Filipe Amarante Santos^a, J. O. Cardoso^b, Edgar Camacho^b, Alexandre Velhinho^b, Francisco Manuel Braz Fernandes^b, Andrea Micheletti^c

^aCERIS and Civil Engineering Departament, Faculty of Sciences and Technology, NOVA University of Lisbon, 2829-516 Caparica, Portugal

^bCENIMAT / I3N - Departamento Ciência dos Materiais, FCT, Universidade NOVA de Lisboa, 2829-516 Caparica, Portugal

^cDipartimento di Ingegneria Civile e Ingegneria Informatica, University of Rome Tor Vergata, Via Politecnico 1, 00133, Rome, Italy

Shape memory alloys (SMA) present interesting functional characteristics (shape memory effect and superelasticity) that make them quite attractive for a wide range of applications. These functional characteristics are a consequence of phase transformations that take place within well-defined temperature or stress ranges, depending on being thermal- or stress-induced. These temperature/stress ranges are functions of chemical composition and heat treatment of the material. For applications requiring a wider controllable range, a wider temperature/stress range than that associated to a specific composition/heat treatment may be required. In such a situation, the possible solution will be to use a functionally graded material. The purpose of this work is to provide a basic design methodology for functionally graded shape memory alloy wires. The evolution of the wires subjected to load and temperature changes is simulated by integrating a simple system of ordinary differential equations through standard numerical routines. To describe the constitutive behavior of SMA cables, we choose the Tanaka–Voigt model since it can easily be implemented and adjusted to a wide set of experimental data. A benchmark of our procedure is presented on a three-element system simulating a functionally graded SMA wires. We consider only SMA elements with superelastic behavior, i.e. they are in austenitic phase at ambient temperature. Furthermore, we assume that martensitic phase transformations induce negligible temperature changes in SMA elements, because of the limited strain rates associated with small nodal velocities.