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Tips & Tricks for FEA Modeling of Rubber and Elastomers - Part 1

Typical Uniaxial Hyperelastic Engineering Test Data: Force (stress) vs. displacement (strain) | FEA Consulting
March 11, 2016 By: Peter Barrett

Are you having problems solving a detailed stress analysis of an O-ring or seal? This post provides a series of tips for enhancing the accuracy and convergence of your simulation. 

Materials such as rubber or elastomers are typically modeled with Hyperelastic constitutive models because they typically exhibit the following characteristics:

  • By definition, the material behavior is elastic, where there is no permanent set, and the material loads and unloads up and down the same stress-strain curve.
  • The relationship between stress and strain is highly nonlinear and typically softer in tension vs. compression. The tension portion of the stress-strain curve often has an initial softening slope before significant stiffening, while the compressive part of the curve is quite a bit stiffer. (See Figure 1 above.)
  • There is little volume change in the material and thus it acts as either fully or nearly fully incompressible.  This would be equivalent to setting Poisson’s ratio to 0.499.. in a linear elastic model, which creates an incompressible material response.
  • The material response is isotropic and isothermal (stress vs. strain and thermal expansion coefficients are the same in all directions)

Obtaining both an accurate and converged solution in any nonlinear analysis is a challenge. Here are my top three tips, in order of importance, specifically associated with modeling hyperelastic materials.  I’ll reveal four more tips in Part 2 of this post, so stay tuned!

1) Material Testing:  Accurate material test data is a must when simulating the large strain response of rubber and elastomer materials.  At least two material tests from the list below are needed to get good calibration between test and computer model. 

  • Uniaxial Tension
  • Uniaxial Compression
  • Biaxial Tension (Circular or rectangular specimen)
  • Planar Shear
  • Simple Shear
  • Volumetric Test (Button specimen)

The test data should represent, as closely as possible, the in-situ material properties. Because, manufacturing processes, such as the rate of injection molding, can change the final material characteristics. 

2) Material Law Selection: There are many materials laws available to simulate hyperelastic materials using finite elements.  Some of the more common laws include Mooney-Rivlin, Ogden, Yeoh, Blatz-Ko, Arruda-Boyce.  Selecting the best material law plays an import role in the success of your analysis. Select a material law with the best curve fit over the range of expected stresses and strains.  This topic has been discussed in a previous CAE Associates Blog post. Selecting the best material law can be a bit of trial and error process using test data curve fit compatibility and solution robustness (see item 3 below) as selection criteria. 

I would suggest starting with the simpler laws first, such as the two term Mooney Rivlin, and also be cognitive of the expected strain levels in your simulation.  For example, if you don’t expect any strains to exceed 30%, there is no reason to look to match strains at 300%, since these will never be encountered in the real problem.  Some FEA codes have automated curve fitting capabilities that can be used to quickly test a number of different laws and automatically determine the necessary law coefficients.  ANSYS Workbench’s engineering data curve fitting is illustrated in Figure 2, where four laws are compared with each being the better fit to test data, depending on the anticipated simulation response.


Figure 2: ANSYS Engineering Data Comparison of Hyperelastic Material Law Curve Fitting

3) Test the Material Law:  The one element test case should be used to determine the robustness of the material model by imposing tension, compression and shear loads on both regular and irregular single element shapes.  When comparing to test data be sure to convert the test data from engineering to true stress / log strain for direct comparison with FEA results.  Comparing the convergence efficiency between multiple material models on the single element model can be the deciding factor when more than one material law might fit the test data adequately by saving significant CPU time and convergence headaches with the real model.

Watch for Part 2 of this post. Tips 4 - 7 will include some great information about element formulation, meshing and loading. If you have any of your own tips, please share them below in the comments!