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

Active knits are a unique architectural approach to meeting emerging smart structure needs for distributed high strain actuation with simultaneous force generation. This paper presents an analytical state-based model for predicting 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 on the basis of 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. This 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 (250% recoverable strain and over 50% actuation). The two-dimensional analytical model of the garter stitch active knit provides the ability to predict the kinetic actuation performance, providing the basis for the design and synthesis of large stroke, large force distributed actuators that employ this novel architecture.