Nonlocal elasticity in shape memory alloys modeled using peridynamics for solving dynamic problems

The work is primarily devoted to the peridynamic model elaborated for a solid body made of shape memory alloys (SMAs). The superelasticity effect is taken into consideration as well as its practical applications. Hence, the numerical simulations, making use of the phenomena of superelasticity, are carried out for the model of an SMA wire to investigate mechanical energy dissipation. The nonlocal peridynamic model of an SMA component is derived based on the theory proposed by Lagoudas—introduced to describe the phenomenon of solid phase transitions that occur in SMA. The results of the conducted experimental work are applied by the authors to validate the elaborated model. Moreover, an alternative verification of the peridynamic model is also performed using other numerical tool—the finite element code based on the analytical approach for modeling SMA, developed by Auricchio. The hysteretic character of the stress–strain relationship for the modeled SMA component, which undergoes the superelasticity effect, is shown using quasi-static peridynamic simulations. Finally, the capability of energy dissipation when cyclic loading for the elaborated nonlocal model is investigated via dynamic simulations. The numerical results obtained for the studied case are discussed to show the applicability of the presented modeling approach in the field of structural dynamics. A particular focus is placed on the available structural stiffness control functionality in mechanical systems equipped with SMA and efficiency of energy dissipation in SMA-based dampers, which may be effectively applied to suppress mechanical vibrations. Both mentioned application areas for SMA are of the authors’ special concern in the designing process of the nonlinear supporting structure in gas foil bearings, which is also discussed in the final part of the paper to highlight the practical aspects of the conducted research.