Advanced Modeling of SMA Flag-Shaped Hysteresis for Nonlinear Time-History Analysis in SAP2000

Superelastic shape memory alloys (SMAs) introduce supplementary energy dissipation with minimal residual deformation, which is desired in earthquake engineering–related applications (e.g., SMA bracing systems or SMA-based isolation systems). An appropriate phenomenological model of SMA flag-shaped hysteresis is essential to simulate the seismic response of structures equipped with such devices. In the structural analysis and design software SAP2000, no element is available specifically for modeling SMAs. The CSi knowledge base webpage suggests a parallel combination of elementary multilinear-elastic (MLE) and multilinear-plastic (MLP) link elements. This modeling strategy, widely used in the literature, can be affected by the cumulative damage in the MLP link elements after the first plastic excursion. As demonstrated in this technical note, the cumulative damage in MLP elements leads to incorrect modeling of the SMA flag-shaped hysteresis in nonlinear time-history analysis (NLTHA). This issue encountered in the model suggested in the CSi knowledge base webpage is resolved by an alternative modeling strategy proposed in this work, which makes use of parallel MLE and MLP link elements along with series gap and hook spring elements available in SAP2000. The proposed approach not only eliminates the cumulative damage of MLP links over repeated cycles, but also lends itself to a more general representation of the flag-shaped hysteresis of SMAs than do other formulations proposed in the literature, thus proving to be a simple and versatile modeling strategy.