New phenomenological behavior laws for rubbers and thermoplastic elastomers

A phenomenological study of rubber-like materials undergoing pure homogeneous strain such as uniaxial tension, pure shear and (equi-) biaxial tension, leads to a generalized strain energy density representation for hyperelastic incompressible elastomeric material behavior. Based on experimental observations, an additional decomposition of the strain energy density into two functions, each depending on one of the non-constant principal strain invariants, has been assumed. A new building process of these functions is then proposed combined with a simple and fast parameter identification. The former is progressive and requires only two sets of data. An excellent agreement between theory and experimental data has been observed on numerous experiments. The new model seems particularly well adapted to account for the state of strain response dependence for rubbers as for thermoplastic elastomers.