A Microscopic Model for the Reinforcement and the Nonlinear Behavior of Filled Elastomers and Thermoplastic Elastomers (Payne and Mullins Effects)

We extend a model regarding the reinforcement of nanofilled elastomers and thermoplastic elastomers. The model is then solved by numerical simulations on mesoscale. This model is based on the presence of glassy layers around the fillers. Strong reinforcement is obtained when glassy layers between fillers overlap. It is particularly strong when the corresponding clusters-fillers + glassy layers-percolate, but it can also be significant even when these clusters do not percolate but are sufficiently large. Under applied strain, the high values of local stress in the glassy bridges reduce their lifetimes. The latter depend on the history, on the temperature, on the distance between fillers, and on the local stress in the material. We show how the dynamics of yield and rebirth of glassy bridges account for the nonlinear Payne and Mullins effects, which are a large drop of the elastic modulus at intermediate deformations and a progressive recovery of the initial modulus when the samples are subsequently put at rest, respectively. These mechanisms account also for dissipative properties of filled elastomers. In particular, our results allowed also for explaining semiquantitatively the results obtained by Payne in his 1963 study. Our model opens the way for predicting mechanical behavior of nanofilled elastomers according to the filler structures and dispersion, polymer-filler interactions, and temperature, in order to prepare systems with tailored properties.