ABSTRACT
Filled rubber has a complex mechanical response which depends on temperature, load history and deformation rate. More specifically, the material relaxes under load and becomes softer. The degree of softening is a function of maximum load and time spent at the respective load level. Although this effect is understood rather well at low strains in terms of breakdown of the filler network, it remains an open question what happens at high strains. It may be this lack of understanding that only a few models deal with the phenomenon (Carleo, Barbieri, Whear, and Busfield 2018). An extension of a recently published micromechanical model is presented (Plagge and Klüppel 2017), which focuses on the time- and load dependent breakdown of rubber-filler structure to explain softening. The model is based on the assumption of a microscopically heterogeneous material with differently strain-amplified rubber-filler domains. The free energy density of the model is simplified to contain only elementary mathematical functions. The maximum amplification factor of the system is assumed to decrease according to a simple differential equation, whose relaxation time is reduced if local load surpasses a critical value. It is shown that the formalism automatically generates logarithmic stress relaxation as observed in experiments performed at different temperatures and deformation states. Moreover, a similar approach is used to create nonlinear Prony elements which naturally generate Payne-effect like behavior and may be used to represent viscoelastic data obtained at strains outside the linear regime.
