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 .
This paper proposes a hypothesis for the tunable rheology of skeletal muscle and tests it using published datasets and simulations. Skeletal muscle's rheology, how it deforms under forces, is neurally modulated and crucial for animal movement. Muscle's force-length response is well-studied under fixed and time-varying stimulation. Under fixed stimulation, oscillatory force measurements characterize muscle rheology using dynamic material moduli. Under time-varying stimulation, work loops characterize work production and absorption using force-length curves obtained under periodic length oscillations. But unlike fixed-stimulus measurements, work loops exhibit unusual but functionally critical features like work-producing loop reversals and self-intersections. We tested the hypothesis that work loops emerge by splicing the rheological responses obtained under fixed stimulation and found that it accurately predicts the loops in experimental data on sculpin skeletal muscle and in numerical sarcomere simulations. Thus, classical rheological loops and splicing underlie the emergent shape of muscle work loops under steady dynamical conditions .
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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,
This paper proposes a hypothesis for the tunable rheology of skeletal muscle
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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
tests it using published datasets and simulations. Skeletal muscle's rheology, how it deforms under forces, is neurally modulated and crucial for animal movement. Muscle's
R
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
response is well-studied under fixed and time-varying stimulation. Under fixed stimulation, oscillatory force measurements characterize muscle rheology using dynamic material moduli. Under time-varying stimulation, work loops characterize work production and absorption using
R
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
curves obtained under periodic length oscillations. But unlike fixed-stimulus measurements, work loops exhibit unusual but functionally critical features like work-producing loop reversals and self-intersections. We tested the hypothesis that work loops emerge by splicing the rheological responses obtained under fixed stimulation and found that it accurately predicts the loops in experimental data on sculpin skeletal muscle and in numerical sarcomere simulations. Thus, classical rheological loops and splicing underlie the emergent shape of muscle work loops under steady dynamical conditions