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). •A novel physical theory for the mechanical description of filled rubber is presented.•Fit quality up to large strains, for different speeds and temperatures is very good.•Parameters behave physically correct while changing filler or curing agent level.•A fast, robust and accurate numerical implementation is possible.•Probably reorganization of structures on different scales determines rubber behavior.