Rheology of tunable materials.

Materials with tunable mechanical properties are ubiquitous in biology and engineering, such as muscle, the cytoskeleton, soft robotic actuators, and magnetorheological fluids. Their functionality arises through an external signal that modulates intrinsic mechanical properties, like neural spikes in muscle. However, current rheological methods assume approximately invariant mechanical properties during measurement, and thus cannot be used for characterizing the rheology of tunable materials. Here, we develop a geometric framework for characterizing tunable materials by combining classical oscillatory rheology that uses Lissajous force-length loops to characterize non-tunable materials, with the technique of work loops that is used to study muscle's work output under varying stimulation. We derive the force-length loop under varying stimulation by splicing Lissajous loops obtained under constant stimulation. This splicing approach captures the force-length loop shapes in muscle that are not seen in non-tunable materials, and yields a nondimensional parametrization for the space of possible responses of tunable materials.