Hyperelastic Material Modeling

Hyperelasticity is a type of constitutive behaviour for materials like natural rubber that exhibit large non-linear elastic deformations. These materials return to their original shape upon unloading, following a nonlinear stress-strain relationship.

Hyperelastic models are essential in simulating the behavior of elastomeric polymers, rubbers, and biological tissues, which undergo significant deformations. They are frequently used in the manufacture of gaskets and seals.

Key Concepts:

• Strain-Energy Density Function: The core principle of hyperelastic models is the strain-energy density function (W), which defines the stored energy per unit volume as a function of the deformation. Different hyperelastic models have different forms of this function, but they all share the goal of accurately describing the material's response to deformation.
• Constitutive Models: Several constitutive models exist to represent hyperelastic materials, each with its own strain-energy density function. Common models include:
  • Neo-Hookean Model: A simple model suitable for small to moderate strains.
  • Mooney-Rivlin Model: Accounts for both the first and second invariants of the deformation tensor, providing better accuracy for larger strains.
  • Ogden Model: Uses a series of terms with different exponents and coefficients, offering great flexibility in fitting experimental data.
  • Arruda-Boyce Model: Specifically designed for polymers, capturing the entropic elasticity of the polymer chains.
• Stress-Strain Relationship: The stress in a hyperelastic material is derived from the strain-energy density function. The relationship is generally nonlinear and depends on the specific form of the function chosen. For isotropic materials, the Cauchy stress tensor (σ) can be expressed in terms of the principal stretches or the invariants of the deformation gradient.

To illustrate the application of hyperelastic models, consider the following example using the Treloar's data for natural rubber :

1. Select AMDC-Data File as the Objective operation.
2. Change the Material Class to "Thermoset"
3. Select the default File Type, uniaxial test data (UXT), and then click the Hyperelastic button to import the file. The Import Hyperelastic UXT Data File dialog box is displayed.

   
   
   

4. Select the required Hyperelastic Data Import option to import the data. Continue with the default Engineering Stress and Strain for this example.
5. Click Import File to import Trelaor's UXT data. The Hyperelastic Fitting data is imported into the application and the plot is displayed.

   
   
   

6. Adjust the Fitting Results to read the plot curve details. In the following example, Yeoh Model values are adjusted for C20 and C30 parameters.

   
   
   

7. Click Save Changes to save the edits.
8. Click the Approve Model Fit check box to approve the model fit data.
9. In the File Management pane, click File Preview.
10. Click OK on the Extra Information dialog box to continue with the default values.

    
    
    

    The Optistruct Input card is displayed in the preview pane.

    
    
    

11. One may modify the text of the model fit file to suit specific needs. Additionally, one can adjust the units and repeat the file preview process to view the file details in the new units.
12. Click Export File to export model fit data to the Project Folder.