Summary
This paper addresses the problem of contact detection in discrete element multibody dynamic simulations. We present an overview of the problem and a detail description of a new object representation scheme called the discrete function representation (DFR). This representation is designed to reduce the computational cost of both contact detection and the more difficult problem of contact resolution. The scheme has a maximum theoretical complexity of orderO(N) for contact resolution between bodies defined byN boundary points. In practice, the discrete element method constrains overlap between objects and the actual complexity is approximately\(O(\sqrt {(N)} \) giving a speedup of nearly 2 orders of magnitude over traditional algorithms for systems with more than 1000 objects. The technique is robust and is able to handle convex and concave object geometries, including objects containing holes. Examples of relatively large discrete element simulations in three dimensions are presented.
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References
Barr, A. (1981), “Super quadrics and angle preserving transformations”,IEEE, Computer Graphics and Applications,1, 1.
Baraff, D. (1990), “Curved surfaces and coherence for non-penetrating rigid body simulation”, InProceedings of ACM SIGGRAPH,24.
Bouma, W. J. and Vanecek, G. Jr. (1991), “Collision detection and analysis in a physically based simulation”, In2nd Eurographics Workshop on Animation and Simulation, Vienna.
Beazley, D. M. and Lomdahl, P. S. (1995), “Large-scale molecular dynamics on mpps.”,SIAM News,28, 2.
Canny, J. (1988),The complexity of Robot Motion Planning, ACM doctoral dissertation award 1987, MIT Press, Cambridge, MA, USA, ACM Distinguished Dissertation Series.
Cundall, P. A. and Hart, R. D. (1989), “Numerical modeling of discontinua”, InProceedings of the 1st U.S. Conference on discrete Element Methods (DEM), see ref. 14. Colorado School of Mines, Golden, CO.
Cundall, P. A. and Strack, O. D. L. (1979), “A distinct element model for granular assemblies”,Geotechnique, pp. 29–47, 65.
Dvorkin, P. (1994), “Efficient collision detection for real-time simulated environments”, Master's thesis, Media Lab, Massachusetts Institute of Technology.
Williams, R. J., Hocking, G. and Mustoe, G. G. W. (1987), “Dymanics analysis for three dimensional contact and fracturing of multiple bodies”, InProceedings of NUMETA 1987, Numerical Methods in Engineering, Theory and Application, Rotterdam, Balkema.
Greengard, F. L. (1988),The Rapid Evaluation of Potential Fields in Particle systems, ACM Distinguished Dissertation 1987, ACM Distinguished Dissertation Series 1987.
Hahn, J. K. (1988), “Realistic animation of rigid bodies”,ACM Computer Graphics,22, 4, pp. 299–306.
Vanecek, G. Jr. (1994), “Towards automatic grid generation using binary space partition trees”, Technical report, Department of Computer Science, Purdue University, West Layfayette, IN 47907.
Knuth, D. E. (1973),The Art of Computer Programming, Volume 3,Sorting and Searching, Addison Wesley, Reading, Mass, USA.
Mustoe, G. G., Henriksen, M. and Huttelmaier, H. P. (Eds.) (1989),Proceedings of the 1st U. S. Conference on Discrete Element Methods (DEM), Colorado School of Mines, Golden, CO.
Munjiza, A. and Owen, D. R. J. (1993), “Discrete elements in rock blasting”, InProceedings of the 2nd International Conference on Discrete Element Methods (DEM), pp. 287–300.
Munjiza, A., Owen, D. R. J. and Williams, J. R. (1994), “On a rational approach to rock blasting”, InProceedings of the 8th International Conference on Computer Methods and Advances in Geomechanics, H. J. Siriwardane and M. M. Zaman (Eds.), volume I, pp. 857–862.
Moore, M. and Wilhelms, J. (1988), “Collision detection and response for computer animation”,ACM Computer Graphics,22, 4, pp. 289–297.
Tang Tat Ng and Fang, H. E. (1995), “Cyclic behavior or arrays of ellipsoids with different particle shapes”, InProceedings of Joint ASME Applied Mechanics and Materials Summer Conference, Mechanics of Materials with Discontinuities and Heterogeneities Symposium,201, pp. 59–70, UCLA, Los Angeles.
