Summary
In this work different models for the simulation of granular material are investigated. Due to the fact that a detailed simulation considering complex shapes of the bodies is very time consuming, methods from molecular dynamics (MD) are used. By means of granular matter simulations large systems like bulk solids, silicic or sand e.g. in silos, or other systems like carriage systems can be investigated. The MD method is combined here with ideas from multibody systems, so that it is possible to determine the collisions and the motion of differently shaped bodies. Here, particles are modeled as rigid bodies, where the interaction is described by means of elastic contact forces. The particles considered are convex or non-convex three-dimensional polyhedra.
After neighboring body pairs are found, the very time consuming collision detection for polygonal bodies can be accomplished. In order to check whether there is a collision between two neighboring body pairs, it has to be checked, whether there is a vertex of one body inside the other body. It will be focused also on the calculation of the contact forces in normal and tangential direction.
Research Project B7 “Hybrid Multibody Simulations of Poured Particles”
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. P. Allen and D. J. Tildesley. Computer Simulations of Liquids. Clarendon Press, Oxford, 1989.
D. Baraff. Dynamic Simulation of Non-Penetrating Rigid Bodies. Cornell University Ithaka, Ph.D. Thesis 92–1275, 1992.
L. Brendel and S. Dippel. Lasting contacts in molecular dynamics simulations. In Physics of Dry Granular Materials — NATO ASI Series E 350, pages 313–318. Kluwer Academic Publishers, Dordrecht, 1998.
P. A. Cundall and O. D. L. Strack. A discrete numerical model for granular assemblies. Geotechnique, 29(1):47–65, 1979.
P. Eberhard. Kontaktuntersuchungen durch hybride Mehrkörpersystem / Finite Elemente Simulationen. Shaker, Aachen, 2000.
D. Fincham and B. J. Ralston. Molecular dynamics simulation using CRAY-1 vector processing computer. Computer Physics Communications, 23:127–134, 1981.
Y. Gonthier, J. McPhee, C. Lange, and J.-C. Piefboeuf. A regularized contact model with asymmetric damping and dwell-time dependent friction. Multibody System Dynamics, 11(3):209–233, 2004.
L. Greengard. The Rapid Evaluation of Potential Fields in Particle Simulation. MIT Press, Cambridge, 1987.
K. H. Hunt and F. R. E. Grossley. Coefficient of restitution interpreted as damping in vibroimpact. ASME Journal of Applied Mechanics, 7:440–445, 1975.
Y. Kishino, editor. Powders & Grains, Balkema, Rotterdam, 2001.
H. M. Lankarani and P. E. Nikravesh. Continuous contact force models for impact analysis in multibody systems. Nonlinear Dynamics, 5:193–207, 1994.
S. Luding. Collisions and contacts between two particles. In Physics of Dry Granular Media — NATO ASI Series E 350, pages 285–304. Kluwer Academic Publishers, Dordrecht, 1998.
S. Luding. Die Physik trockener granularer Medien. Logos, Berlin, 1998.
D. W. Marhefka and D. E. Orin. A compliant contact model with nonlinear damping for simulation of robotic systems. IEEE Transaction on Systems, Man and Cybernetics — Part A: Systems and Humans, 29(6):566–572, 1999.
B. Muth, M.-K. Müller, P. Eberhard, and S. Luding. Contacts between many bodies. Machine Dynamics Problems, 28(1):101–114, 2004.
B. Muth, G. Of, P. Eberhard, and O. Steinbach. Collision detection for complicated polyhedra using the multipole method or ray crossing (submitted 2006).
J. T. Oden and E. B. Pires. Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity. Journal of Applied Mechanics, 50(1):67–76, 1983.
J. O’Rourke. Computational Geometry in C, 2. Edition. Cambridge University Press, Cambridge, 1998.
F. Pfeiffer and C. Glocker. Multibody Dynamics with Unilateral Contacts. Wiley, New York, 1996.
J. Pfister and P. Eberhard. Frictional contact of flexible and rigid bodies. Granular Matter, 4(1):25–36, 2002.
T. Pöschel and V. Buchholtz. Static friction phenomena in granular materials: Coulomb law vs. particle geometry. Physical Review Letters, 71(24):3963–3974, 1993.
T. Pöschel and S. Luding, editors. Granular Gases, Springer, Berlin, 2001.
B. Quentrec and C. Brot. New method for searching for neighboring molecular dynamics. Journal of Computational Physics, 13:430–432, 1973.
D. C. Rapaport. The Art of Molecular Dynamics Simulation. Cambridge University Press, Cambridge, 1995.
V. Rokhlin. Rapid solution of integral equations of classical potential theory. Journal of Computational Physics, 60:187–207, 1985.
W. Schiehlen and P. Eberhard. Technische Dynamik. B.G. Teubner, Stuttgart, 2004.
A. Schinner. Fast algorithms for the simulations of polygonal particles. Granular Matter, 2(1):35–43, 1999.
R. Tykhoniuk, J. Tomas, S. Luding, M. Kappl, L. Heim, and H.-J. Butt. Adhesion, inelastic contact behavior and simulation of shear dynamics of ultrafine cohesive powder. In Powders and Grains 2005, pages 499–503. Balkema, Leiden, 2005.
L. Verlet. Computer experiments on classical fluids. I. Thermodynamical properties of Lennart-Jones molecules. Physical Review, 159(1):98–103, 1967.
P. A. Vermeer, S. Diebels, W. Ehlers, H. J. Herrmann, S. Luding, and E. Ramm, editors. Continuous and Discontinuous Modelling of Cohesive Frictional Materials, Springer, Berlin, 2001.
O. R. Walton and R. L. Braun. Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks. Journal of Rheology, 30(5):949–980, 1986.
W. Wessel. Kontakterkennung räumlicher polyhedraler Körper mit Hilfe von Methoden der Molekulardynamik. University of Stuttgart, Student-Thesis STUD-212, 2004.
P. Wriggers. Computational Contact Mechanics. John Wiley & Sons, Chichester, 2002.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Eberhard, P., Muth, B. (2006). Dynamics of Poured Polyhedra of Different Shape. In: Helmig, R., Mielke, A., Wohlmuth, B.I. (eds) Multifield Problems in Solid and Fluid Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 28. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-34961-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-34961-7_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34959-4
Online ISBN: 978-3-540-34961-7
eBook Packages: EngineeringEngineering (R0)