Checking Hyper-Elastic Material Models

non-linear-thumbWhen using hyper-elastic materials, analyst often have little material data to assist them. Fortunate engineers will have a tensile stress-strain curve; a lucky few will also have a simple shear stress-strain curve as well. Where do you start?

To gain confidence in the procedure which is typically used, a set of FEA models were run in a closed loop. The loop consists of assuming some material parameters, running FEA models based upon those parameters, and then using the FEA results to recover the material parameters using ANSYS’s built in hyper-elastic curve fitting.

To isolate the material model from boundary conditions effects, simple FEA models that are 3D but have 1D stress states are used. The figures below show tensile and shear models that can be used to verify material models.
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For this article, a 2 Parameter Mooney-Rivlin material model with values consistent with typical Imperial units was selected. The figure below shows the data entry including a value of zero for d which indicates that the material is fully incompressible.
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The tensile test FEA model was run with this 2 parameter MR model. The engineering stress-strain results were extracted from the results using /post26 APDL. The results are graphed and listed in the figure below. We use APDL because there are some calculations involved with getting engineering results. For example, the engineering stress was calculated by dividing the reaction force at node n1 by the original area like this:

RFORCE,2,n1,F,z,Fz_2
QUOT,3,2, , , , , ,-1/area_,1,

cs3This test data was then used in ANSYS’s curve fitting routine. The results of the curve fitting are shown below. The parameters from the curve fitting results are < 0.01% different than the assumed inputs. This is a reassuring result. Note that this is one instance in ANSYS that you are required to use engineering data (for hyper-elastic curve fitting only).
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In recent versions of ANSYS, a hyper-elastic response function was introduced. This allows the user to enter the test data and use it without curve fitting. The figure below shows how uniaxial tension test data is entered and the response function activated to use it.
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As expected, the response function matched the /post26 output exactly. This method offers a clear advantage in that the user doesn’t need to assume a material model.
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The next step in this verification process was to run some simple shear FEA models to compare the curve fitting results. The plot below shows the engineering shear stress-strain curve using the 2 parameter MR model from above.
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The data was curve fitted as shown in the figure below. This time both the uniaxial tension and simple shear data are entered. The resulting 2 parameter model differs (<2%) from the entered model.
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These new values were used in the FEA models. As shown in the figures below, the change in material parameters (<2%) did not significantly change the tensile or shear stress-strain results (<1%). This raises some interesting questions regarding the 2 parameter MR model that will be explored at a later date.
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