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The application of computational mechanics analysis
techniques to elastomers presents unique challenges in modeling the following
characteristics:
– The load-deflection behaviour of an elastomer is markedly
non-linear.
– The recoverable strains can be as high 400 % making it
imperative to use the large
deflection theory.
– The stress-strain characteristics are highly dependent on
temperature and rate effects are pronounced.
– Elastomers are nearly incompressible.
– Viscoelastic effects are significant.
The ability to model the special elastomer characteristics
requires the use of sophisticated material models and non-linear Finite element
analysis tools that are different in scope and theory than those used for metal
analysis. Elastomers also call for superior analysis methodologies as
elastomers are generally located in a system comprising of metal-elastomer parts
giving rise to contact-impact and complex boundary conditions. The presence of
these conditions require a judicious use of the available element technology
and solution techniques.
FEA Support Testing
Most commercial FEA software packages use a curve-fitting
procedure to generate the material constants for the selected material model.
The input to the curve-fitting procedure is the stress-strain or stress-stretch
data from the following physical tests:
1 Uniaxial
tension test
2 Uniaxial
compression test OR Equibiaxial tension test
3 Planar
shear test
4 Volumetric
compression test
A minimum of one test data is necessary, however greater
the amount of test data, better the quality of the material constants and the
resulting simulation. Testing should be carried out for the deformation modes
the elastomer part may experience during its service life.
Curve-Fitting
The stress-strain data from the FEA support tests is used
in generating the material constants using a curve-fitting procedure. The
constants are obtained by comparing the stress-strain results obtained from the
material model to the stress-strain data from experimental tests. Iterative
procedure using least-squares fit method is used to obtain the constants, which
reduces the relative error between the predicted and experimental values. The
linear least squares fit method is used for material models that are linear in
their coefficients e.g Neo-Hookean, Mooney-Rivlin, Yeoh etc. For material
models that are nonlinear in the coefficient relations e.g. Ogden etc, a
nonlinear least squares method is used.
Verification and Validation
In the FEA of elastomeric components it is
necessary to carry out checks and verification steps through out the analysis.
The verification of the material model and geometry can be carried out in three
steps,
_ Initially a single element
test can be carried out to study the suitability of the chosen material model.
_ FE analysis of a tension
or compression support test can be carried out to study the material
characteristics.
_ Based upon the feedback
from the first two steps, a verification of the FEA model
can be carried out by applying the main
deformation mode on the actual component
on any suitable testing machine and verifying the results computationally.
Figure 1: Single Element Test
Figure(1) shows the single element
test for an elastomeric element, a displacement
boundary condition is applied on a face, while constraining the movement of the opposite face. Plots A and B show the deformed and undeformed plots for the single element. The load vs. displacement values are then compared to the data obtained from the experimental tests to judge the accuracy of the hyperelastic material model used.
Figure 2: Verification using an FEA Support Test
Figure (2) shows the verification
procedure carrying out using an FEA support test.
Figure shows an axisymmetric model of the
compression button. Similar to the single
element test, the load-displacement values from
the Finite element analysis are compared to the experimental results to check
for validity and accuracy. It is possible that the results may match up very
well for the single element test but may be off for the FEA support test verification
by a margin. Plot C shows the specimen in a testing jig. Plot D and E show the undeformed
and deformed shape of the specimen.
Figure(3) shows the verification
procedure that can be carried out to verify the FEA
Model as well as the used material model. The procedure also validates the boundary conditions if the main deformation mode is simulated on an testing machine and results verified computationally. Plot F shows a bushing on a testing jig, plots G and H show the FEA model and load vs. displacement results compared to the experimental results. It is generally observed that verification procedures work very well for plane strain and axisymmetric cases and the use of 3-D modeling in the present procedure provides a more rigorous verification methodology.
Figure 3: FEA Model Verification using an Actual Part
AdvanSES provides Hyperelastic, Viscoelastic Material Characterization Testing for CAE & FEA softwares.
Unaged and Aged Properties and FEA Material Constants for all types of Polymers and Composites. Mooney-Rivlin, Ogden, Arruda-Boyce, Blatz-ko, Yeoh, Polynomials etc.