Rate-dependent thermo-mechanical modelling of superelastic shape-memory alloys for seismic applications

Experimental tests performed on superelastic shape-memory alloys (SMAs) show a significant dependence of the stress-strain relationship on the loading - unloading rate, coupled with a not negligible oscillation of the material temperature. This feature is of particular importance in view of the use of such materials in earthquake engineering, where the loading rate affects the structural response. Motivated by this observation and by the limited number of available works on the modelling of SMAs for seismic applications, the present article addresses a uniaxial constitutive model for representing the system rate-dependent thermo-mechanical behavior of superelastic SMAs. The model is based on a single internal scalar variable, the martensite fraction, for which different rate-independent evolutionary equations in rate form are proposed. Moreover, it takes into account the different elastic properties between austenite and martensite. The whole model is then thermo-mechanically coupled with a thermal balance equation. Hence, it considers mechanical dissipation as well as latent heat and includes temperature as a primary independent variable, which is responsible for the dynamic effects. The article also provides a description for the integration, in time, of the constitutive equation and presents the solution algorithm of the corresponding time-discrete problem. Finally, results from numerical analyses are reported and the ability of the model to simulate experimental data obtained from uniaxial tests performed on superelastic SMA wires and bars at frequency levels of excitation typical of earthquake engineering is assessed.