# Superelastic Shape Memory Alloy Honeycomb Damper
## 5 Improvement of SHD
### Validation of Optimization  
A numerical model of the SHD system was developed using an optimization approach. The strain distribution of this model was then compared to that of the original model in order to assess the efficacy of the optimization scheme. The minimum thickness of the non-horizontal cell wall ends was computed as:  
\[b_{1}=\sqrt[3]{\frac{12M_{p1}}{t\cdot\omega_{1}E_{M}}}=\sqrt[3]{\frac{12\times 6 \times 1.40625\times 10^{-12}\times 0.0019\times 0.5}{0.1\times 0.3867\times 0.0225}}=0.002531 \text{ m} \tag{10}\]  
Figure 15 shows the optimized numerical model of SHD. \(R\) represents the radius of the chamfer angle (unit: mm).  
The fracture strain distribution of the optimized model is depicted in Figure 16b. After optimization, there has been a significant reduction in the tension concentration within the specimen. The maximum strain of the optimized model is 6.59% at 10.3% overall strain. The results suggest that the implementation of the honeycomb structure design method resulted in a 1.56-fold increase in the deformation capacity of the SMA materials. Furthermore, the even distribution of cell wall deflection can be attributed to the fillet and variable wall thickness scheme. The stress in the compressed cell walls is greater than the Martensite initial stress of 418 MPa, as shown in Figure 16a. It signifies that the SMA material's superelastic characteristic is completely utilized in these components. As a result, fatigue fractures in SMA honeycomb can be effectively delayed, thereby preventing the premature failure of SHD. While the fracture strain of SMA plates remains below 6%, the implementation of a honeycomb structure, which leverages the geometrical nonlinearity property, can result in an enlargement of the damper's macroscopic stain to 10.3%.  
In Figure 17, a comparison is made between the responses of the specimen and the optimized SHD during the final axial tension and compression cycle, where the specimen's response was 10 mm and the SHD's response was 15 mm per cycle. When subjected to 15 mm of compression or tension, the static residual deformation of the optimized SHD remains below 0.1 mm. Minimum ratios of static residual displacement to maximal displacement are 0.7% or less. In the optimized SHD, the maximum deformation, maximum force, and dissipated energy, which are calculated as the area in a hysteretic loop, are both substantially increased. The specimen experiences a maximum deformation of 10 mm, a maximum force of 2.01 kN, and a dissipation of energy of 1.38 J during the final experimental hysteretic cycle. In the optimized SHD, however, the maximum deformation increased to 15 mm, the maximum force to 14.2 kN, and the dissipated energy to 5.39 J. The maximum force, maximum deformation, and dissipated energy of the optimized SHD are enhanced by 606%, 50%, and 291%, respectively, when compared to the specimen.  
Figure 15: Optimized numerical model of SHD.  
When enlarged by a factor of 10, the optimal SHD has a width of around 750 mm, a length of 1700 mm, and a depth of 150 mm. The deformation and force capability will increase to 150 mm and 1420 kN, respectively. Dampers of this magnitude, capable of accommodating large displacements and forces, can be utilized in the construction of simply supported bridges, which are commonly constructed worldwide.  
Figure 16: Responses of the optimized SHD numerical model: (**a**) stress distribution and (**b**) strain distribution.  
Figure 17: Comparison of the responses of the experimental results of the specimen and the optimized SHD.