Toward Development of a Plate Discrete Element Method: Geometry and Kinematics

Shapes of constituent particles have a prominent effect on the macroscopic responses of granular assemblies. Clayey minerals often possess a plate-shaped geometry with a large surface-to-volume ratio. It is difficult to model such a geometry with spheres or clusters of spheres in a conventional discrete element method (DEM). In this study, we present a new DEM for plate-shaped particles with a focus on particle geometry and kinematics. The moment of inertia for a general convex plate is given and unit quaternions are adopted to represent the angular degrees of freedom. In addition, the equation of motion for rotation is proposed to be solved in a body-fixed rather than in a space-fixed reference frame. We present simulations of the rotation of a system of plate-shaped particles under the conservation of angular momentum without external torque. The results demonstrate the necessity and importance of enforcing the unity constraint on the quaternions numerically solved from the equation of motion for rotation.