A method for representing boundaries in discrete element modelling. I. Geometry and contact detection

The discrete element method for analysis of the dynamic behaviour of discontinuous media is well established. However, its application to engineering problems is still limited to simplified representations of structural boundaries and their kinematics. In this paper a method is developed for representing three-dimensional boundaries of arbitrary geometry and for modelling the interaction between boundary objects and particles within the discrete element modelling framework. The approach, which we term the finite wall method, uses planar triangular elements to approximate the boundary surface topology. Any number of wall elements can be used to model the shape of the structure. A contact detection scheme is presented for boundary surfaces and spheres based on a series of vector projections to reduce the problem dimensionally. The algorithm employs spatial sporting to obtain the set of potential contacts between spheres and wall elements prior to contact resolution. In a further stage, all possible contact conditions including contact with surfaces, edges and corners are explicitly determined. Part I of this two-part series of papers describes the finite wall method for representation of surface geometry and fully elaborates the method for detecting and resolving contact between boundary wall elements and spheres. In Part II the finite wall method is extended to apply kinematics to linearly independent boundary objects using combinations of translational and rotational motion. An approach is developed for coupling the DEM with the FEM for the purpose of optimising the design of structures which are dynamically interacting with particulate media.