A number of physical situations require us to model contact, and achieving proper load
transfer between the contacting bodies is essential in those cases.
However, in some mechanical assemblies, the components may not be touching each other
initially.
In such cases, contact between those components may not be detected and this may result in
rigid body motion, which we can not solve for in a static analysis since the matrix
is singular.
Ansys Mechanical has a few options to overcome these challenges and help achieve contact
in such cases.
In this video, we will discuss the challenges associated with rigid body motion between
contacting surfaces.
We also demonstrate one possible way of resolving the issue by using Contact Stabilization Damping.
Ready? Let's go!
When we model contact, we expect force transfer to occur between the contacting bodies.
This force transfer occurs only when the parts are touching each other.
If there is an initial gap, which in Ansys Mechanical shows up as an Open status for
the contact, the initial contact stiffness is zero.
This may result in convergence issues due to rigid body motion, and the inability to
obtain a solution.
Such convergence issues due to the presence of an initial gap are especially common when
the simulation is force-controlled.
You can think of it this way.
In a simplified expression of the equation of motion F=K*U, and solving for u, we have
displacement equals Force divided by stiffness.
If the stiffness is zero, the displacement is infinite, and hence we call this
rigid body motion.
Another challenge we may face is that in some cases, two parts may appear to be touching
each other, but there may still be a small numerical gap present.
For example, consider a case where we have geometry with some curvature.
When we mesh this geometry, the curvature is approximated by a finite number of straight
element edges, if we use lower order elements.
In such cases, although the initial solid bodies were in contact, the meshed
bodies may have some initial numerical gap between them.
So how do we deal with such challenges?
There are a few ways to get around these issues.
The first and probably the most obvious one is to move the CAD bodies to touch each other.
But, in a complex assembly, such as the one shown here, it is not easy to move the
CAD parts without affecting the rest of the assembly.
Even so, despite the solid bodies visibly being in initial contact, there may still
be a numerical gap left.
If this is the case, or due to some other reasons where you cannot move the CAD parts
to establish initial contact, we can use the Adjust to Touch option.
To use this option, select the contact where the initial gap occurs.
Under its Details, go to Geometric Modification, then Interface Treatment and choose the
Adjust to Touch option.
This would adjust the contact such that there is no gap between the contacting bodies.
However, in some cases, this may change the nature of the problem.
For example, consider this front end loader bucket model.
After heavy use, there may be some wear and tear in the joints over time and this may
create some clearance between the components of the pin joint.
Using the Adjust to Touch method would remove this clearance which does not represent the
physical situation correctly.
For such cases, we can use Contact Stabilization Damping.
Since the two components are not in contact initially, there is bound to be some rigid
body motion between the two till contact is established.
Contact Stabilization Damping introduces damping between the contact and target element faces
that resists the relative motion via a damping force that is proportional to their
relative velocities.
The Contact Stabilization Damping can be thought of as a viscous dashpot connecting
the target and contact surfaces.
It is a helpful tool, but the value we specify for it requires careful consideration.
If the damping value is too low, contact damping will be ineffective and we might continue
to have convergence issues.
On the other hand, if a very high value of damping is specified, that case can be visualized
as a very viscous fluid filling up the gap between the two bodies.
In such a case, excessive forces may be transferred between the two surfaces while still being
in an Open state.
This is why it is important to use an appropriate value of Contact Stabilization Damping.
When the two bodies touch each other and the contact is closed, their relative velocities
essentially become zero, due to which the damping force applied is also gradually decreased.
Contact Stabilization Damping does not have a physical basis, and is only a numerical
technique used to achieve convergence.
Thus, any energy contributed by Contact Stabilization is an artificial artifact and should be kept
to a minimum.
After solving a system, it is important to check the Stabilization Energy and ensure
that it is a small percentage of the strain energy.
Some of you may be familiar with another form of Stabilization available in Ansys Mechanical,
known as Nonlinear Stabilization, and it's important to understand when to use these
two different Stabilization methods.
Nonlinear Stabilization also helps prevent rigid body motion, but it is used for solving
a model with global instability such as buckling, a plastic hinge or other.
Contact Stabilization on the other hand acts locally at the specified contact and is used
when the rigid body motion occurs due to initial gap between contacting parts.
Let’s use an example to illustrate the use of Contact Stabilization Damping.
The example we will use is a pin in a hole which is extremely common in structures and
is used to transfer load and permit rotation.
We may find such connections on heavy equipment or in a building or even a bridge.
Let’s use this bucket loader for our example, and we will focus on a small portion of the
model for simplicity.
Our goal is to obtain the localized stress distribution in the pin/hole connection.
Let’s look at a section cut to show how it is assembled.
