Examining the smooth and nonsmooth discrete element approaches to granular matter

Abstract

SUMMARYThe smooth and nonsmooth approaches to the discrete element method (DEM) are examined from a computational perspective. The main difference can be understood as using explicit versus implicit time integration. A formula is obtained for estimating the computational effort depending on error tolerance, system geometric shape and size, and on the dynamic state. For the nonsmooth DEM (NDEM), a regularized version mapping to the Hertz contact law is presented. This method has the conventional nonsmooth and smooth DEM as special cases depending on size of time step and value of regularization. The use of the projected Gauss-Seidel solver for NDEM simulation is studied on a range of test systems. The following characteristics are found. First, the smooth DEM is computationally more efficient for soft materials, wide and tall systems, and with increasing flow rate. Secondly, the NDEM is more beneficial for stiff materials, shallow systems, static or slow flow, and with increasing error tolerance. Furthermore, it is found that just as pressure saturates with depth in a granular column, due to force arching, also the required number of iterations saturates and become independent of system size. This effect make the projected Gauss-Seidel solver scale much better than previously thought.

Particle-based solid for nonsmooth multidomain dynamics

“…The versatile and widely used discrete element method (DEM) [6] for simulating particulate solids have been extended to the framework of nonsmooth dynamics [4,5,7,8]. When the lengthscale of deformations is much larger than the particle size, it is more computationally favourable to Fig.…”

“…This becomes straightforward when the regularisation is introduced by potential energy as quadratic functions in g, i.e. U ε (q) = 1 2 g T ε −1 g. This has been exploited in previous work to constraint-based mod-elling of lumped element beams [29], wires [30], meshfree fluids [31], and granular material [8].…”

“…2.3 and in greater detail in [8]. A contact situation between a solid and three rigid bodies is illustrated in Fig.…”

“…Experiments show that further iterations do not necessarily reduce the errors. For large contact systems (>1000 contacts), with many complementarity conditions, both normal and friction constraints may be moved to an iterative projected GaussSeidel solver [8].…”

Outlet design optimization based on large-scale nonsmooth DEM simulation

“…In the present paper we use a nonsmooth DEM (nDEM) [8] approach, also referred to as the nonsmooth contact dynamics method [6]; [3]. The particular variant of nonsmooth DEM used in the present paper is described in more detail in an accompanying paper [10]. The nonsmooth approach allows for time integration using time-steps much larger than the characteristic elastic response time and considerable speed-up can be achieved as compared to standard, or smooth, DEM.…”