3. Hyperelastic, isotropic and incompressible behavior law

Once the tensors of strain and stress have been defined, and the equations of motion established (not recalled in this article), it is necessary to propose a relationship (or relationships) governing the mechanical response of the material, i.e. expressing stress as a function of strain. This type of equation is known as a behavioral law. Several theories have been developed to describe the mechanical response of elastic materials, i.e. for reversible transformations, subjected to large deformations. Today, however, authors agree on the relevance of the theoretical framework of hyperelasticity.

In this section, the theory is first presented; the main results are given without demonstration (often requiring complex mathematical developments).