The discrete element method with deformable particles

Abstract

Summary This work presents a new original formulation of the discrete element method (DEM) with deformable cylindrical particles. Uniform stress and strain fields are assumed to be induced in the particles under the action of contact forces. Particle deformation obtained by strain integration is taken into account in the evaluation of interparticle contact forces. The deformability of a particle yields a nonlocal contact model, it leads to the formation of new contacts, it changes the distribution of contact forces in the particle assembly, and it affects the macroscopic response of the particulate material. A numerical algorithm for the deformable DEM (DDEM) has been developed and implemented in the DEM program DEMPack. The new formulation implies only small modifications of the standard DEM algorithm. The DDEM algorithm has been verified on simple examples of an unconfined uniaxial compression of a rectangular specimen discretized with regularly spaced equal bonded particles and a square specimen represented with an irregular configuration of nonuniform‐sized bonded particles. The numerical results have been verified by a comparison with equivalent finite element method results and available analytical solutions. The micro‐macro relationships for elastic parameters have been obtained. The results have proved to have enhanced the modeling capabilities of the DDEM with respect to the standard DEM.

Convergence and stability analysis of the deformable discrete element method

“…As a consequence of this modification, the formation of new contacts has been induced and a nonlocal contact model with mutual dependence of the contacts experienced by the particles has been obtained. A similar effect, the nonlocal contact model and formation of new contacts, has been obtained by Rojek et al assuming the particles are deformed globally under the uniform internal stress. It has also been shown that the deformable DEM (DDEM) developed in the work of Rojek et al broadens the range of the macroscopic Poisson's ratio in comparison to the values achievable in the standard DEM (SDEM).…”

“…The normal force f n combines with the tangential contact force f T yielding the total contact force between the considered pair of particles f c expressed as In this work, it is assumed that the tangential contact force is unaffected by the particle deformation, and it is calculated taking any model used in the SDEM. In general formulation, other contact force components such as damping force can also be included in the contact interaction model (cf the work of Rojek et al). Here, in order to keep the simplicity of the analyzed formulation, we will focus on the evaluation of elastic normal force given by Equation .…”

“…The iterative solution within the explicit time integration that is used in the DEM would spoil its major advantage—an efficient solution for a single time step. Therefore, the solution algorithm proposed in the work of Rojek et al employs an explicit dependence, which can be written generally as follows: The contact forces at the n th time step are evaluated taking the strains obtained for the contact forces from the previous time step. The algorithm for the deformable discrete elements is incorporated into the explicit time integration solution.…”

“…Numerical studies have comprised simulations of uniaxial compression of rectangular samples discretized with particles arranged in the regular SC and HCP configurations and a more realistic square sample with particles arranged in an irregular configuration. The results have allowed us to establish the criteria for choosing microscopic parameters in the calibration of the DDEM models, cf the work of Rojek et al, ensuring a stable solution.…”

“…This work is aimed to study numerical properties of the solution scheme employed in the DDEM and presented in the work of Rojek et al In the DDEM formulation, the volume‐averaged stress derived in terms of contact forces is taken as particle stress from which strains are evaluated using the inverse constitutive relationship. The contact forces are evaluated in terms of overlap of the globally deformed particles, which in turn determines the particle deformation, hence implying an implicit relationship for the contact forces.…”