The capability of three seperable finite-strain viscoelastic models to predict response of a filled rubber material

Three integral-based finite strain viscoelastic models under the assumption of time-strain separability have been investigated within this work. To this end, experimental investigation has been conducted on a carbon black filled rubber, a mixture of natural rubber and bromobutyl. The monotonic tests were performed to capture the long-term response of the material. Relaxation tests were intented to identify the time-dependent material properties, and completed with a dynamic mechanical analysis. Models under consideration are Christensen, Fosdick and Yu and Simo model implemented in the finite element solver Abaqus. Under the assumption of an homegeneous incompressible material with a Mooney-Rivlin elastic potential, the response of the three models is compared for uniaxial tension and simple shear motions in time and frequency domains with respect to strain-rate, frequency and static predeformation dependencies. The equilibrium and non-equilibrium stress is predicted in a limited range mainly related to the choice and identification of the hyperelastic model. For stress relaxation, the long-term response is asymptotically reached with good accuracy, while the hysteritic response is mainly overestimated for Christensen model, and better approximated for both Fosdick and Yu and Simo models. In the frequency domain, Fosdick and Yu model shows no dependence on the predeformation. Christensen model is likely adapted to unfilled rubbers, and is unable to predict the softening effect due to the static predeformation effect. Simo model shows better prediction capabilities with a minimal set of material parameters.