Hysteresis model of shape memory alloy wire-based laminated rubber bearing under compression and unidirectional shear loadings

Smart lead rubber bearings (LRBs), in which a shape memory alloy (SMA) is used in the form of wires, are a new generation of elastomeric isolators with improved performance in terms of recentering capability and energy dissipation capacity. It is of great interest to implement SMA wire-based lead rubber bearings (SMA-LRBs) in bridges; however, currently there is no appropriate hysteresis model for accurately simulating the behavior of such isolators. A constitutive model for SMA-LRBs is proposed in this study. An LRB is equipped with a double cross configuration of SMA wires (DC-SMAW) and subjected to compression and unidirectional shear loadings. Due to the complexity of the shear behavior of the SMA-LRB, a hysteresis model is developed for the DC-SMAWs and then combined with the bilinear kinematic hardening model, which is assumed for the LRB. Comparing the hysteretic response of decoupled systems with that of the SMA-LRB shows that the high recentering capability of the DC-SMAW model with zero residual deformation could noticeably reduce the residual deformation of the LRB. The developed constitutive model for DC-SMAWs is characterized by three stiffnesses when the shear strain exceeds a starting limit at which the SMA wires are activated due to phase transformation. An important point is that the shear hysteresis of the DC-SMAW model looks different from the flag-shaped hysteresis of the SMA because of the specific arrangement of wires and its effect on the resultant forces transferred from the wires to the rubber bearing.