Tang Tat Ng and Fang, H. E. (1995), “Cyclic behavior or arrays of ellipsoids with different particle shapes”, InProceedings of Joint ASME Applied Mechanics and Materials Summer Conference, Mechanics of Materials with Discontinuities and Heterogeneities Symposium,201, pp. 59–70, UCLA, Los Angeles.
Tang Tat Ng and Xiaoshan Lin (1993), “Numerical simulations of naturally deposited granular soil with ellipsoidal elements”, InProceedings of 2nd International Conference on Discrete Element Methods (DEM), pp. 557–567, see ref. 32. Dept. of Civil and Environmental Engineering, Massachusetts Institute of Technology, IESL Publications.
Pentland, A. P. (1991), “Computational complexity versus simulated environments”, InACM SIGGRAPH Computer Graphics,24, 2, pp. 185–192.
Pentland, A. P. and Williams, J. R. (1989), “Good vibrations: Modal dynamics for graphics and animation”,ACM Computer Graphics,23, 3.
Rogers, D. (1985), “Procedural Elements for Computer Graphics”, McGraw Hill.
Sedgewick, R. (1990),Algorithms in C., Addison Weslye.
Swegle, J. W. (1993), “Search algorithm”, Technical report, Sandia National Laboratories, Solid and Structural Mechanics Dept., Albequerque, New Mexico, 87185, External Distribution Memo.
Ting J. M., Khwaja, M. Meachum, L. and Rowell, J. (1993), “An ellipse-based discrete element model for granular materials”,Int. J. for Num. and Anal. Meth. in Geomech.,17, pp. 603–623.
Ting, J. M., Khwaja, M. Meachum, L. and Rowell, J. (1993), “An ellipse-based discrete element model for granular materials”,Int. J. for Num. and Anal. Meth. in Geomech.,17, pp. 603–623.
Trent, B. C. and Margolin, L. G. (1992), “A numerical laboratory for granular solids”,Engineering Computations,9, pp. 191–197.
Taylor, L. M. and Preece, D. S. (1992), “Simulation of blasting induced rock motion using spherical element models”,Engineering Computations,9, 2, see ref. 14. Colorado School of Mines, Golden, CO.
Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T. (1998),Numerical Recipes in C., Cambridge University Press, 1st edition.
Williams, J. R. (1988), “Contact analysis of large numbers of interacting bodies using discrete modal methods for simulating material failure on the microscopic scale”,Int. J. of Comp. Aided Engng.—Engng. Computations,5, 3.
Williams, J. R. and Mustoe, G. G. W. (Eds.) (1993),Proceedings of the 2nd International Conference on Discrete Element Methods (DEM)., Dept. of Civil and Environmental Engineering, Massachusetts Institute of Technology, IESL Publications.
Williams, J. R. and O'Connor, R. (1995), “A linear complexity intersection algorithm for discrete element simulation of arbitrary geometries”,Int. J. of Comp. Aided Engng.—Engng. Computations,12, 2, Special Edition on Discrete Element Methods.
Williams, J. R. and O'Connor, R. (1995), “A linear complexity intersection algorithm for discrete element simulation of arbitrary geometries”,Engng. Computations,12, pp. 185–201.
Williams, J. R. and Pentland, A. (1989), “Superquadrics object representation for dynamics of multi-body structures”, InProceedings of ASCE Structures, San Francisco, CA.
Williams, J. R. and Pentland, A. (1992), “Superquadrics and modal dynamics for discrete elements in interactive design”,Int. J. of Comp. Aided Engng.—Engng. Computations,9, 2.
Warren, M. S. and Salmon, J. K. (1993), “A parallel hashed octreen-body algorithm”, InProceedings of Supercomputing 3, Los Alamitos. IEEE Comp. Soc.
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Williams, J.R., O'Connor, R. Discrete element simulation and the contact problem. Arch Computat Methods Eng 6, 279–304 (1999). https://doi.org/10.1007/BF02818917
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DOI: https://doi.org/10.1007/BF02818917