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The science
What is modelled
A thin NiTi wire is heated by an electric current. Between As = 57 °C and Af = 83 °C it transforms from martensite to austenite and contracts by up to 4.5 %, lifting a load against a return spring; on cooling the transformation reverses between Ms = 62 °C and Mf = 39 °C, so the heating and cooling paths differ (hysteresis).
Equations
C dT/dt = V²/R − (G_mount + h·A_s)(T − Ta), R = ρ_e L / A. Phase: smoothstep of (T − As)/(Af − As) when heating and of (T − Mf)/(Ms − Mf) when cooling, relaxed with time constants 0.65 s and 1.05 s. Force balance: F_stall(1 − x/x_free) = F_load + k x.
Honest simplifications
Lumped (uniform temperature and stress), an illustrative NiTi parameter set rather than a calibrated alloy, a smooth phase curve instead of a measured transformation, and a quasi-static force balance followed by a damped carriage response.
Built-in checks
The steady temperature against V²/(R·G), the force balance residual at full transformation, and the hysteresis width against the transformation temperatures.