Mixed FEM–Crushable DEM Nested Scheme in Second-Order Computational Homogenization for Granular Materials
Publication: International Journal of Geomechanics
Volume 16, Issue 5
Abstract
A mixed FEM–crushable discrete-element method (DEM) nested scheme in the frame of second-order computational homogenization for granular materials was proposed. The particle breakage followed by the discontinuity and dissipative relative movements between each of two immediate neighboring particles were modeled at the mesoscale to perform both the downscaling and upscaling between the mixed FEM at the macroscopic continuum scale and the crushable DEM at the mesoscopic discrete particle assembly scale. To develop the crushable DEM for modeling the mesostructural evolution within representative volume elements (RVEs) assigned to integrating points of the macroscopic Cosserat continuum in the homogenization, two grain breakage models consisting of crushing criteria and the fracture mode for an individual crushable particle were developed. Not only the contact forces, but also contact moments exerted on each individual grain via the contacting points on the grain surface, were taken into account to set up the proposed crushing criteria. The stress measures, responsible for the particle breakage, involved both the average Cauchy stress tensor and the average couple stress tensor exerted on a crushable particle modeled as the Cosserat continuum. A fracture mode to specify how a crushable parent particle is replaced with a specific arrangement of postcrushing fragments was proposed and implemented. The mass conservation in the postcrushing replacement of fragments was ensured, whereas neither overlaps among the fragments nor overlaps with the fragments of the immediate neighboring particles of the crushable parent particle were introduced. The numerical results demonstrate the performance of the proposed mixed FEM–crushable DEM nested scheme in the frame of second-order computational homogenization for granular materials and the effects of the particle breakage on the failure behavior of the overall geostructure.
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Acknowledgments
The authors acknowledge the support of this work by the National Natural Science Foundation of China through contract/grant number 11372066, and the National Key Basic Research and Development Program (973 Program) through contract number 2010CB731502.
References
Alam, M., and Luding, S. (2003). “First normal stress difference and crystallization in a dense sheared granular fluid.” Phys. Fluids., 15(8), 2298.
Alam, M., Shukla, P., and Luding, S. (2008). “Universality of shear-banding instability and crystallization in sheared granular fluid.” J. Fluid Mech., 615, 293–321.
Alonso-Marroquin, F. (2011). “Static equations of the Cosserat continuum derived from intra-granular stresses.” Granular Matter, 13(3), 189–196.
Arslan, H., Baykal, G., and Sture, S. (2009). “Analysis of the influence of crushing on the behavior of granular materials under shear.” Granular Matter, 11(2), 87–97.
Åström, J. A., and Herrmann, H. J. (1998). “Fragmentation of grains in a two-dimensional packing.” Eur. Phys. J. B, 5(3), 551–554.
Ben-Nun, O., and Einav, I. (2010). “The role of self-organization during confined comminution of granular materials.” Philos. Trans. R. Soc. London, Ser. A, 368(1910), 231–247.
Chang, C. S., and Kuhn, M. R. (2005). “On virtual work and stress in granular media.” Int. J. Solids Struct., 42(13), 3773–3793.
Chen, W. F., and Mizuno, E. (1990). Nonlinear analysis in soil mechanics, theory and implementation, Elesvier Science, New York.
Cheng, Y. P., Bolton, M. D., and Nakata, Y. (2004). “Crushing and plastic deformation soils simulated using DEM.” Géotechnique, 54(2), 131–141.
Cheng, Y. P., Nakata, Y., and Bolton, M. D. (2003). “Discrete element simulation of crushable soil.” Géotechnique, 53(7), 633–641.
Cundall, P. A., and Strack, O. D. L. (1979). “A discrete numerical model for granular assemblies.” Géotechnique, 29(1), 47–65.
D'Addetta, G., Ramm, E., Diebels, S., and Ehlers, W. (2004). “A particle center based homogenization strategy for granular assemblies.” Eng. Comput., 21(2/3/4), 360–383.
Duxbury, P. G., and Li, X. K. (1996). “Development of elasto-plastic material models in a natural co-ordinate system.” Comput. Methods Appl. Mech. Eng., 135(3–4), 283–306.
Ehlers, W., Ramm, E., Diebels, S., and D'Addetta, G. (2003). “From particle ensembles to Cosserat continua: Homogenization of contact forces towards stresses and couple stresses.” Int. J. Solids Struct., 40(24), 6681–6702.
Einav, I. (2007). “Breakage mechanics—Part I: Theory.” J. Mech. Phys. Solids, 55(6), 1274–1297.
Elghezal, L., Jamei, M., and Georgopoulos, I. O. (2013). “DEM simulations of stiff and soft materials with crushable particles: An application of expanded perlite as a soft granular material.” Granular Matter, 15(5), 685–704.
