A physically based model of stress softening and hysteresis of filled rubber including rate- and temperature dependency

A novel physically based material model is presented that describes the complex stress-strain behavior of filled rubbers under arbitrary deformation histories in a constitutive manner. The polymer response is considered by the extended non-affine tube model. Stress softening is taken into account via the breakdown of highly stressed polymer-filler domains under load and homogenization of the medium. Set stress and hysteresis are introduced via a continuous reformation mechanism, characterized by a single critical stress parameter. The latter is predicted to be dependent on temperature and deformation rate by means of Kramers escape rate. This is confirmed for a wide range of temperatures and speeds by fitting to multihysteresis measurements carried out in a heat chamber. Fitting parameters reveal that the mechanism responsible for hysteresis and set stress takes place on the nanometer scale with energies of roughly 100 kJ/mol. The behavior of the fitting parameters is analyzed for varying filler loadings and crosslinker concentrations in EPDM. Simulations of the stress-strain response for several deformation modes are in good agreement with experiments and its mathematical simplicity makes it very promising for applications with Finite Element Methods (FEM).