In this paper, the compactions
of the elasto-plastic and the visco-plastic granular assemblies are simulated
using the finite element method. Governing equations for motion and deformation
for particles, including coupling of rigid body motion and deformation for
deformable bodies, are investigated. An implicit discrete element method for
block systems is developed to make visco-plastic analysis for the assemblies.
Among particles, three different contact types, cohering, rubbing and sliding,
are taken into account. To verify accuracy and efficiency of the numerical
method, some numerical example is simulated and the results are in a satisfactory
agreement with the solutions in literatures. The effects of frictional condition,
the initial solid volume ratio, the number of particles in the assembly, and
different types of compact- tion on the compaction of the elasto-plastic
and the visco-plastic aggregates are investigated. It is demonstrated that the
effect of frictional condition, the initial solid volume ratio, the number of
particles in the assembly, and different types of compaction on the global
behavior of the elasto-plastic the visco-plastic granular assemblies under compacting
are considerable. The numerical model is extended to simulate the compaction of
aggregates consisting of mixed particles of different viscous incompressible
materials. It is indicated that, with minor modification, the method could be
used in a variety of problems that can be represented using granular media,
such as asphalt, polymers, aluminum, snow, food product, etc.
Cite this paper
P. He, Y. Wu and H. Chen, "The Compactions of Elasto-Plastic and Visco-Plastic Granular Assemblies," Open Journal of Civil Engineering, Vol. 3 No. 1, 2013, pp. 29-44. doi: 10.4236/ojce.2013.31005.
References
[1] H. M. Jaeger and S. R. Nagel, “The Physics of Granular Materials,” Physics Today, Vol. 49, No. 4, 1996, pp. 32- 38. doi:10.1063/1.881494
[2] S. Luding, “Stress Distribution in Static Two Dimensional Granular Model Media in the Absence of Friction,” Physical Review E, Vol. 4, No. 55, 1997, pp. 4720-4729.
doi:10.1103/PhysRevE.55.4720
[3] Y. M. Bashir and J. D. Goddard, “A Novel Simulation Method for the Quasi-Static Mechanics of Granular Assemblages,” Journal of Rheology, Vol. 5, No. 35, 1991, pp. 849-885. doi:10.1122/1.550160
[4] M. A. Tzaferopoulos, “On the Numerical Modeling of Convex Particle Assemblies with Friction,” Computer Methods in Applied Mechanics and Engineering, Vol. 127, No. 1-4, 1995, pp. 371-386.
doi:10.1016/0045-7825(95)00852-8
[5] S. N. Coppersmith, C. H. Liu and O. Narayan, “Model for Force Fluctuations in Bead Packs,” Physical Review E, Vol. 5, No. 53, 1996, pp. 4673-4685.
doi:10.1103/PhysRevE.53.4673
[6] H. G. Matuttis, “Simulations of the Pressure Distribution under a Two Dimensional Heap of Polygonal Particles,” Granular Matter, Vol. 2, No. 1, 1998, pp. 83-91.
doi:10.1007/s100350050013
[7] M. Satake, “Tensorial form Definitions of Discrete-Mechanical Quantities for Granular Assemblies,” International Journal of Solids and Structures, Vol. 41, No. 21, 2004, pp. 5775-5791. doi:10.1016/j.ijsolstr.2004.05.046
[8] F. Emeriault and C. Claguin, “Statistical Homogenization for Assemblies of Elliptical Grains: Effect of the Aspect Ratio and Particle Orientation,” International Journal of Solids and Structures, Vol. 41, No. 2, 2004, pp. 5837- 5849. doi:10.1016/j.ijsolstr.2004.05.047
[9] S. J. Antony and R. Kuhn, “Influence of Particle Shape on Granular Contact Signatures and Shear Strength: New Insights from Simulations,” International Journal of Solids and Structures, Vol. 41, No. 21, 2004, pp. 5863-5870.
doi:10.1016/j.ijsolstr.2004.05.067
[10] Y. C. Wu, E. G. Thompson, P. R. Heyliger and Z. H. Yao, “The Compaction of Blended Aggregates of Non-Spherical Linear Viscous Particles,” Computer Methods in Applied Mechanics and Engineering, Vol. 193, No. 36-38, 2004, pp. 3871-3890. doi:10.1016/j.cma.2004.02.008
[11] Y. C. Wu, “Automatic Adaptive Mesh Upgrade Schemes of the Step-by-Step Incremental Simulation for Quasi Linear Viscoplastic Granular Materials,” Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2008, pp. 1479-1494. doi:10.1016/j.cma.2007.11.020
[12] Y. Wu, J. Xiao and C. Zhu, “The Compaction of TimeDependent Viscous Granular Materials Considering Inertial Forces,” Acta Mechanica Solida Sinica, Vol. 24, No. 6, 2011, pp. 495-505.