A physically motivated model for filled elastomers including strain rate and amplitude dependency in finite viscoelasticity

The Dynamic Flocculation Model (DFM) is a micro-structure based model of rubber reinforcement which is developed on a physical framework to describe the non-linear and inelastic mechanical behavior of filled elastomers (Klüppel, 2003). This one-dimensional material law has been implemented into the finite element code using the concept of representative directions (Freund et al., 2011), which allows the generalization of one-dimensional model to compute three dimensional stress-strain states. The model shows very good agreement with the standard quasi-static multi-hysteresis tests on CB-filled elastomers like NR, SBR or EPDM among others. An extension of this model to include time dependent effects allows to consider the filler induced dynamic response such as strain rate dependency, amplitude dependency and stress relaxation. The physical hypothesis of characterizing the filler clusters as time-dependent parameters is described in Juhre et al. (2013). In this work contribution the quasi-static DFM model was extended to include the time-dependent effects using first-order differential relaxation equation which evolves as a function of time. Subsequently, the corresponding parameters were identified through curve fitting and the model was further validated against associating experiments. The influence of each parameter on the course of change in material behavior has been investigated. The major advantage of the model is its physically meaningful parameters and the ability to reproduce the material response at different loading rates under arbitrary deformation using the single parameter set for each rubber compound.