Modelling Mullins and cyclic stress-softening in filled rubbers

The study of the stress-strain responses of a carbon-black filled rubber submitted to cyclic uniaxial tension loadings evidenced two specific features common to filled rubbers. First, as originally shown by (Mullins and Tobin 1965), the Mullins softened stress-strain responses collapse into a single master curve by introducing strain amplification factors. Second, the cyclic softened stress-stretch responses collapse into a single stress-stretch response by applying stretch intensity factors. Several Mullins softening models from the literature are confronted to the experimental evidence of the existence of a master curve. Then, a model framework is proposed in order to reproduce the cyclic softening and successfully tested in uniaxial tension.