Shape-memory alloys: Modelling and numerical simulations of the finite-strain superelastic behavior

Shape-memory alloys (SMA) show features not present in materials traditionally used in engineering; as a consequence, they are the basis for innovative applications. The present work proposes a step toward the development of a computation tool to be used during the design of SMA-based devices. To reach this goal, we develop a constitutive model which reproduce the superelastic behavior of shape-memory alloys at finite strains. For an isothermal case we discuss in detail the numerical implementation within a finite-element scheme as well as the form of the algorithmically consistent tangent. To assess the viability of the proposed approach we simulate the response of some simple SMA typical structures (uniaxial test, four-point bending test) as well as an application with possibly a very high impact in different medical fields.