A Model for the Mullins Effect in Multinetwork Elastomers

Double and triple network (TN) elastomers can be made by infusing monomers into a single network (SN) polymer, causing it to swell, and then polymerizing and cross-linking the monomers. The result is a double network (DN) elastomer in which one network is stretched and the other is in hydrostatic compression. TN systems are made by repeating the process starting with the DN material. The multinetwork (MN) elastomers exhibit a Mullins effect in which softening occurs upon a first cycle of loading, with the elastomer stiffness recovered above the previous maximum strain. The Mullins effect is attributed to rupture of the stretched network, eliminating the constraint on the compressed network, thereby motivating straining at the lower stiffness of the remaining material. A model for this process is developed, based on the previous work of Horgan et al. (2004, A Theory of Stress Softening of Elastomers Based on Finite Chain Extensibility, Proc. R. Soc. A, 460(2046), pp. 1737-1754). In the proposed model, a composite stiffness for the MN system is developed and a damage process introduced to degrade the contribution of the stretched network. The damage model is designed to account for the progressive elimination of chains that are most highly loaded in the stretched network, so that the undamaged stiffness is restored when the strain rises above levels previously experienced. The proposed model reproduces the behavior of the Mullins effect in the MN system.