HIA: A Hybrid Integral Approach to model incompressible isotropic hyperelastic materials—Part 1: Theory

• Hyperelastic model constructed from the molecular and phenomenological theories.
• The phenomenological integral density takes into account the effect of non-affine deformation.
• The model contains six rheological parameters, connected to the polymer chemistry and to the macroscopic behavior.
• Four sets of experimental data from the literature (Treloar, Yeoh–Fleming, Arruda–Boyce and Nunes–Moreira) are used to identify the rheological parameters and to assess the proposed model.

This paper provides a new constitutive model for rubber-like materials. The model adds to the 8-chain density introduced by Arruda and Boyce, two phenomenological components: an original part made of an integral density and an interleaving constraint part represented by a logarithmic function as proposed by Gent and Thomas. The model contains six rheological parameters connected to the polymer chemistry and to the macroscopic behavior. Four sets of experimental data from the literature are used to identify the rheological parameters and to assess the proposed model. The model is able to reproduce with a good accuracy experimental data performed under different loading conditions such as uniaxial and equibiaxial tension, uniaxial compression, pure and simple shear as well as the Mooney plot.