Machine Design

Start here when simulating rubber and foams

Little-known features in FEA software convert test data into inputs for simulating hyperelastic materials.

Bob Williams
Product Manager
Algor Inc.
Pittsburgh, Pa.

Engineers at Applied Concepts, Medina, Minn., used Algor's Mechanical Event Simulation software to find stresses over time, along with residual stresses, in an automotive tire and wheel during a simulated curb hit. A Mooney-Rivlin hyperelastic-material model accurately simulated the large deformation and strain of the rubber.

An engineer with test data has selected the Ogden material model for a simulation. Constants required to define hyperelastic material properties (in the upper right) are calculated from stressstrain test data read into Algor's curvefitting tool.

Accurate material-data inputs are essential for any computer-aided-engineering analysis. But when simulating products that will use hyperelastic materials such as rubber and foam, how do you obtain accurate values for material properties? Or if physical test data is available, how do you convert it into constants and values needed by material models?

Properties for steel, aluminum, and other familiar materials are in most engineering hand-books along with exact values needed for finiteelement analysis (Young's modulus and Poisson's ratio). Hyperelastic-material properties, however, are not so readily found. And once found, determining input values from the complex property data is often more daunting than simply entering E = 30e6 and v = 0.3.

Hyperelastic materials are highly compressible and withstand large deformations and strains. Typically, analyses of rubber involve up to 200 to 300% strain while foam handles up to 600 to 700% strain. Unlike common metals, which can be defined by relatively simple bilinear stress-strain curves with discernible yield points, hyperelastic materials are characterized by continuous change in the slope of their stress-strain curves. Hence, hyperelastic materials require more stressstrain data points to accurately model the curve.

Most FEA vendors provide material libraries that include values for hyperelastic materials. Additionally, commercial engineering material databases provide online access for many more. MatWeb, for example, lists more than 51,000 material datasheets, which can be imported into some analysis software.

Companies, however, are increasingly using new and proprietary materials for which they have only raw experimental data for stress, strain, and other physical properties. They must then perform calculations on stress-strain data to determine the material constants required by the software. But when the constants are unknown, FEA programs often have a tool to determine them.

Algor's FEA software, for example, has a graphically driven curve-fitting tool that calculates appropriate material parameters from physical test data. It lets users:

  • Plug in stress-strain data (either manually or from a comma-separated-value file) from simple tension, equibiaxial, pure-shear, or volumetric tests.
  • Calculate constant values for the selected hyperelastic-material model (including Mooney-Rivlin, Arruda-Boyce, Ogden, Blatz-Ko, and Hyperfoam).
  • View a graph of stress-strain test data and the fitted curve to confirm correlation.
  • Input constants directly into data-entry fields. Hyperelastic-material models need from two to nine constants before they can return useful information.

These tools for automating hyperelastic-material property data entry help ensure accurate material data and results. With the data conveniently and accurately defined, analyses can proceed like any other simulation. This makes analyzing rubber and foam products faster, easier, and more reliable.

A brief review of material models

The accuracy of simulating a hyperelastic material depends on the selected material model. Here are a few of the frequently mentioned models and where they work best.

Nearly incompressible

Mooney-Rivlin works with incompressible elastomers with strain up to 200%. Rubber for an automobile tire is an example.

Arruda-Boyce is well suited for rubbers such as silicon and neoprene with strain up to 300%. This model provides good curvefitting even when test data are limited.

Ogden works for any incompressible material with strain up to 700%. This model gives better curve fitting when data from multiple tests are available.


Blatz-Ko works specifically for compressible polyurethane foam rubbers.

Hyperfoam can simulate any highly compressible material such as a cushion, sponge, or padding.

Algor Inc.,
(412) 967-2700,
(540) 552-5300,

TAGS: Materials
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