Nonlinear dynamics and chaos in shape memory alloy systems

•Development of constitutive models for shape memory alloys.•Nonlinear dynamics of smart systems and structures with shape memory alloy elements, discussing complex behaviors as chaos.•Vibration reduction of SMA systems including adaptive–passive vibration absorbers and impact systems.•Numerical simulations and experimental investigation of smart material systems.

Smart material systems and structures have remarkable properties responsible for their application in different fields of human knowledge. Shape memory alloys, piezoelectric ceramics, magnetorheological fluids, and magnetostritive materials constitute the most important materials that belong to the smart materials category. Shape memory alloys (SMAs) are metallic alloys usually employed when large forces and displacements are required. Applications in aerospace structures, rotordynamics and several bioengineering devices are investigated nowadays. In terms of applied dynamics, SMAs are being used in order to exploit adaptive dissipation associated with hysteresis loop and the mechanical property changes due to phase transformations. This paper presents a general overview of nonlinear dynamics and chaos of smart material systems built with SMAs. Oscillators, vibration absorbers, impact systems and structural systems are of concern. Results show several possibilities where SMAs can be employed for dynamical applications.