This topic discusses the modeling of Shape Memory Alloy (SMA) elements in ETABS, SAP2000, and CSiBridge. The hysteresis loop of an SMA element looks like a flag. Such a hysteresis has the benefit of some energy dissipation along with minimal residual deformations upon removal of the load, hence is mostly preferred for re-centering devices.
Figure 1. Idealized Stress-Strain Curve of Superelastic SMAs
It is possible to simulate superelastic SMA behavior in CSI programs using multiple link elements as described in Andrawes, B., and DesRoches, R. (2005).“Unseating prevention for multiple frame bridges using superelastic devices.”Smart Mater. Struct.,14(3), S60–S67.
Figure 2. Schematic diagram of Superelastic SMA Model Using Two Links Element from Adrawes and DesRoches 2005
Define two link properties and assign them to two link elements in parallel. A multi-linear plastic link using the Pivot model is used to define the hysteresis loop, and a multi-linear elastic link is used to shift the hysteresis loop away from the origin. For example, the following flag-shaped force-deformation behavior in Figure 3 can be obtained using the two link properties defined in Figures 4:
Figure 3. Force-Deformation curve. Example of Superelastic SMA Modeled Using Two Links elements
Figure 4a. Multi-linear Plastic link property using Pivot hysteresis
Figure 4b. Multi-linear Elastic link property