Development of new constitutive equations for the Mullins effect in rubber using the network alteration theory

During cyclic loading, both natural and synthetic elastomers exhibit a stress-softening phenomenon known as the Mullins effect. In the last few years, numerous constitutive equations have been proposed. The major difficulty lies in the development of models which are both physically motivated and sufficiently mathematically well defined to be used in finite element applications. An attempt to reconcile both physical and phenomenological approaches is proposed in this paper. The network alteration theory of Marckmann et al. [Marckmann, G., Verron, E., Gornet, L., Chagnon, G., Charrier, P., Fort, P., 2002. A theory of network alteration for the Mullins effect. J. Mech. Phys. Solids 50, 2011–2028] is considered and modified. The equivalence between three different strain energy functions is then used to develop two new constitutive equations. They are founded on phenomenological strain energy densities which ensure simple numerical use, but the evolution of their material parameters during stress-softening is based on physical considerations. Basic examples illustrate the efficiency of this approach.