The material laws such as Hooke’s law describe the mechanics within the body,
and this is captured by the governing equations of motion.
But these equations do not account for the mechanics between two different
bodies. This is captured by another form of constitutive model called as contact model.
When two objects come in contact, they exert forces on each other,
and this is how they detect each other. In this process, they may deform each other
and result in distribution of contact pressure over the area of contact.
Capturing this distribution is the main objective of the contact model.
The contact model is used to study how the forces are transferred between two bodies which in turn
helps us assess engineering designs.
For instance, ergonomically it is comfortable to sit on a foam cushion
as opposed to wooden or stone bench even though we exert the same force which is the body weight.
This is because the foam cushion is softer
and deforms so the same force is distributed over larger area and reduces contact pressure.
The contact forces when transferred between two bodies, can be split into two vector components,
one in the normal direction and the other in tangential direction.
The normal component tries to prevent the bodies from penetrating each other and the
tangential component tries to arrest any relative sliding between the bodies.
Depending on how these two components are developed between the bodies there are three
types of contacts that are generally seen. The bonded contact
The frictionless contact and The frictional contact.
There are still normal forces acting into the bodies that prevents them from penetrating which
is common among all three types. Let’s look at the each of these contact types and see
where the differences in contact forces arises.
Let’s start with the bonded contact. As the name suggests, in this type of contact,
the two surfaces are bonded to each other. So, they do not penetrate each other,
they do not separate from each other and they do not slide over each other.
So, both the normal and the tangential components
are so strong that they resist any force that tend to cause relative motion between them.
In other words, both the components tend to infinity as we apply more forces.
Such contacts are not physically possible but they’re very useful in modeling several
situations such as welded joints, adhesive contacts and even idealized bolted connections
where the mating surfaces remain attached until a limiting force is applied.
Now, let’s look at the next type of contact which is frictionless contact. This type of contact has
two main differences compared to bonded contact.
First, it does not offer any tangential force,
so the surfaces are free to slide over each other without any resistance.
Second, while it offers normal forces into the bodies to prevent penetration, it does not offer
out of body forces that can prevent the surfaces from separating.
This is also an unrealistic type of contact but it’s very useful in modeling systems such
as well lubricated surfaces, or objects that are mounted by magnetic levitation,
which is becoming popular among train transportation.
And finally, the frictional contact, perhaps the most commonly found contact type.
This contact type is like frictionless contact in terms of normal forces.
It resists bodies penetrating but does not resist the bodies separating from each other.
The complexity of this type arises in the tangential direction,
it offers a finite amount of resistance to sliding and the surfaces can slide over
each other only when the applied force is more than the frictional force.
So, if we apply Coulomb’s law of friction, which is a commonly used constitutive law for friction,
then the tangential contact force offered is nothing but
the product of the normal contact force to the coefficient of friction.
So, we discussed how the contact forces are decomposed into a normal
and a tangential component. But how are these forces calculated to begin with?
The contact forces at the interface of two mating surfaces depend on several factors such as
The material properties of both the bodies, the shape and surface roughness of the two bodies,
the kinematics of the bodies and many other factors.
An accurate calculation of contact forces
is the key in capturing contact behavior.