Contact Force
When considering the motion of particles, numerous forces need to be taken into account. This means there are many factors to consider as “applied forces” in the equations of motion. These forces include “gravity,” “adhesive forces” between particles, “fluid resistance” when considering fluid interactions, and so on – the list can be extensive. Among these factors, the interaction force between particles, commonly known as “contact force,” is almost always crucial to consider, and it’s a distinctive aspect of DEM calculations.
Therefore, in this context, I’d like to focus on the concept of “contact force,” which is particularly significant when discussing the forces acting on particles.
Contact forces
Contact forces can be divided into two components: the normal contact force, acting perpendicular to the contact surface, and the tangential contact force, acting along the direction of contact. Together, these components form the complete contact force. In terms of their directions, the normal force acts along the line connecting the centers of the particles in contact, while the tangential force acts on the surface between the particles, as if a piece of paper were placed between them.
The equations describing contact forces involve combining the contributions of the normal and tangential forces, as illustrated in the equation below:
- Normal Direction Contact Force
The normal direction contact force on the contact surface can be divided into two types: the static normal contact force determined by the positions of the particles, and the dynamic normal contact force determined by the relative velocity difference between the particles.
- Static Normal Contact Force
One characteristic of particles considered in DEM simulations is that there are no strict restrictions on overlap. This means that overlapping can occur between walls or particles. The reason behind this is that overlap is utilized in the calculation of contact forces.
In the case of the static component of the normal direction contact force, the force is calculated based on the overlap between particles. The force becomes stronger as the overlap increases, exhibiting a repulsive nature.
- Dynamic Normal Contact Force
In the case of the dynamic component of the normal direction contact force, the force is calculated based on the relative velocity between particles. The force becomes stronger as the relative velocity increases, exerting a larger force on the particles.
Moreover, since we are considering relative velocities, the direction of the force also depends on whether one particle is moving faster or slower than the other particle.
- Tangential Contact Force
Similarly to the normal direction, the tangential contact force with respect to the contact surface can also be divided into static and dynamic components. The static tangential contact force depends on the relative positions of particles, while the dynamic tangential contact force is determined by the relative velocity between particles.
- Static Tangential Contact Force
Among the tangential contact forces, the static component is calculated based on the displacement of the contact point between particles. The force increases with larger displacements, exhibiting a repulsive behavior.
- Dynamic Tangential Contact Force
Among the tangential contact forces, the dynamic component follows a similar concept to the normal direction. It’s calculated based on the relative velocity between particles. The force becomes larger as the relative velocity increases, showing a tendency for stronger forces on particles with higher relative velocities. However, the directions of consideration differ. The calculation of dynamic forces in the normal direction and the tangential direction are based on the velocity components corresponding to their respective force directions.
Tangential Contact Force with Sliding Behavior
In the presented explanation of tangential contact forces, we did not consider situations where particles might exhibit a sliding behavior, also known as “slip.” If we were to account for sliding, how would the calculation of tangential contact forces change?
When sliding occurs, the frictional force between particles is considered as the tangential contact force. In other words, the equations used for calculating tangential contact forces would change between situations with and without sliding. This is because the behavior changes significantly between scenarios with and without sliding, making it natural for the equations to reflect these differences.
