## 2 Methods  
Explicit finite element analysis [46; 47; 48; 49] was carried out using a commercial finite element package (Abaqus/Explicit) [50] as the solver. The incident bar and flange of the SHTB were modelled as a single-piece solid body without a specimen and transmission bar. The striker was modelled as a separate solid body. The bar length, measured from the flange end (impact surface) to the free end for specimen contact, was 2000 mm. The gap between the inner surface of the hollow striker and outer surface of the bar was 0.01 mm. The striker was initially 0.1 mm away from the flange (impact surface). The initial velocity of the striker was set as 15 m/s.  
Two bar diameters (\(D_{\text{b}}\)) were considered: 10 and 20 mm. The flange heights (\(H_{\text{f}}\)) were 2.071 and 4.142 mm, respectively, to make the cross-sectional area ratios of the flange to bar unity for both bar diameters (10 and 20 mm). To achieve a neat tensile pulse in the incident bar, the striker thickness (\(T_{\text{s}}\)) was the same as the flange height (\(H_{\text{f}}\)) [18]; the cross-sectional areas of the flange (\(A_{\text{f}}\)) and hollow striker (\(A_{\text{s}}\)) were the same. The case where \(A_{\text{s}}\) (=\(A_{\text{f}}\)) = 0.5\(A_{\text{b}}\) was also modelled, as a control case.  
Half of the two-dimensional axisymmetric geometry was modelled considering the symmetry of the model. The geometry of the model was discretised using four-node bilinear axisymmetric quadrilateral elements (CAX4R). When the mesh sensitivity was tested separately using mesh sizes less than approximately 1 \(\times\) 1 mm\({}^{2}\) (radial \(\times\) axial dimensions), the stress profile monitored at the strain gauge position exhibited no appreciable change. Based on this result (not shown here), the element size of approximately 0.5 \(\times\) 0.5 mm\({}^{2}\) was employed herein for the flange, striker, and bar. An example of the finite element model near the flange structure region is presented in Figure 2.  
The kinematic contact condition was applied to the master-slave contact pair, set for the impact surfaces of the striker and flange. Friction between the contact surfaces was not considered. The solver utilises the central difference time integration method. To ensure solution stability, a stable time increment for each time integration was calculated by the solver by considering the wave speed and minimum element length.  
While versatile bar materials such as magnesium, aluminium, titanium alloy, and steel are used in contemporary SHTBs, steel was considered in this study. Although the properties of structural steel vary depending on the type and manufacturer, their density, elastic modulus, and Poisson's ratio were selected arbitrarily herein by referring to the properties of various steel grades [51]: 7800 kg/m\({}^{3}\), 210 GPa, and 0.3, respectively. Although the properties were selected as such, the conclusions drawn out in this study based on the linear elastic analysis are believed to be applicable to the aforementioned bar materials, as well [52]. As all parts of the SHTB model deform elastically, plastic deformation was not considered.  
In the post-processing stage, the axial stress component (\(\sigma_{\text{yy}}\)) in the incident bar was extracted from a surface element at 1000 mm in the incident bar to avoid the interaction with the reflected wave from the free end of the bar at the specimen side. In experiment setups, the axial strain is usually measured at such a strain gauge position.