Abstract
The aim of this work is the choice of relevant constitutive equations for rubber-like materials subjected to intermediate strain rates loading conditions (from 1 to 100 s(-1)). Classically, these materials are considered as large strain elastic solids and the constitutive equations are hyperelastic with more or less complicated free energy densities. In order to phenomenologically take into account the change of response (from rubber-like to glassy) of the polymers and investigate their damping properties at different strain rates, incompressible hyper-viscoelastic models must be considered. Two different approaches have been proposed in the bibliography: (i) the internal variable approach in which the strain is multiplicatively split into an elastic and a viscous part, the latter being driven by an evolution equation (similarly as for elastoplastic materials) and (ii) the integral approach that states that the response at a given time explicitly depends on the strain history of the material. We compare simple models derived from both approaches; their elastic parts are neo-Hookean and their viscous parts are (i) a Maxwell model and (ii) a basic time integral. It finally leads to two three-parameter constitutive equations. Simulating uniaxial tension-compression cycles at different strain rates, we demonstrate that the two approaches are not equivalent for intermediate strain rates, even if both are able to predict material strengthening and hysteresis; we investigate their differences and peculiarities.