Shape Recovery in Viscoelastic Silicone Rubber and the Fractional Zener Model

Viscoelastic silicone rubber (VSR) is a remarkable shape-memory solid. The material's polymer network retains a memory of its shape history, so its current and future shapes depend strikingly on its past shapes. Although VSR's memory fades gradually and it has a permanent (cured-in) shape to which it will eventually return when left alone, VSR can be taught new shapes and retain them for significant lengths of time. To examine VSR's ability to learn, remember, and recover shapes, this work focuses on a simple experiment. A VSR that has relaxed into its permanent shape is suddenly compressed to about 80% of its original height. After a specific period of compression, the VSR is released and allowed to return to its permanent shape. Having learned a new shape during the compression period, however, the VSR is reluctant to return and takes seconds, minutes, or hours to do so, depending on how long it was compressed. In addition to observing these behaviors experimentally in VSR, we show that those behaviors are well-described by the Fractional Zener model. That model involves time derivatives of non-integer order and those generalized time derivatives have memory. Both VSR and the Fractional Zener model describing it are acutely aware of the past. The model's mathematical machinery make it possible to design VSR behaviors based on physical parameters, although some of the model's relationships are not yet known in closed form. VSR's existence as a practical material means that devices can be designed and produced that use a memory of past shapes to do things that would otherwise be difficult or impossible to make.