  The dynamical electric behavior of a NiTi smart alloy thin filament when
driven by time varying current pulses is studied by a structure-based
phenomenological model that includes rate-based effects. The simulation model
relates the alloy's electrical resistivity to the relative proportions of the
three main structural phases namely Martensite, Austenite and R-phase,
experimentally known to exist in NiTi alloy lattice structure. The relative
proportions of the phases depend on temperature and applied stress. Temperature
varies due to the self-heating of the filament by the Joule effect when a
current pulse passes and also due to convective/radiative interchange with the
ambient. The temperature variation with time causes structural phase
transitions, which result in abrupt changes in the sample resistivity as the
proportions of each lattice phase vary. The model is described by a system of
four 1st-order nonlinear differential-algebraic equations yielding the temporal
evolution of resistivity and output voltage across the filament for any given
time-varying input current pulse. The model corresponds to a 4th-order extended
memristor, described by four state variables, which are the proportions of each
of the three NiTi lattice phases and temperature. Simulations are
experimentally verified by comparing to measurements obtained for samples
self-heated by triangular current input waveforms as well as for passively
samples with no current input. Numerical results reproduce very well
measurements of resistance vs. temperature at equilibrium as well as the full
dynamics of experimentally observed I-V characteristic curves and resistance
vs. driving current for time-varying current input waveforms of a wide range of
frequencies (0.01-10~Hz).
