Nonlinear oscillations and chaotic response of Shape Memory Alloys

Shape Memory Alloys (SMAs) present unusual behaviour compared to more standard linear elastic materials. Indeed, they can accomodate large re-versibe strain (pseudo-elasticity) or recover their shape, after being strained, by simple heating (shape memory effect). These behaviours are due to a displacive first order phase transformation called martensitic transformation. These features promote their use in many applications ranging from biomedical field to spatial domain. In the current work, we focus on the pseudoelastic behaviour. To this end, the thermomechanical constitituve law developped by Moumni and Zaki [1] is used. Firstly, the behaviour is reduced to a single degree of freedom. Secondly, inertial effect is considered and the forced oscillations of a device witnessing a pseudoelastic behaviour are studied. The analysis of the results through frequency-response curves and Poincare maps reveals softening behaviour, jump phenomena, symmetry-breaking bifurcations and occurence of chaos. Results are in good agreement with those found in the literature [2] and using a different modelisation of the shape-memory effect.