Constitutive modeling of carbon nanotube rubber composites on the basis of chain length statistics

A constitutive model for carbon nanotube (CNT) reinforced rubbers is proposed on the basis of the polymer chain length statistics. Rubbers both with conventional fillers like silica or carbon black (hybrid system) and without them are considered. The reinforcement by CNTs is explained by additional cross-linking which influences the probability density function of polymer chain lengths. The change in the probability density function is statistically reasoned and incorporated into a full network model based on the numerical integration over the unit sphere. This full network model is able to describe typical inelastic effects of filled rubbers as for example the Mullins effect, strain induced anisotropy and permanent set. The so obtained model demonstrates good agreement with experimental data on CNT blended rubbers available in literature.