  Shape Memory Alloys (SMAs) are a class of smart materials that exhibit a
macroscopic contraction of up to 5% when heated via an electric current. This
effect can be exploited for the development of novel unconventional actuators.
Despite having many features such as compactness, lightweight, and high energy
density, commercial SMA wires are characterized by a highly nonlinear behavior,
which manifests itself as a load-, temperature-, and rate-dependent hysteresis
exhibiting a complex shape and minor loops. Accurate modeling and compensation
of such hysteresis are fundamental for the development of high-performance SMA
applications. In this work, we propose a new dynamical model to describe the
complex hysteresis of polycrystalline SMA wires. The approach is based on a
reformulation of the Muller-Achenbach-Seelecke model for uniaxial SMA wires
within a hybrid dynamical framework. In this way, we can significantly reduce
the numerical complexity and computation time without losing accuracy and
physical interpretability. After describing the model, an extensive
experimental validation campaign is carried out on a 75 {\mu}m diameter SMA
wire specimen. The new hybrid model will pave the development of hybrid
controllers and observers for SMA actuators.
