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

Abstract

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