Acta Mechanica Solida Sinica

, Volume 24, Issue 6, pp 495–505

# The Compaction of Time-Dependent Viscous Granular Materials Considering Inertial Forces

• Yuching Wu
• Jianzhuang Xiao
• Cimian Zhu
Article

## Abstract

In the present paper, compactions of time-dependent viscous granular materials are simulated step by step using the automatic adaptive mesh generation schemes. Inertial forces of the viscous incompressible aggregates are taken into account. The corresponding conservation equations, the weighted-integral formulations, and penalty finite element model are investigated. The fully discrete finite element equations for the simulation are derived. Polygonal particles of aggregates are simplified as mixed three-node and four-node elements. The automatic adaptive mesh generation schemes include contact detection algorithms, and mesh upgrade schemes. Solutions of the numerical simulation are in good agreement with some results from literatures. With minor modification, the proposed numerical model can be applied in several industries, including the pharmaceutical, ceramic, food, and household product manufacturing.

## Key words

granular material automatic adaptive mesh generation finite element method time-dependent aggregates

## References

1. [1]
Reddy, J.N., On penalty function methods in the finite element analysis of flow problem. International Journal of Numerical Methods in Fluids, 1982, 2: 151–171.
2. [2]
Prasad, N.S., Hari, B.S. and Ganti, S.P., An adaptive mesh generation scheme for finite-element analysis. Computers & Structures, 1994, 50(1): 1–9.
3. [3]
Lee, C.K. and Hobbs, R.E., Automatic adaptive finite element mesh generation over rational B-spline surfaces. Computers & Structures, 1998, 69(5): 577–608.
4. [4]
Lewis, R.W., Gethin, D.T. and Yang, X.S.S., A combined finite-discrete element method for simulating pharmaceutical powder tableting. International Journal of Numerical Methods in Engineering., 2005, 62(7): 853–867.
5. [5]
Wu, Y.C., Automatic adaptive mesh upgrade schemes of the step-by-step incremental simulation for quasi linear viscous granular materials. Computer Methods in Applied Mechanics and Engineering, 2008, 197: 1479–1494.
6. [6]
Hughes, T.J.R., Liu, W.K. and Brooks, A., Review of finite element analysis of incompressible viscous flows by penalty function formulation. Journal of Computational Physics, 1979, 30: 1–60.
7. [7]
Reddy, J.N., On the finite element method with penalty for incompressible fluid flow problems. In: The Mathematics of Finite Elements and Applications III, New York: Academic Press, 1979.Google Scholar
8. [8]
Engelman, M., Sani, R., Gresho, P.M. and Bercovier, M., Consistent vs. reduced integration penalty methods for incompressible media using several old and new elements. Intrenational Journal of Numerical Methods in Fluids, 1982, 2: 25–42.
9. [9]
Hughes, T.J.R., Franca, L.P. and Balestra, M., A new finite element formulation for computational fluid dynamics, V. Circumventing the Babuska-Brezzi condition: A stable Petrov-Galerkin formulation for the Stokes proble accommodating equal-order interpolations. Computer Methods in Applied Mechanics and Engineering, 1986, 59: 85–99.
10. [10]
Shiojima, T. and Shimazaki, Y., A pressure-smoothing scheme for incompressible flow problems. International Journal of Numerical Methods in Fluids, 1989, 9: 557–567.
11. [11]
Reddy, M.P. and Reddy, J.N., Finite-element analysis of flows of non-Newtonian fluids in three-dimensional enclosures. International Journal of Non-Linear Mechanics, 1992, 27: 9–26.
12. [12]
Jaeger, H.M. and Nagel, S.R., Physics of the granular state. Science, 1992, 255: 1523.
13. [13]
Jaeger, H.M., and Nagel, S.R., The physics of granular materials. Physics Today, 1996, 49(4): 32–38.
14. [14]
Herrmann, H.J. and Luding, S., Modeling granular media with the computer. Continuum Mechanics and Thermodynamics, 1998, 10: 189–231.
15. [15]
Radjai, F., Jean, M., Moreau, J.J. and Roux, S., Force distribution in dense two-dimensional granular systems. Physics Review Letter, 1996, 2(77): 274.
16. [16]
Bashir, Y.M., and Goddard, J.D., A novel simulation method for the quasi-static mechanics of granular assemblages. Journal of Rheology, 1991, 5(35): 849–885.
17. [17]
Matuttis, H.G., Simulation of the pressure distribution under a two dimensional heap of polygonal particles. Granular Matter, 1998, 2(1): 83–91.
18. [18]
Nadai, A., Theory of Flow and Fracture of Solids, vol. II. New York: McGraw-Hill, 1963.Google Scholar
19. [19]
Cuitino, A.M., Alvarez, M.C., Roddy, M.J. and Lordi, N.G., Experimental chracterization of the behavior of granular visco-plastic and visco-elastic solids during compaction. Journal of Material Science, 2001, 36: 5487–5495.
20. [20]
Joseph, M. Powers, Two-phase viscous modeling of compaction of granular materials. Physics of Fluids, 2004, 16(8): 2975–2990.
21. [21]
Peter, R.L. and Ruth, E.C., Changes in small-angle X-ray scattering during powder compaction—An explanation based on granule deformation. Powder Technology, 2010, 198: 404–411.