechkov, S., Sausset, F.: Generic behaviours in impact fragmentation. Europhys. Lett. 81, 44002 (2008)
Silbert, L.E., Grest, G.S., Brewster, R., Levine, A.J.: Rheology and contact lifetimes in dense granular flow. Phys. Rev. Lett. 99, 068002 (2007)
Singh, A., Magnanimo, V., Saitoh, K., Luding, S.: The role of gravity or pressure and contact stiffness in granular rheology. New J. Phys. 17, 043028 (2015)
Staron, L., Vilotte, J.P., Radjai, F.: Preavalanche instabilities in a granular pile. Phys. Rev. Lett. 89, 204302 (2002)
Taboada, A., Chang, K.J., Radjai, F., Bouchette, F.: Rheology, force transmission, and shear instabilities in frictional granular media from biaxial numerical test using the contact dynamics method. J. Geophys. Res. 110, 1–24 (2005)
Taboada, A., Estrada, N., Radjaï, F.: Additive decomposition of shear strength in cohesive granular media from grain-scale interactions. Phys. Rev. Lett. 97, 098302 (2006)
Thornton, C.: Force transmission in granular media. KONA Powder Part. 15, 81–90 (1997)
Thornton, C., Yin, K.K., Adams, M.J.: Numerical simulation of the impact fracture and fragmentation of agglomerates. J. Phys. D Appl. Phys. 29, 424–435 (1996)
Torquato, S.: Random Heterogeneous Materials—Microstructure and Macroscopic Properties. Springer, New York (2002)
Wang, J., Yan, H.: On the role of particle breakage in the shear failure behavior of granular soils by dem. Int. J. Numer. Anal. Meth. Geomech. 37, 832–854 (2013)
Wittel, F., Carmona, H., Kun, F., Herrmann, H.: Mechanisms in impact fragmentation. Int. J. Fract. 154, 105–117 (2008)
Acknowledgements
Farhang Radjai would like to acknowledge the support of the ICoME2 Labex (ANR-11-LABX-0053) and the A*MIDEX projects (ANR-11-IDEX-0001-02) cofunded by the French program Investissements d’Avenir, managed by the ANR, the French National Research Agency.
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Saeid Nezamabadi, Thanh Hai Nguyen, Jean-Yves Delenne and Farhang Radjai state that there are no conflicts of interest.
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Nezamabadi, S., Nguyen, T.H., Delenne, JY. et al. Modeling soft granular materials. Granular Matter 19, 8 (2017). https://doi.org/10.1007/s10035-016-0689-y
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DOI: https://doi.org/10.1007/s10035-016-0689-y