Hyper-elastic materials

The stress-strain relationship for an optimally elastic material that emerges from a strain energy density function is known as a hyper-elastic or Green elastic material. A specific instance of a Cauchy elastic material is the hyperelastic material. For many materials, linear elastic models do not adequately capture the actual behaviour of the materials. Rubber, which has a non-linearly elastic, isotropic, and incompressible stress-strain relationship, is the most prevalent example of this type of material. It is possible to simulate the stress-strain behaviour of such materials using hyperelasticity. Unfilled, vulcanised elastomers frequently behave in a way that nearly resembles the hyperelastic ideal. The hyperelastic idealisation is also frequently used to simulate filled elastomers and biological tissues. The Neo-Hookean and Mooney-Rivlin solids, the first hyperelastic models, were created by Ronald Rivlin and Melvin Mooney. Since then, several more hyperelastic models have been created. The Arruda-Boyce model and the Ogden model are two more popular hyperelastic material models.