Introduction
The discrete element method (DEM) is an intuitive method in which discrete particles collide with each other and with other surfaces during an explicit dynamic simulation. Typically, each DEM particle represents a separate grain, tablet, shot peen, etc. DEM is not applicable to situations in which individual particles undergo complex deformation. Therefore, DEM is unlike, and conceptually simpler than, the smoothed particle hydrodynamic (SPH) method in which groups of particles collectively model a continuum body (see Smoothed Particle Hydrodynamics).
For example, DEM is well-suited for particle mixing applications, such as that shown in Figure 1. In this application DEM is used to model the initially separated blue and white particles, and rigid finite elements are used to model two mixing augers and the box-shaped container. The sequence of deformed plots in Figure 1 shows the particle response as the augers turn. DEM results for simulations such as this are often best viewed with animations. Another example of using DEM for a mixing application is described in Mixing of granular media in a drum mixer.

Each DEM particle is modeled with a single-node element of type PD3D. These elements are rigid spheres with specified radii. Nodes of PD3D elements have displacement and rotational degrees of freedom. Rotations of DEM particles can significantly influence contact interactions when friction is considered.
General contact definitions are easily extended to include interactions among DEM particles and interactions between DEM particles and finite-element-based (or analytical) surfaces. Large relative motion among particles is typical for DEM applications. Particle-to-particle interactions can involve like or unlike particles. Each particle can be involved in many contact interactions simultaneously. DEM particle interactions use finite contact stiffness, which introduces some compliance into the particle systems. For example, the contact stiffness can be specified such as to reflect the macroscopic stiffness of a packed granular material model with DEM.
For example, consider the interactions between the two spherical particles shown in Figure 2.

The three cases show two undeformed spheres just touching, two deformed spheres pushed toward one another with contact strictly enforced, and two rigid spheres pushed toward one another with some penetration. The distance between the centers of the spheres is the same for the cases shown in the middle and on the right in Figure 2. The physical behavior corresponds to the middle case. The case on the right corresponds to a DEM approximation. If the variable δ is defined as
where r1 and r2 are the radii of the two spheres and d is the distance between the sphere centers, δ=0 when the undeformed spheres are just touching and δ>0 if the distance between the sphere centers is less than the combined radii. For the DEM approximation, δ corresponds to the maximum penetration distance between the particles. You can improve the accuracy for some DEM applications by tuning the contact stiffness relationship (contact force F versus penetration δ ) for DEM particles to reflect the Hertz contact solution (middle case in Figure 2). See Mixing of granular media in a drum mixer for further discussion of tuning the contact stiffness.