Welcome to this Ansys How To Series video.
Hyperelastic materials are intended to represent a class of materials known as elastomers.
A typical application of elastomers is in sealing where the material is undergoing a
large deformation.
The stress-strain relationship of hyperelastic materials is usually highly nonlinear.
Different from plastic materials which are also nonlinear, the deformation of hyperelastic
material is not permanent, meaning that the deformation is recoverable upon unloading.
During the deformation, there is often negligible volume change for hyperelastic materials.
We call this incompressible behavior.
Also, such materials can perform differently in tension, compression, and shear.
Because of these unique challenges, such materials are typically represented mathematically by
a strain energy density expression, from which stresses and strains are derived.
Given stress-strain data from experiments for a specific material, engineers usually
do curve fitting to find out the parameters needed for hyperelasticity model.
And these parameters will be used to fully describe stress strain relationship.
However, what if the stress-strain data we have in hand is uniquely complex and cannot
be well captured by the conventional strain energy density functions?
In this How To video, we introduce the response function feature provided by Ansys.
By this method, instead of curve fitting for a hyperelasticity model, we can directly utilize
the experimental data to simulate the hyperelastic materials.
Hyperelasticity is a type of mathematical material model people developed to describe
the behavior of certain materials.
Theoretically, we can only call a material hyperelastic when there is a strain energy
density function that exists for it.
Let's use capital "W" to represent a certain strain energy density function.
Depending on different hyperelasticity models, the expression of "W" is different.
The derivative of "W" with respect to a strain component determines
the corresponding stress component.
This leads to the stress strain relationship for the hyperelastic material.
In simulating hyperelastic materials, engineers are usually given stress-strain data from experiments.
For example, from tensile test, shear test, biaxial test etc.
With this data, one can choose an appropriate strain energy density function
to do curve fitting.
However, a question arises at this point.
Can all experiment data be curve fitted to a hyperelasticity model in an exact manner?
Unfortunately, the answer is no.
Although varieties of hyperelasticity models have been developed, it might happen that
the data you are given might not fit any of them to sufficient accuracy.
For such cases, Ansys provides "Response Function" as an alternative method in characterizing
hyperelastic material behavior.
Response Function is uniquely designed to derive the stress state directly from
experimental data.
Note that Response Function is still based on the idea of using a strain energy density
function to characterize the material.
The difference here is that the use of strain energy density function is implicit without the need
to find the expression.
So, this term, the derivative of "W" with respect to strain component will be directly related
to the test stress-strain data.
Compare to Curve Fitting method, Response Function is easier to set up as it only needs
to read in the test data.
It is able to handle more complex nonlinear stress-strain relationship that conventional
method cannot.
However, we all know there is no such thing as a free lunch.
Using Response Function put some limitations of the input test data
and the simulation as well.
First of all, the test data must envelop the full range and should include all modes, including
tension, compression and shear of stress states expected in the application.
And also, Response Function method may be slightly more computationally expensive in
terms of number of iterations to solve and CPU run time.
Now let's move to an example using Response Function to solve for hyperelasticity.
In this exercise, we are given experimental data that represents the combined uniaxial
stress-strain relationship in both tension-compression.
By way of background information, the phenomenological behavior of this material fits that of
a long chain molecular structure that is highly nonlinear and elastic with different behaviors in
tension and compression.
Hence, the material is an elastomer and should be represented with one of
the hyperelastic options.
The question to consider first is, of the many options available, which one would best
be suited to represent this material in a real-world application?
For this particular application, a logical first step would be to try curve fitting the
data to one or more of the standard options available under the Hyperelastic folder
available in Engineering Data.
To do this, the uniaxial compression data is first converted into the equivalent equibiaxial
format and read in separately from the tension data.
We then run the curve fitter for different conventional options.
Notice how the curve fit for Yeoh Model seems to be ok for a lower strain range.
However, for the higher strain range, the fit appears to break down.
