Abstract
This paper aims to develop a generic framework for detecting contact between cylindrical particles in discrete element modelling based on a full exploitation of the axi-symmetrical property of cylinders. The main contributions include: (1) A four-parameter based local representative system is derived to describe the spatial relationship between two cylinders so that the 3D cylinder–cylinder intersection problem can be reduced to a series of 2D circle–ellipse intersections, which considerably simplifies the contact detection procedure. (2) A two-stage contact detection scheme is proposed in which no-overlap contact pairs are identified in the first overlap check stage, and then the actual overlap region is determined in the second resolution stage and represented by two schemes: the layered representation which is generic, and the edge representation which is numerically more efficient but less accurate. (3) The most significant contribution is the development of two theorems that establish a fundamental relationship between the contact point and contact normal of two contacting cylinders, offering a simple approach to determining the normal direction based on the contact point and vice versa. These theorems are valid not only for cylinders, but also for any axi-symmetrical shapes and their combinations. Some numerical issues are discussed. Numerical examples are presented to illustrate the capability and applicability of the proposed methodologies.
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