A hyperelastic or Green elastic material is an ideally elastic material for which the stress-strain relationship derives from a strain energy density function. The hyperelastic material is a special case of a Cauchy elastic material. The behavior of unfilled, vulcanized elastomers often conforms closely to the hyperelastic ideal. Filled elastomers and biological tissues are also often modeled via the hyperelastic idealization.

Ronald Rivlin and Melvin Mooney developed the first hyperelastic models, the Neo-Hookean and Mooney-Rivlin solids. Many other hyperelastic models have since been developed. Models can be classified as:

1) phenomenological descriptions of observed behavior,

2) mechanistic models deriving from arguments about underlying structure of the material

3) hybrids of phenomenological and mechanistic models

Phenomenological models

Mooney-Rivlin, Ogden, Polynomial, Yeoh

Mechanistic models

Arruda-Boyce, Neo-Hookean

Hybrid models

Gent

References

• R.W. Ogden: Non-Linear Elastic Deformations, ISBN 0486696480

Continuum mechanics | Rubber properties