High Deformation Elastomeric Materials
Rubber Seals, Dampers, Foams… How to Deal with Hyperelastic Materials?
Hyperelastic constitutive laws are used to model materials that respond elastically when subjected to very large strains. They are mainly used to model rubber-like behavior of polymers and foams subjected to reversible deformations. Typical examples include rubber seals and elastomer parts for dampening vibrations or shocks.
If you are simulating hyperelastic parts, what is the best procedure? In no specific order, here are some of the important steps in preparing your simulation model:
- Get the appropriate material data, possibly from experiment (uniaxial, biaxial and shear testing)
- Find the material model that best represents the data
- Make sure the geometry is appropriate for simulation, avoiding singularities
- Carefully mesh the parts
- Use appropriate solver technology to handle the potentially large strains in your model
- Make sure you have robust contact capabilities to handle frictional contact
The process starts with identifying the proper material model. Assuming the user was able to get experimental data for a typical hyperelastic characterization (see, for example, http://www.axelproducts.com/pages/hyperelastic.html), the right material model can be found by performing data fitting. Data fitting essentially involves finding the parameters of a given material model that closely match the experimental data.
Mooney-Rivlin coefficients from experimental data fitting
ANSYS Mechanical offers a variety of hyperelastic models including Mooney-Rivlin, neo-Hookean, or Bergstrom-Boyce. When fitting your experimental data, also pay attention to the amount of strain to which your part will be subjected. For large strain cases, you will want the material model to fit the experimental curve as best as possible up to high strains.
Then comes the meshing of your model. Traditionally, hexahedral elements with eight nodes have been preferred to ensure proper convergence and a high level of deformations.
Hexahedral mesh of an elastomeric joint
There are alternatives to hexahedral elements though. Linear tetrahedrons as implemented in ANSYS Mechanical offer a nice alternative that is worth considering when the geometry of the hyperelastic part is complex. Creating hexahedral meshes can be time consuming, while tetrahedral meshes can be highly automated. Similar results can be achieved with either mesh type assuming the proper mesh density is used. Your choice of element topology will be guided by considering the time spent setting up the model, especially for complex geometries, as well as the mesh density you can afford to keep your simulation running in a reasonable amount of time. Note that parallel computing can be very helpful in reducing the computation time.
Solver technology also plays an important role in solving hyperelastic models. Proper efficiency of Newton-Raphson algorithms are key in ensuring convergence and quality of the results, especially for large strains.
Deformation contour of an elastomeric joint
In some cases, deformations may be so extreme that remeshing or adaptive meshing techniques will be required to achieve high strains. Such solutions are also available in ANSYS Mechanical. In this case, the remeshing of regions of interest is handled during the solution process as shown below, without the need for manual operations.