Two-dimensional analytical model and experimental validation of garter stitch knitted shape memory alloy actuator architecture

Active knits are a unique architectural approach to meet the industrial need for high strain and simultaneous force generation. This paper presents an analytical state-based model to predict the actuation response of a Shape Memory Alloy (SMA) garter knit textile. Garter knits generate significant contraction against moderate to large loads when heated due to the continuous interlocked network of loops of SMA wire. For this knit architecture, the states of operation are defined based on the thermal and mechanical loading of the textile, the resulting phase change of the SMA, and the load path followed to that state. Transitions between these operational states induce either stick or slip frictional forces depending upon the state and path, which affect the actuation response. A load-extension model of the textile is derived for each operational state using Elastica Theory and Euler-Bernoulli beam bending for the large deformations within a loop of wire based on the stress strain behavior of the SMA material. This provides kinematic and kinetic relations which scale to form analytical transcendental expressions for the net actuation motion against an external load. The model was validated experimentally for an SMA garter knit textile over a range of applied forces with good correlation for both the load-extension behavior in each state as well as the net motion produced during the actuation cycle. Throughout the experiments, large strains (up to 250% recoverable, over 50% actuation strain) against moderate forces (order of tens of Newtons) were achieved which demonstrates promise for a wide range of applications.