Modeling the stress-strain behavior of rubber

This review focuses on models for rubber that have been used to solve practical problems, either analytically or through the use of finite element analysis (FEA). The emphasis is on the mathematical structure of fully three dimensional models and the scope of behavior that they describe. The mechanisms that are responsible for the behavior are referred to in passing, and prominence is given to models with firm mechanistic foundations. The review starts with definitions of stress and of measures of deformation, and shows how even the simplest model, classical elasticity theory with appropriate values of shear and bulk moduli, gives useful analytical expressions for many products. Viscoelasticity and hyperelasticity are briefly discussed, as well as the more recently introduced models for inelastic effects, notably the Mullins and Payne (or Fletcher-Gent) effects. Some phenomena not yet addressed by models implemented in commercial FEA packages, such as set, cyclic creep and cyclic stress relaxation, are mentioned, and indications of emerging approaches to modeling them are given.