On consistent tangent operator derivation and comparative study of rubber-like material models at finite strains

Rubber-like materials can deform largely and non-linearly upon loading and return to the initial configuration when the load is removed. Such rubber elasticity is achieved due to very flexible long chain molecules and a three-dimensional network structure that is formed via cross-linking or entanglements between molecules. Over the years, to model the mechanical behaviour of such randomly-oriented micro-structure, several phenomenological and micro-mechanically motivated network models for nearly incompressible hyperelastic polymeric materials have been proposed in the literature. For comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous defomation modes, i.e. uniaxial tension, equibiaxial tension and pure shear have been derived and the performances of the models are analysed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)