If the pin and hole are modeled with no gaps, then we are likely to achieve load transfer
across the joint and not experience rigid body motion.
As we mentioned we may need to set the behavior on the contact to Adjust To Touch to account
for any numerical gaps, but in this case, that would change the physics of the problem
if we wished to retain the clearance between pin and hole.
While we are using a small portion of the model, recall that moving the CAD parts to
physically touch, though ideal, may be challenging when modeling an entire, complex assembly.
Thus, in this case, we are considering a situation where we are not able to move the CAD parts
to the just touching position while wishing to maintain the clearance between the pin and the hole
Thus, Contact Stabilization Damping can be helpful in such situations.
For our setup we have the bucket fixed on these faces.
The arm with the integrated pin is pulled with a large force as shown.
We also hold the arm in the local y and z directions to keep the arm from rotating and translating,
but it is free to move in the direction of the force application.
For simplicity of this example, we have not included the contact between the plates, so
as to focus our attention on the contact between the pin and the hole.
This is the reason we need to constrain displacement in the z-direction.
However, in actual practice, we would include those contacts and then we would not need
to fix the displacement in the local z-direction.
Asymmetric frictionless contact is setup between the pin and the hole.
Now let’s insert the contact tool, generate the initial contact results.
and check the status of the contact.
We see that the contact is in an Open state by the status of Near Open and a large gap
is indicated.
In the Analysis Settings we have turned on Large Deflection,
then Automatic Time Stepping with initial substeps of 5, maximum of 20
and minimum of 1. Let’s run the model.
Ok, we see the solver stops and if we look at the Solution Information Solver Output,
we can see some messages.
The first message indicates that the model is experiencing rigid body motion.
The second message tells us to check the contacts to make sure they are closed.
Since the contacts are Open, for this specific case, we need some type of stabilization to
get past these errors.
Since we know we have an Open contact, we can use a stabilization scheme which will
affect only the contact region and not affect the entire model on a global level.
For this reason, we do not use the Nonlinear Stabilization, but instead choose the
Contact Stabilization Damping.
To include Contact Stabilization Damping for this contact , go to the Details of the contact
and under Advanced, specify the value of Stabilization Damping Factor to be 0.05.
The value chosen may require trial and error as the damping factor can be very
problem specific and there is no clear, simple way to compute the appropriate value.
As mentioned before, we need to be careful when using Contact Stabilization Damping.
This is an artificial damping scheme used to aid in numerical convergence, and there
is no physical basis for Contact Stabilization Damping.
So, any energy contributed to the model due to Contact Stabilization is artificial energy
and hence it needs to be very small compared to the physical strain energy, so as to not
change the physics of the problem.
For this reason, whenever we use Contact Stabilization, it is a good practice to monitor the
Stabilization Damping Energy.
To do this, right-click on Solution Information, Insert Contact.
In the Details window, under Definition, select the Type to be Stabilization energy and choose
the appropriate contact in the Contact Region.
We also right-click on Solution Information and Insert Stiffness Energy Tracker, which
represents the stiffness energy, also known as the Potential energy of the entire system.
Let’s go to the Solution branch and Insert Total Deformation and Equivalent Stress.
Now let’s solve the simulation.
The simulation solves to completion this time.
Before we look at any of the global results, let’s look at the Contact Stabilization Energy
and ensure that it is very small as compared to the Stiffness energy.
To plot the two energies together, press Ctrl and select the two trackers.
We see that the Contact Stabilization energy, which is an artificial energy, is very small
as compared to the physical Stiffness energy.
So Contact Stabilization Damping has not changed the physics of this problem.
We can then move on to check the global contours of Total Deformation and Equivalent Stress
Here we can see the pin is in contact with the hole, and the stress plot shows that
force is being transmitted.
Looking at this with the section cut to see inside, we can also confirm that the pin is
indeed in contact with the hole.
Likewise, we can verify the force balance, by dragging and dropping our Fixed Support
onto Solution to give us the reaction force from the Fixed Support.
Here we can see the reaction force matches our applied force and hence proper load transfer
has occurred.
So let’s summarize the important points in this video.
First, we learnt that rigid body motion may occur due to the initial Open status of contacts.
Hence, it is important to ensure that contacts are defined properly, without initial gaps.
There are several options available to prevent rigid body motion for nonlinear contacts,
such as moving the CAD bodies, or using the Adjust to Touch Interface treatment.
If neither option may suffice, then we can use Contact Stabilization Damping.
We need to be careful while using this option and pick a proper value of the Contact Stabilization
Damping, such that the Stabilization energy is very small as compared to the
Stiffness energy of the entire system.
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To find more information about preventing rigid body motion in contact or other topics,
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