Hyperelasticity

The deformation of hyperelastic materials, such as rubber, remains elastic up to large strain values (often well over 100%). The stress-strain behavior of typical rubber materials is elastic but highly nonlinear and it depends on the loading mode. Different stress-strain behaviors are observed for elastic materials in uniaxial tension, biaxial tension, or pure shear types of loading.

Typical stress-strain curve for rubber

Because of the complex behavior that hyperelastic materials exhibit, their elastic constants are derived from a strain energy potential function, which defines the strain energy stored in the material per unit of reference volume (volume in the initial configuration).

There are several forms of strain energy potentials available to model approximately incompressible isotropic elastomers:

• Polynomial models (Mooney-Rivlin, Blatz-Ko, and Yeoh models)
• Ogden model
• Arruda-Boyce model
• Marlow model
• van der Waals model

To define the material parameters for a hyperelastic material model, you usually provide experimental test data from:

• Uniaxial tension and compression
• Equibiaxial tension and compression
• Planar tension and compression (pure shear)
• Volumetric tension and compression (needed if the material's compressibility is important)

Experimental tests for defining hyperelastic material behavior