ABSTRACT
Strain-induced softening of rubber has been broadly discussed for over five decades now and today is commonly referred to as Mullins effect. It has been pointed out by Harwood, Payne, & Whittaker (1971), that filled and unfilled rubbers show such behavior. For being much more pronounced for filled rubber compounds, the most researches explain the Mullins effect as an effect of the filler as well as the filler-matrix interaction. In fact, the presence of filler causes a stiffening of the material. We pursue a theory thatin outline follows Johnson & Beatty (1993). As a microstructural motivation of their work, the filler is concerned as an effectively rigid fraction of the material. The softening is represented, in a rather phenomenological sense, as a degeneration of the rigid fraction under deformation. The following section deals with the origins of the theory and adaptions leading to the present model. In Section 3 we present the generalization of
analogously holds for the determination of Young’s modulus E of rubber compounds depending on the modulus E0 of the unfilled matrix material and the volume fraction cv of the carbon black particles. The relation then reads
E E v v0 2( )c. + .1 2+ 5 1c 4 1 . (1)
Later Mullins & Tobin (1965) described the large strain behavior by combining this relation with the Mooney-Rivlin law of rubber hyperelasticity. If the filler now is considered to be rigid, then the matrix material undergoes higher strains compared to an unfilled material. Therefore, the factor X cv v. .1 2 5 1+c 4 1
2 can be motivated as an amplification factor for the applied strain ε in order to account for the effective strain εeff of the rubber matrix following
ε εeff X . (2)
As a consequence, any desired uniaxial material model can be enhanced with such kind of theory by replacing the actual strain by the effective strain. This benefit appears to be one reason why today the theory is widely spread and is adapted continously.
