Abstract
Within this contribution the mechanical behavior of dry frictional granular material is modeled by a three-dimensional discrete element method (DEM). The DEM uses a superquadric particle geometry which allows to vary the elongation and angularity of the particles and therefore enables a better representation of real grain shapes compared to standard spherical particles. To reduce computation times an efficient parallelization scheme is developed which is based on the Verlet list concept and the sorting of particles according to their spatial position. The macroscopic mechanical behavior of the particle model is analyzed through standard triaxial tests of periodic cubical samples. A technique to accurately apply stress boundary conditions is presented in detail. Finally, the triaxial tests are used to analyze the influence of the sample size and the particle shape on the resulting stress-strain behavior.
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References
The OpenMP API specification for parallel programming. http://openmp.org.
Agnolin, I., Roux, J.N., On the elastic moduli of three-dimensional assemblies of spheres: Characterization and modeling of fluctuations in the particle displacement and rotation. Int. J. Solids Struct. 45(3–4):1101–1123, 2008.
Antony, S.J., Kruyt, N.P., Role of interparticle friction and particle-scale elasticity in the shearstrength mechanism of three-dimensional granular media. Phys. Rev. E 79(3), 2009.
Antony, S.J., Kuhn, M.R., Influence of particle shape on granular contact signatures and shear strength: New insights from simulations. Int. J. Solids Struct. 41(21):5863–5870, 2004.
Azema, E., Radjai, F., Saussine, G., Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles. Mech. Mater. 41(6):729–741, 2009.
Bardet, J.P., Vardoulakis, I., The asymmetry of stress in granular media. Int. J. Solids Struct. 38(2):353–367, 2001.
Barr, A.H., Superquadrics and angle-preserving transformations. IEEE Comput. Graphics Appl. 1(1):11–23, 1981.
Belheine, N., Plassiard, J.P., Donze, F.V., Darve, F., Seridi, A., Numerical simulation of drained triaxial test using 3D discrete element modeling. Comput. Geotech. 36(1–2):320–331, 2009.
Clayton, C.R.I., Abbireddy, C.O.R., Schiebel, R., A method of estimating the form of coarse particulates. Geotechnique 59(6):493–501, 2009.
da Cruz, F., Emam, S., Prochnow, M., Roux, J.N., Chevoir, F., Rheophysics of dense granular materials: Discrete simulation of plane shear flows. Phys. Rev. E 72(2), 2005.
Hertz, H., Über die Berührung fester elastischer Körper (On the contact of elastic solids). Journal für die reine und angewandte Mathematik 92:156–171, 1882.
Ishibashi, I., Perry, C., Agarwal, T.K., Experimental determinations of contact friction for spherical glass particles. Soils Found. 34(4):79–84, 1994.
Kingston, E., Clayton, C.R.I., Priest, J., Best, A., Effect of grain characteristics on the behaviour of disseminated methane hydrate bearing sediments. In: Proceedings of the 6th International Conference on Gas Hydrates. 2008.
Lin, X., Ng, T.T., A three-dimensional discrete element model using arrays of ellipsoids. Geotechnique 47(2):319–329, 1997.
Lings, M.L., Dietz, M.S., An improved direct shear apparatus for sand. Geotechnique 54(4):245–256, 2004.
Mindlin, R.D., Compliance of elastic bodies in contact. J. Appl. Mech. 16:259–268, 1949.
Munjiza, A., The Combined Finite-Discrete Element Method. Wiley, 2004.
Ouadfel, H., Rothenburg, L., An algorithm for detecting inter-ellipsoid contacts. Comput. Geotech. 24(4):245–263, 1999.
Rowe, P.W., The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proc. R. Soc. London, Ser. A 269(1339):500–527, 1962.
Salot, C., Gotteland, P., Villard, P., Influence of relative density on granular materials behavior: DEM simulations of triaxial tests. Granular Matter 11(4):221–236, 2009.
Schnaid, F., A study of the cone-pressuremeter test in sand. Ph.D. Thesis, University of Oxford, 1990.
Thornton, C., Numerical simulations of deviatoric shear deformation of granular media. Geotechnique 50(1):43–53, 2000.
Verlet, L., Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard–Jones molecules. Phys. Rev. 159(1):98–103, 1967.
Wellmann, C., Lillie, C., Wriggers, P., Comparison of the macroscopic behavior of granular materials modeled by different constitutive equations on the microscale. Finite Elem. Anal. Des. 44(5):259–271, 2008.
White, D.J., Bolton, M.D., Displacement and strain paths during plane-strain model pile installation in sand. Geotechnique 54(6):375–397, 2004.
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Wellmann, C., Wriggers, P. (2011). Homogenization of Granular Material Modeled by a 3D DEM. In: Oñate, E., Owen, R. (eds) Particle-Based Methods. Computational Methods in Applied Sciences, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0735-1_8
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DOI: https://doi.org/10.1007/978-94-007-0735-1_8
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