Geers, M. G. D., Kouznetsova, V. G., and Brekelmans, W. A. M. (2010). “Multi-scale computational homogenization: Trends and challenges.” J. Comput. Appl. Math., 234(7), 2175–2182.
Jensen, R. P., Plesha, M. E., Edil, T. B., Bosscher, P. J., and Kahla, N. B. (2001). “DEM simulation of particle damage in granular media—Structure interfaces.” Int. J. Geomech., 1–19.
Kaneko, K., Terada, K., Kyoya, T., and Kishino, Y. (2003). “Global-local analysis of granular media in quasi-static equilibrium.” Int. J. Solids Struct., 40(15), 4043–4069.
Kouznetsova, V., Geers, M. G. D, and Brekelmans, W. A. M. (2002). “Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme.” Int. J. Numer. Methods Eng., 54(8), 1235–1260.
Kouznetsova, V., Geers, M. G. D, and Brekelmans, W. A. M. (2004). “Multi-scale second-order computational homogenization of multi-phase materials: A nested finite element solution strategy.” Comput. Methods. Appl. Mech. Eng., 193(48–51), 5525–5550.
Li, X. K., Chu, X. H., and Feng, Y. T. (2005). “A discrete particle model and numerical modeling of the failure modes of granular materials.” Eng. Comput., 22(8), 894–920.
Li, X. K., Du, Y. Y., and Duan, Q. L. (2013). “Micromechanically informed constitutive model and anisotropic damage characterization of Cosserat continuum for granular materials.” Int. J. Damage Mech., 22(5), 643–682.
Li, X. K., Du, Y. Y., Duan, Q. L., and Ju, J. W. (2015). “Thermodynamic framework of damage-healing-plasticity and net damage variable for granular materials.” Int. J. Damage Mech.
Li, X. K., Liang, Y. B., Duan, Q. L., Schrefler, B. A., and Du,Y. Y. (2014). “A mixed finite element procedure of gradient Cosserat continuum for second-order computational homogenisation of granular materials.” Comput. Mech., 54(5), 1331–1356
Li, X. K, Liu, Q. P, and Zhang, J. B. (2010a). “A micro-macro homogenization approach for discrete particle assembly—Cosserat continuum modeling of granular materials.” Int. J. Solids Struct., 47(2), 291–303.
Li, X. K, Zhang, J. B., and Zhang, X. (2011). “Micro-macro homogenization of gradient-enhanced Cosserat media.” Eur. J. Mech. A. Solids, 30(3), 362–372.
Li, X. K, Zhang, X., and Zhang, J. B. (2010b). “A generalized Hill’s lemma and micromechanically based macroscopic constitutive model for heterogeneous granular materials.” Comput. Methods Appl. Mech. Eng., 199(49–52), 3137–3152.
Lobo-Guerrero, S., and Vallejo, L. E. (2005). “Discrete element method evaluation of granular crushing under direct shear test conditions.” J. Geotech. Geoenviron. Eng., 1295–1300.
Lobo-Guerrero, S., Vallejo, L. E., and Vesga, L. F. (2006). “Visualization of crushing evolution in granular materials under compression using DEM.” Int. J. Geomech., 195–200.
McDowell, G. R., and Harireche, O. (2002). “Discrete element modelling of yielding and normal compression of sand.” Géotechnique, 52(4), 299–304.
Onck, P. R. (2002). “Cosserat modeling of cellular solids.” Comptes. Rendus. Mecanique, 330(11), 717–722.
Pasternak, E., and Mühlhaus, H. B. (2005). “Generalised homogenisation procedures for granular materials.” J. Eng. Math., 52(1–3), 199–229.
Scholtes, L., Chareyre, B., Nicot, F., and Darve, F. (2009b). “Micromechanics of granular materials with capillary effects.” Int. J. Eng. Sci., 47(1), 1460–1471.
Scholtes, L., Hicher, P. Y., Nicot, F., Chareyre, B., and Darve, F. (2009a). “On the capillary stress tensor in wet granular materials.” Int. J. Numer. Anal. Methods Geomech., 33(10), 1289–1313.
Terada, K., and Kikuchi, N. (2001). “A class of general algorithms for multi-scale analyses of heterogeneous media.” Comput. Methods Appl. Mech. Eng., 190(40–41), 5427–5464.
Tsoungui, O., Vallet, D., and Charmet, J. C. (1999). “Numerical model of crushing of grains inside two-dimensional granular materials.” Powder Technol., 105(1–3), 190–198
Information & Authors
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Published In
International Journal of Geomechanics
Volume 16 • Issue 5 • October 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jun 16, 2015
Accepted: Oct 20, 2015
Published online: Feb 8, 2016
Discussion open until: Jul 8, 2016
Published in print: Oct 1, 2016
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