Modeling the dynamical behavior of memristive {NiTi} alloy at constant stress for time-varying electric current input signals.

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).