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Shape memory alloys (SMAs) show size effect in their response. The critical stresses, for instance, for the start of martensite and austenite transformations are reported to increase in some SMA wires for diameters below 100 μm. Simulation of such a behavior cannot be achieved using conventional theories that lack an intrinsic length scale in their constitutive modeling. To enable the size effect, a thermodynamically consistent constitutive model is developed, that in addition to conventional internal variables of martensitic volume fraction and transformation strain, contains the spatial gradient of martensitic volume fraction as an internal variable. The developed theory is simplified for 1D cases and analytical solutions for pure bending of SMA beams are presented. The gradient model captures the size effect in the response of the studied SMA structures.
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