Electro-thermo-mechanics of resilient contractile fiber bundles as robotic actuators

A mathematical model is presented for the dynamic response of contractile fiber bundles embedded in or around elastic springs that are either linear helical compression springs or hyperelastic springs such as rubber-like materials. The fiber bundle is assumed to consist of a parallel array of contractile fibers made form either contractile polymeric muscles such as polyacrylic acid plus sodium acrylate cross-linked with bisacrylamide (PAAM) or polyacrylonitrile (PAN) fibers. The proposed model considers the electrically or pH-induced contraction of the fibers which may include resistive heating of the fiber in case of shape-memory alloys. The theory then branches out to two different descriptions of such processes for ionic polymeric gel fiber bundles and shape-memory alloy fiber bundles. The governing equations have been derived and numerical simulations are carried to understand the dynamic response of such actuators