In this particular example, if the application were not going to be loaded into this higher
strain range, perhaps we could accept one of these options.
However, what if the application will load the material into this higher range as well?
This is where the Response Function can be very helpful.
To implement the Response Function, we begin by creating a new material model
in Engineering Data.
Expand the Hyperelastic Folder and insert the Response Function.
The original experimental stress-strain curve, with compression and tension combined together,
is then read in as Uniaxial Test Data.
That is it!
No curve fitting required.
From here, the response function material is ready for use.
At this point, it is worth digressing briefly to discuss the various options for
entering the experimental data for use with the Response Function.
The so-called Response Function is the derivative of "W" with respect to the
first or second strain invariants, which provides information on the stiffness of
the material in different modes of deformation.
When we use combined uniaxial tension and compression, then only the derivative with
respect to the first strain invariant is used, which typically provides a reasonable approximation
for other modes of deformation, knowing that we don't even have such data entered.
On the other hand, we can input uniaxial tension, uniaxial compression or equibiaxial tension,
and planar shear doing so we will use the derivative with respect to the second strain
invariant, which results in more accurate modeling, but the downside is that, if you
don't have enough data, the derivative with respect to the second strain invariant can
more easily lead to non-physical behavior.
Thus, the takeaway is that, if you have limited test data, use combined uniaxial
tension and compression.
If you have more data, then use 3 sets of test data, preferably.
In our case, since we have combined tension and compression data we imported this combination
as Uniaxial Test Data.
So now we are ready to use this material in the model.
Again, no curve fitting is needed with the Response Function.
From here, we now open the Mechanical GUI.
The geometry in this demo represents a typical section of a standard pull test specimen that
might have been used to generate uniaxial stress-strain data.
If this material data set is being used for the first time, this is always a good place to start.
Such a model can be used to echo back the original data as a means to validate the material
model selection and setup before moving on to your real-world application.
That is what we are going to do here.
Since this model represents a pull test specimen, we will only be validating the tension part
of the stress-strain curve.
Under the geometry folder, we reassign the material to the newly created material that
we called "Elastomer (RF)".
It should be available in the pulldown menu of the details window.
Under the mesh folder, we force lower order elements.
This is recommended for hyperelastic materials as it will reduce the likelihood of element
formulation errors that can sometimes occur with higher order elements
under excessive distortion.
The boundary conditions are setup to represent the pull test scenario.
The Analysis Settings are specified sufficiently to capture enough solution sets so as to generate
an accurate stress-strain representation.
Note, since this is a hyperelastic material, Large Deflection must be turned ON.
We are now ready to run the analysis.
Once the solution is complete, chart tools have been setup under the solution branch
to extract the force deflection curve and uniaxial stress strain curve.
The derived results are represented as true stress- strain.
In order to echo back the original test data, these results are exported into a separate
Excel spreadsheet and a simple conversion to engineering stress-strain data is performed.
After this conversion, we can see that the Response Function hyperelastic material model
does in fact follow the experimental stress-strain data in tension, even at the highest
strain levels.
It is worth mentioning that once the loading exceeds the original experimental data,
we can expect the force deflection curve to become a flat line.
The hyperelastic materials are intended to represent a class of materials that exhibit
highly nonlinear behavior with large deflection and different responses
in different modes of loading.
Because of complexities in stress-strain relationships, the conventional hyperelastic strain energy
density functions are not always sufficient to fully characterize the material.
The Response Function Hyperelastic option is designed to utilize the experimental stress-strain
data directly during constitutive calculation.
This method eliminates the need for curve fitting and provides a workable alternative
to overcome the limitations of the conventional method.
Response Function is easier to set up but requires that the experimental data completely
envelop the entire strain range of interest and it should ideally include the dominant
stress states encountered in the actual application.
To find more information about hyperelasticity or other topics, check our channel for more
How To videos and visit ansys.com/courses today!