We reproduced mechanical behaviors, such as the reinforcement effect, hysteresis, and stress softening, of filled rubber under cyclic deformations using coarse-grained molecular dynamics simulations. We measured polymer density distribution in the nonload equilibrium state and conformational changes in polymer chains during deformation for dispersed and aggregated filler structures. We found that the polymer–filler attractive interactions increase the polymer density in the vicinity of fillers and decrease the polymer density in the other regions. The polymer bonds that connect polymer particles away from fillers are extended when the polymer density decreases. This alteration increases the modulus of the polymer phase, and the reinforcement effect appears. For aggregated filler structures, the polymer chains interacting with adjacent fillers act as a bridge between these fillers and increase the modulus, especially when the strain is low.

To test the mechanisms of hysteresis and stress softening, we measured the changes in the polymer paths. A polymer path is the minimal path of polymer networks between two fillers; in other words, it is the “bridge” that connects two fillers. We found that the polymer paths increase in length, especially during primary loading, because of polymer adsorption/desorption on the filler surface to adjust the change of filler positions. It was also found that the influence of the filler structure diminishes in the first loading. During subsequent unloading, a long path does not become a short path again but will be folded even though the filler distance reduces. Hence, the change in the polymer paths in the second cycle is smaller than that in the first cycle because the polymer path is just unfolded. We confirmed the hysteresis and stress-softening result from these conformational changes. In this article, we also discuss the recovery mechanism for stress softening and the history dependence.

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