Preliminary results unifying discontinuous deformation analysis (DDA) and the distinct element method (DEM)

Abstract

Discontinuous deformation analysis (DDA) and the distinct element method (DEM) are discrete element methods for solving the same class of problems: the elements are rigid or homogenously deformable, and contacts form and break as the system evolves in time. Both methods were originally developed algorithmically, DDA using the principle of virtual work and DEM from the balance equations. Differences between the two methods are algorithmic: coupled contacts (DDA) versus uncoupled contacts (DEM), and right Riemann time integration in accelerations (DDA) versus central difference time integration in velocities (DEM). Here a theory for discrete element methods is developed based on Cosserat points, taking an algorithmically neutral point of view. Changing the point of view away from algorithmic details exposes the mechanics underlying discrete element technology. Application of Hamilton’s principle of least action applied to the resulting lagrangian induces the balance equations, which are discretized using generalized Newmark schemes. Notational conventions useful for specific numerical implementations (DDA or DEM) may then be chosen by practitioners according to taste and utility.