Strain Rate Dependent Micro- to Macroscopic Deformation Behavior of Carbon-Black Filled Rubber under Monotonic and Cyclic Straining

A constitutive equation of rubber is derived by employing a nonaffine molecular chain network model for an elastic deformation behavior and the reptation theory for a viscoelastic deformation behavior. The results reveal the roles of the individual springs and dashpot, and the strain rate dependence of materials in the monotonic and cyclic deformation behaviors, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress-stretch curves under cyclic deformation processes of carbon black filled rubber..