Phenomenological modelling of strain-induced structural changes in filler-reinforced elastomers - A time domain formulation of the Kraus model

When exposed to cyclic strain-controlled loadings, filler-reinforced elastomers exhibit pronounced softening: under large strains it is known as the Mullins effect and under small strains as the Payne effect. These phenomena are frequently interpreted as a dynamic state of equilibrium between breakage and recovery of physical bonds linking adjacent filler clusters. The Kraus model describes the amplitude dependence of dynamic moduli but no equivalent formulation exists in the time domain. Motivated by this deficiency, we develop a theory of viscoelasticity formulated in the time domain. To take the changes in the carbon black network into account, the model contains process-dependent viscosities. They depend on a variable, which is a measure for the number of broken bonds. Assuming a power law between the viscosities and this variable, the resultant constitutive theory leads to the Kraus model in the case of harmonic strains.