Simulating Rubber and Foam Materials

		Bob Williams Product Manager ALGOR, Inc. Pittsburgh, PA
	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 curve-fitting 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. Compressible Blatz-Ko works specifically for compressible polyurethane foam rubbers. Hyperfoam can simulate any highly compressible material such as a cushion, sponge or padding.

Integrated tools for automatically converting test data into analysis software inputs make simulating rubber and foam faster, easier and more accurate.

This article was published in Machine Design, "Start Here When Simulating Rubber and Foams", November 17, 2005.

For any computer-aided engineering analysis, accurate material data inputs are essential for obtaining accurate results. When simulating product designs made of rubber, foam or other hyperelastic materials, the analyst faces unique challenges including, "How can I obtain accurate material property values?" and, "How do I convert the physical test data into the values required for the analysis software's data input fields?"

Properties for familiar materials, such as steel and aluminum, can be found in almost any engineering handbook along with the exact values required as inputs for finite element analysis (e.g., Young's modulus, Poisson's ratio, etc.). Hyperelastic material properties, however, might not be found so readily. Additionally, once found, determining analysis input values from the complex physical property data is often more daunting than simply entering "Ε=30e6" and "ν=0.3".

ALGOR's Mechanical Event Simulation software solved for stresses over time, including residual stresses, in an automotive tire and wheel assembly when the tire impacted a curb. A Mooney-Rivlin hyperelastic material model was used to accurately simulate the large deformation and large strain of the rubber material. (Model courtesy of Applied Concepts, Medina, Minnesota.)

Hyperelastic materials, such as rubber and foam, are highly compressible and can undergo large deformation and large strain. Typically, analyses of rubber can involve up to 200-300% strain and up to 600-700% strain for foam. Unlike common metals, which can be defined by a relatively simple bi-linear stress-strain curve with a discernible yield point, hyperelastic materials are characterized by continuous change in the slope of the stress-strain curve. Hence, hyperelastic materials require more stress-strain data points to accurately model the curve.

Most FEA vendors provide users with libraries of material data including hyperelastic materials. Additionally, commercial engineering material databases provide online access for many more materials (for example, MatWeb provides more than 50,000 material data sheets), which can be conveniently imported into analysis software. But what happens in the increasingly common event that the user is considering a proprietary or new material for which he or she only has the raw experimental data for stress, strain and other physical properties? Calculations must be performed on the stress-strain data to determine the material constants required by the analysis software. If the user does not know these constants, some FEA vendors provide a tool to determine the values.

For example, ALGOR provides an easy-to-use, graphically driven curve-fitting utility that automatically calculates the appropriate material parameters from the physical test data. Built into its FEA and Mechanical Event Simulation (MES) software, ALGOR's curve-fitting utility allows the user to:

• plug in stress and strain data (either manually or from a CSV file);

• calculate constant values for the selected hyperelastic material model (including Ogden, Mooney-Rivlin, Blatz-Ko, Arruda-Boyce and Hyperfoam);

• view a graph of the stress-strain test data and the fitted curve to confirm correlation; and

• input the calculated constants (two, five or nine depending on the material model) directly into the material property data entry fields.

Constants required for material property definition of rubber, foam and other hyperelastic materials are calculated automatically from stress-strain test data by ALGOR's built-in curve-fitting utility.

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