On the adhesive JKR contact and rolling models for reduced particle stiffness discrete element simulations

Abstract

Discrete Element Method (DEM) simulations are a promising approach to accurately predict agglomeration and deposition of micron-sized adhesive particles. However, the mechanistic models in DEM combined with high particle stiffness for most common materials require time step sizes in the order of nano seconds, which makes DEM simulations impractical for more complex applications. In this study, analytically derived guidelines on how to reduce computational time by using a reduced particle stiffness are given. The guidelines are validated by comparing simulations of particles with and without reduced particle stiffness to experimental data. Then two well-defined test cases are investigated to show the applicability of the guidelines. When introducing a reduced particle stiffness in DEM simulations by reducing the effective Young's modulus from E to E mod , the surface energy density γ in the adhesive Johnson-Kendall-Roberts (JKR) model by Johnson et al. [1] should be modified as γ mod = γ (E mod /E) 2/5. Using this relation, the stick/rebound threshold remains the same but the collision process takes place over a longer time period, which allows for a higher time step size. When rolling motion is important, the commonly used adhesive rolling resistance torque model proposed by Dominik and Tielens [2, 3], Krijt et al. [4] can be used by modifying the contact radius ratio (a/a 0) 3/2 to (a mod /a 0,mod) 3/2 , whilst keeping the other terms unaltered in the description of the rolling resistance torque M r,mod = −4F C (a/a 0) 3/2 ξ. Furthermore, as the particle stiffness is reduced from E to E mod , the time period for collisions (or oscillations when particles stick upon impact) ∆t col is found to vary as ∆t col,mod = ∆t col (E/E mod) 2/5. As the collision duration and the collision time step size are directly related, this criterion can be used to estimate how much the time step size can be changed as a reduced particle stiffness is introduced. Introducing particles with a reduced particle stiffness has some limitations when strong external forces are acting to break-up formed agglomerates or re-entrain particles deposited on a surface out into the free stream. Therefore, care should be taken in flows with high local shear to make sure that an external force, such as a fluid drag force, acting to separate agglomerated particles, is several orders of magnitude lower than the critical force required to separate particles.

Jamming during particle spreading in additive manufacturing

“…We therefore follow the criterion proposed by Behjani et al [36], Haervig et al [37] and Washino et al [38] for scaling down Young's modulus and adhesive surface energy, so that the time step can be increased significantly:…”

A fast adhesive discrete element method for random packings of fine particles

“…Kobayashi et al (2013) simply regarded the adhesive force as a constant external force and then reduced it to recover the original value of the critical sticking velocity. Similar ideas were adopted by Gu et al (2016) and by Haervig et al (2017), who modified the van der Waals force between particles to conserve the cohesive energy during a quasi-static two-particle collision, and by Washino et al (2018) who derived a series of generic scaling to modify external attractive forces. In these previous studies, the adhesive force model has been modified based on the simple case of binary collision, thus is suitable only for the collision-dominated process, like fluidization process with a velocity much higher than the minimum fluidization value (Kobayashi et al, 2013;Gu et al, 2016) or powder flow in a mixer with high rotating rate (Washino et al, 2018).…”

“…And a remarkable increase of the critical sticking velocity v C , defined as the maximum impact velocity at 5 which a particle hitting the surface will stick (i.e., e = 0), is also observed. To address this issue, it has recently been suggested that a reduced surface energy should be used to balance the nonphysical effect caused by reduced stiffness so that the outcome of the collision will remain the same (Haervig et al, 2017;Washino et al, 2018). Figure 2: The coefficient of restitution e as a function of impact velocity v 0 for particles with Youngs modulus E = 10 8 Pa (circles), 5×10 8 Pa (squares), and 10 9 Pa (diamonds).…”

A methodology for calibration of DEM input parameters in simulation of segregation of powder mixtures, a special focus on adhesion

“…Nevertheless, it is a very computationally expensive method for modelling a real granular process, as the number of particles in practice is excessive. This shortcoming is partially compensated by scaling-up the particle size, scaling-down the materials stiffness, and/or using simplified representation of particles (coarse-graining) in DEM simulations [1,2]. This helps modelling the process by a smaller number of computational elements and larger time steps than for the real system, both of which significantly reduce the computational cost.…”

“…Utilising a scaled DEM input parameter adventitiously may produce misleading results. The scaling issue becomes more critical when the materials under study are cohesive, where depending on the utilised contact model, scaling the particle size and stiffness changes the interparticulate attractive forces considerably [2,3]. This change in micromechanics of the granular system leads to unrealistic bulk behaviours.…”