Constitutive modelling of rubbers: Mullins effect, residual strain, time-temperature dependence

Filled rubbers are an important part of engineering materials because they have unique properties such as large deformability, increased stiffness and energy dissipation ability. The complexity of the material model parameter identification and the consideration of essential behaviours such as temperature dependence or residual strain may be a great challenge during the constitutive modelling. In this paper, a hyper-visco-pseudo-elastic constitutive equation is introduced and applied to model the complex behaviour of filled rubbers by considering (i) the Mullins effect, (ii) the temperature effect, and (iii) the effect of residual strains. The time-independent material response is provided by the modified Dorfmann–Ogden pseudo-elastic material model, while the time and temperature dependence is taken into consideration by the Prony series-based linear viscoelastic theory and the time-temperature superposition principle. Furthermore, by assuming homogeneous deformations, numerical stress solutions are presented to perform the material model calibration simple and fast, even when considering uniaxial tension/compression and simple shear simultaneously. The material model can be adapted to handle any hyperelastic model, arbitrary damage and residual strain variable, user-defined time-temperature superposition function, and any number of Maxwell elements (spring-dashpot terms). Here, the model parameters are determined from uniaxial stress relaxation-recovery tests, as well as cyclic uniaxial tensile and cyclic simple shear tests of different strain rates. Finally, the theoretical results are compared with experimental data for an EPDM rubber filled with 50 phr of carbon black.