The discrete element method (DEM) in Abaqus is intended for modeling events in which large numbers of discrete particles collide with each other and with other surfaces. It is not meant for modeling deformation of a continuum but is useful for simulations involving discontinuous media such as gravel. DEM can be used together with finite elements for modeling discrete particles interacting with deformable continua or other rigid bodies.
IMAGE: Mixing of 7 species of grains exhibiting fragmentation
VIDEO: Mixing of 7 species of grains exhibiting fragmentation
Although PD3D elements that represent discrete particles in a DEM simulation in Abaqus are rigid spheres, it is possible to model grains of complex shapes by clustering together several of these elements. Variation in the number and sizes of PD3D elements connected together to form a cluster allow approximating any complex shapes like ellipsoids, cubes, cylinders etc. Fig 1 shows some approximations of various shapes using clusters of PD3D elements in Abaqus.
Fig 1 Approximation of various shapes using clusters of PD3D elements in Abaqus
The group of particles in a cluster can be held together either using constraints or connectors. BEAM-type multi-point constraints can be defined between nodes of a group of particles to create a rigid cluster. Fig 2 shows an example of a BEAM-type multi-point constraint holding together two PD3D elements forming a rigid cluster.
Fig 2 BEAM-type multi-point constraint holding together two PD3D elements forming a rigid cluster
Connector elements can be defined between nodes of PD3D elements to create a rigid or deformable cluster. Appropriate constitutive behavior can be defined for the connector elements to capture compliant behavior for particle connections within a cluster. This capability also allows the modeling of particle fragmentation. Fig 3 shows examples of connector elements with failure definition holding together multiple PD3D elements forming a cluster that can exhibit fragmentation.
Fig 3 Connector elements with failure definition holding together multiple PD3D elements forming a cluster that can exhibit fragmentation
The particles in a cluster may overlap with each other. Contact forces that try to push apart overlapping particles of a cluster will exist unless contact exclusions are specified among particles of a cluster. It is not possible to generate clusters of PD3D elements using the particle generator tool in Abaqus. However, the setup of initial configuration of large number of clusters can efficiently be automated by writing a python script.
The time increment size for a stable and accurate DEM analysis depends on several different factors, such as the underlying contact properties, the size of the particles, and the relative motion of the particles. Since these controlling factors are problem dependent and vary during the analysis, choosing an appropriate direct time increment for a DEM analysis can be difficult. When the Hertz or JKR-type pressure over-closure is specified, Abaqus/Explicit automatically controls the time increment size to achieve a stable and accurate solution. This is a new DEM feature introduced in Abaqus 2017.
Fig 4 Mixing of 7 species of grains exhibiting fragmentation
An example simulation of mixing of 7 different species of grains (clusters) has been presented here (model with fictitious properties intended for demonstration purposes only). The grains fall down from their initial configuration to the base of the mixer container under gravity in the first step. In the second step, the mixer blade starts rotating about its longitudinal axis and revolving around the longitudinal axis of the mixer container mixing together all 7 species of grains. Fig 4 shows this process and fig 5 shows the arrangement of grains before and after mixing.
Fig 5 Grain arrangement before (left) and after (right) mixing
Forces are generated in the connector elements holding together the individual PD3D elements forming the grains due to collision of the grains with the mixer blade, with other grains and with the mixer container. The clusters for which the components of forces in the connector elements exceed the user specified failure limit fail causing cluster fragmentation. Fig 6 shows the total force in some of the connector elements for this simulation. Fig 7 shows grains of one species before (left) mixing and after mixing (right) showing fragmentation.
Fig 6 Total force in some of the connector elements
Fig 7 Grains of one species before (left) mixing and after mixing (right) showing fragmentation
The input file of this demo model is attached. Here are some resources for more information related to this topic:
1. Abaqus User Documentation
2. Particle Methods in Abaqus: DEM vs. SPH Online Class (https://www.3ds.com/products-services/simulia/services/training-courses/schedule-registration/)
3. SIMULIA Learning Community Webinar – ‘Particle Methods in Abaqus: DEM vs. SPH [Webinar]’ (https://swym.3ds.com/#post:42319)
4. SIMULIA Learning Community Article – ‘Getting Started with Discrete Element Method in Abaqus (with and without Particle Generator)’ (https://swym.3ds.com/#post:41370)
