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What Is Friction? - And How Do We Account For It In FEA?

Friction is an important concept taught in every introductory physics class. However, it is commonly ignored or overlooked when solving physics problems or when performing FEA. In this blog, we will go through what friction is and how we can utilize it in FEA.


What Exactly Is Friction?


Friction is the resistance encountered when objects in contact slide against each other. The basic formula for friction, known as Coulomb’s friction model, is:



Where F is the frictional force, µ is the coefficient of friction, and N is the normal force between the two surfaces. Some properties of friction are:


  1. The coefficient of friction is dependent on the nature of the surfaces in contact – essentially, a higher coefficient of friction means there’s more resistance to sliding. The case of rubber sliding on concrete is an example of a high coefficient of friction – this is how tires are able to grip the road. However, the case of a hockey puck sliding on ice is an example of a low coefficient of friction. Typically, rough and coarse surfaces in contact have higher coefficients of friction while smooth surfaces in contact have lower coefficients of friction.

  2. Friction does not depend on the contact area of the surfaces.

  3. Friction is independent of velocity.

  4. Friction is a nonconservative force – this means the amount of work that friction does depends on the path taken.

Friction can be categorized into a few different types. The main two we’ll be going through in this blog are static and kinetic friction. Other types of friction include fluid friction and rolling resistance. 

 

Frictional Contact in FEA
 

Static friction acts between surfaces at rest. It resists the applied force between the objects. On the other hand, kinetic friction, also known as sliding friction, acts between surfaces moving relative to each other. The kinetic coefficient of friction, µk, is always less than the static coefficient of friction, µs. What this means is that it takes less force to keep an object in motion than to get it started moving in the first place. If you’ve ever tried to slide a heavy box along a floor, you can see this in action – it takes a lot more effort to start moving the box than to keep it moving!


An Example


 
Frictional Contact in FEA
 

As a quick example, let’s use two blocks sliding against each other. We can calculate the maximum static friction force as Ff = µsN = 0.25(100) = 25 N. Static friction will counteract the pushing force F at any value 25N or below. So, if we pushed the block with F = 18 N of force, Ff would be 18 N as well. If we pushed the block with F = 25 N of force, Ff would be 25 N. However, if we pushed the block with F = 30 N of force, Ff would be 25 N initially. Since there is now a resultant force, the upper block will begin moving, meaning kinetic friction will be used instead. The magnitude of kinetic friction is Ff = µkN = 0.20(100) = 20N.


When To Use Friction In FEA


Friction should be added to your contact definition if it is expected that loads will be transmitted along the contact plane. Some applications include bolt preload, tires, and metal forming.


Setting Up Friction In ABAQUS CAE


We can set up friction in Abaqus CAE as an interaction property. In the interaction module, create an interaction property, then select “contact” as the type. From there, create a tangential behavior:

 
Frictional Contact in FEA

Frictional Contact in FEA
 

Abaqus offers different friction formulations. I’ve summarized them in the sections below along with the results of an example. This example is the same setup as the hand calculation example earlier, except that instead of pushing the top block with a force, a velocity of 10 mm/s was applied in the x direction for one second instead. Normal contact behavior was also included, and surface-to-surface discretization was used.


Frictionless Contact In ABAQUS


This allows surfaces in contact to slide freely without friction (µ = 0).

 
Frictional Contact in FEA
 

In our example, the upper block was able to slide with no reaction force in the x direction. Pretty uneventful!

 

Penalty Friction In ABAQUS


This permits some relative motion of the surfaces (an “elastic slip”) when they should be sticking. This is the default way to define friction in Abaqus as this method is a lot easier to solve and the elastic slip is a very small fraction of the element length. This formulation works well for most static applications.

 
Frictional Contact in FEA
 

For our example, we got an x reaction force of 25 N, which is exactly what we’d expect from Coulomb’s friction model.


Static-Kinetic Exponential Decay Friction In ABAQUS


This allows the static and kinetic friction coefficients to be defined directly, assuming that the friction coefficient decays exponentially from the static value to the kinetic value.


Frictional Contact in FEA

In the above equation, dc is the decay coefficient and  is the slip rate. This formulation works well for dynamic loads where the slip rate changes over time.

 
Frictional Contact in FEA
 

We can calculate the expected x direction reaction force from our example to be:


Frictional Contact in FEA

If we were to change the slip rate,  (in this case, the prescribed velocity of the upper block), our friction force would change accordingly.

 

Rough Friction In ABAQUS


This prevents slipping regardless of contact pressure (µ = ∞).

 
Frictional Contact in FEA
 

With rough friction, the reaction force in the x direction diverges and the model does not solve since I’m applying a velocity on a component that can no longer move.


Lagrange Multiplier Friction In ABAQUS


This enforces the sticking constraints at an interface between two surfaces exactly. This method is only available in Abaqus/Standard. Using the Lagrange multiplier not only increases the computational cost of the analysis but also usually increases the number of iterations required to converge. Sometimes, this may even prevent convergence completely, so I would only recommend using this for applications where the stick/slip behavior is absolutely crucial for results.

 
Frictional Contact in FEA
 

In our example, I get an accurate reaction force, but the job does not solve, as it experienced slipping contact chatter, as can be seen in the plot below of the last increment before the job fails:

 
Frictional Contact in FEA
 

When we switch the contact definition to use node-to-surface discretization, the analysis converges properly:

 
Frictional Contact in FEA
 

User-defined Friction In ABAQUS


If none of the other friction formulations are sufficient, the friction model can be defined through a user subroutine. With a user-defined friction model, the shear stress due to friction can be defined as a function of a number of variables, including slip, slip rate, and temperature.


Final Thoughts


In summary, friction is the sliding resistance encountered between two objects in contact. It is proportional to the normal force between the objects and is also affected by the materials of the objects in contact. Abaqus offers several different formulations for modeling friction to match all kinds of analysis needs.


However, there are many problems and modeling techniques involving friction that are a lot more complex than what I’ve been able to cover in this blog. If you’re struggling with a particularly difficult friction problem, our expert engineers are here to help! Reach out to us today!

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