A 1D rate-dependent viscous constitutive model for superelastic shape-memory alloys: formulation and comparison with experimental data

Experimental investigations on superelastic shape-memory alloys (SMAs) show a dependence of the stress-strain relationship on the loading-unloading rate. This feature is of particular importance when utilizing SMA materials for seismic applications, since the loading rate may affect the structural response. Motivated by this observation and by the fact that there exist relatively few studies on the material modelling of SMAs in earthquake engineering, the present work addresses a uniaxial constitutive equation able to describe the rate-dependent behaviour of superelastic SMAs. The formulation of the model is based on two scalar internal variables, the static martensite fraction and the dynamic martensite fraction, for which three different types of evolutionary equations in rate form are proposed. Moreover, the model takes into account the different elastic properties between austenite and martensite. Finally, after discussing two possible approaches for the solution of the corresponding time-discrete framework, the ability of the model to simulate experimental data obtained from uniaxial tests performed on SMA wires and bars at frequency levels of excitation typical of earthquake engineering is assessed.