A Superelastic Shape-Memory-Alloy Beam Model

The present paper proposes a simple shape-memory-alloy beam model, based on the classical Euler-Bernoulli beam theory. Due to restrictive kinematical assumptions, a one-dimensional constitutive equation is used. Thus, the material behavior is described through a simple l-D phenomenological model, which allows for different material responses in tension and compression as well as for different elastic properties between austenite and martensite. Two numerical procedures are developed for the determination of the cross-section response together with a time-step integration algorithm. Then, the implementation of the shape-memory-alloy beam model within a finite-element framework is addressed. Several numerical examples are investigated to assess both the performance of the beam model and the procedure developed. The complex behavior of a typical cross section is emphasized. The results obtained from the simulation of three and four-point bending tests are compared both with experimental results and with numerical solutions obtained from a three-dimensional finite-element scheme.