Tensile-compressive asymmetry influence on shape memory alloy system dynamics

The remarkable properties of shape memory alloys (SMAs) are attracting much technological interest in several science and engineering fields, varying from medical to aerospace applications. Hysteretic response of these systems is one of their essential characteristics being related to the martensitic phase transformation. The dynamical response of systems with SMA actuators presents a rich behavior due to their intrinsic nonlinear characteristic. Since experimental results show that SMAs present an asymmetric behavior when subjected to tensile or compressive loads, it is important to evaluate the influence of this kind of behavior in the nonlinear dynamics of mechanical systems with SMA devices. This article discusses the nonlinear dynamics of shape memory alloy systems, considering the influence of tensile-compressive asymmetry in the thermomechanical behavior of SMAs. An iterative numerical procedure based on the operator split technique, the orthogonal projection algorithm and the fourth-order Runge–Kutta method is developed to deal with nonlinearities in the formulation. A numerical investigation is carried out showing some qualitative results such as chaotic-like response and multi-stability behavior for a single degree of freedom SMA oscillator.