Hyperelastic models for the mechanical response of elastomers

Elastomers, often referred to as rubbers in everyday language, are widely used in industry for anti-vibration applications, such as engine and exhaust mounts in the automotive industry, flexible bonding in naval applications, tires and seals .... These applications benefit from the particular mechanical behavior of these materials, characterized mainly by their ability to withstand very large reversible deformations (several hundred percent). Predicting the mechanical behavior of elastomers in finite element analysis software therefore requires the use of highly non-linear behavior models. This non-linearity is the result both of the large deformations that induce strong changes in geometry, and of the relationship between these deformations and stresses.

Hyperelasticity theory is the basis of all elastomer behavior models. It benefits from a rigorous theoretical framework and has been the subject of a large number of studies since 1940. From this mathematical framework, it is possible to define numerous models predicting the elastic response of elastomers in large deformations. These models are proving effective and are widely available in simulation software. However, their use by engineers in the design phase requires :

• understanding their theoretical formulation;

• development and/or operation of associated experimental trials;

• implementation of techniques for identifying the parameters of these models from test results;

• knowledge of dedicated numerical methods and the difficulties they entail.

The present article deals with these different aspects. In paragraph 1 , elastomers are briefly presented, along with the complexity of their mechanical behavior; the stress-strain curve, which hyperelastic models strive to reproduce, is defined. The necessary reminders of continuum mechanics in large transformations, in particular the definition of the various tensors of strain and stress, are proposed in paragraph