Shape Memory Alloy Twin Microstructure: A 2D Phase-Field Model

This is the 2D companion to the 3D SMA actuator scene, and it reaches the same thermal-heat-engine behaviour by a genuinely different route. Instead of looking a global austenite fraction up from a fitted cosine curve, it discretizes the alloy into a 48×48 lattice of local strain order-parameters and integrates a stochastic, spatially-coupled Ginzburg-Landau equation built on the sixth-order Falk free energy used in real shape-memory-alloy theory. Each lattice cell nucleates martensite or reverts to austenite on its own, driven by its local free-energy landscape plus thermal noise and an elastic coupling to its neighbours that produces genuine self-accommodating twin microstructure at low temperature. The macroscopic austenite fraction, thermal hysteresis width, stress-shifted transformation temperature and load-lifting stroke are all measured outputs of that lattice simulation rather than assumed inputs — including the physically important detail that, with zero applied load, the twins cancel to zero net strain and the actuator does no work, exactly as a real unloaded SMA element would.