Dynamics of Shape Memory Alloys-Based Structures Accounting Minor Hysteresis Loops, Finite Deformation, and Thermomechanical Coupling

Abstract Shape Memory Alloys (SMAs) are notable for their ability to mitigate excess vibrations in structural applications through their energy dissipation phenomenon arising out of the unique stress-temperature-dependent martensitic phase transformation. For effective modeling of SMA-based components under dynamic loading, several factors, namely, the effects of inertia, partial phase transformation, large deformation and thermomechanical coupling, need to be considered. In this study, these interdependent effects are incorporated following Updated Lagrangian-based nonlinear finite element (FE) framework, using the hypoelastic constitutive model, relating logarithmic rate of Kirchhoff stress and that of Hencky strain, and is implemented along with the thermal energy equilibrium equation to account for the material level coupling. The effectiveness of the developed FE model is corroborated through the free and forced vibration responses of several SMA-based structures undergoing large deformation. Most importantly, the combined influence of inertia and transformation-induced latent heat is found to increase the displacement amplitude compared to that of the uncoupled response. Besides, if the minor hysteresis loops are not modeled, the damping capability of SMA is found to be underestimated. Furthermore, the frequency responses of these structures exhibit a shift in the resonating frequency, attributed to the material softening and hysteretic energy dissipation, and the same get affected in presence of thermomechanical coupling and extent of deformation.