Simulation of Cyclic Displacement by Counterpoised Shape Memory Elements

The most common shape memory actuation procedure involves a shape memory element that works against a conventional elastic biasing element. Actuation is provided by the movement of the contact interface separating the two elements. The interface then occupies one location at high temperature and another location at low temperature. Certain applications call for switching between two separate interface locations, both of which are stable at a common ambient temperature. A shape memory element working against a conventional elastic biasing element cannot generally give such capability. However, two shape memory elements working against each other does give this capability, provided that the ambient temperature supports stress-free martensite, and provided as well that the contact interface thermally isolates the elements during short duration heating spikes which trigger such a switch. There is an obvious operational benchmark involving one element with fully oriented martensite and the other element with random martensite. The benchmark operation exchanges these states between the two elements, in which case the device stroke follows immediately from the material’s transformation strain. This benchmark behavior is not achievable due to elastic strain effects. Here we analyze the achievable behavior of such a device using a recent model for shape memory behavior. This model tracks the state of the shape memory material in terms of austenite and two variant martensite. This enables the determination of the device’s shakedown behavior in terms of repeatable per-stroke strain delivery, and also gives the temperature excursions necessary for the associated full displacement.