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CivilComp Proceedings
ISSN 17593433 CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 119
Contact Detection between AxiallyAsymmetric Ellipsoids for Discrete Element Modeling S. Johnson+, J.R. Williams+ and B.K. Cook*
+Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
S. Johnson, J.R. Williams, B.K. Cook, "Contact Detection between AxiallyAsymmetric Ellipsoids for Discrete Element Modeling", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 119, 2004. doi:10.4203/ccp.79.119
Keywords: DEM, discrete element, computational geometry, ellipsoid, contact, collision detection.
Summary
Discrete Element Modeling (DEM) has become an increasingly important tool for
evaluating behavior in highly discontinuous materials such as fractured rock,
erodible sedimentary material, pharmaceutical powders, and agricultural grains. The
practical limits of DEM in both time for simulation and analyzable number of
particles, however, have limited its use in analyzing systems of interest in many
industrial applications. These limits arise due to several key computational
components of the simulation pipeline, including parallelization strategy, particle
representation, contact law, and neighborsorting algorithm. The focus of this paper
is on representing a particle's geometry as a general ellipsoid in a computationally
efficient manner.
Because of the limits of currently available algorithms for determining the exact contact between nonspherical primitives, spheres form the basis for the most popular codes in DEM, including TRUBAL (Cundall [1]), PFC3D (Cundall [2]), and DMC (Taylor and Preece [3]) as well as the application developed in Cleary [4]. However, the sphere has several attributes that, while attractive for computational purposes, limit its ability to capture key behaviors of real particle systems, which typically contain nonspherical particles. Spheres tend to exhibit excessively rolling when subjected to small moments. Because spheres cannot exert a resistive couple (i.e., friction is the only channel by which a resistive couple can be applied), they are unable to represent the particle interlocking observed in many real systems. Some numerical implementations address this by introducing couples artificially by either perturbing the normal force direction so that it does not pass through the centroid or by adding an adjustable "rolling friction" factor (e.g., VuQuoc [5]). Spheres also tend to organize into dense, ordered packings as the coefficient of friction decreases (Grest [6]), which is not representative of the structure found in many naturally occurring materials. Despite these drawbacks, spherebased DEM implementations remain the most common for 3D modeling, since they are simple and compact (only 4 floating point numbers are required to describe the geometry, and contact resolution between spheres is trivial) and hence are fast computationally. A new contact resolution algorithm based on the Method of Equivalent Spheres is presented, which takes advantage of the convexity and smoothly varying curvature of the ellipsoidal geometry in combination with an efficient iterative, vectorbased search algorithm. This algorithm seeks to exploit the smoothly varying convexity of the ellipsoidal geometry through a vector operation based search algorithm, which displays favorable computational resource requirements based on initial estimates of floating point operations per contacting pair. References
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