Mark A. Hopkins
US Army Corps of Engineers ERDC-CRREL, Hanover,
New Hampshire, USA
Received February 2003
Revised July 2003
Accepted July 2003
Engineering Computations
Vol. 21 No. 2/3/4, 2004
pp. 422-430
Emerald Group Publishing Limited
0264-4401
DOI 10.1108/02644400410519866
Keywords Mathematical modelling, Simulation
Abstract A new contact detection technique for discrete element modeling is described. This technique is suitable for a large family of particle shapes that are based on the dilation process from mathematical morphology. In the dilation process an arbitrary shape is dilated by placing the center of a sphere of fixed diameter at every point in the basic shape. Defining a contact between two objects in this class is equivalent to determining which spheres amongst the infinite number that compose each object is in contact. The algorithm is derived for general ellipsoidal particles and demonstrated with a series of biaxial deformation simulations using a range of ellipsoidal particle shapes.
Discrete element modeling (DEM) has generally used simple circular shapes such as two-dimensional disks and three-dimensional spheres and not so simple polygonal and polyhedral shapes. Contact detection ranges from trivial for disks and spheres to non-trivial for polygons and polyhedra. To deal with complex shapes while circumventing the complexities of contact detection, some researchers have constructed bumpy particles from assemblies of spheres. This strategy results in a trade-off between contact simplicity and a large increase in the number of particles and contact searches.
The idea of constructing complex particles from assemblies of spheres is analogous to...
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