# Validation of Seismic Performance of Stainless Press-to-Connect Piping System under Cyclic Loadings
## 3 Validation of FE Model of Elbow Component  
An FE model of a component level such as the elbow joint of a piping system must be reconciled based on experimental test results to develop a high-fidelity FE simulation model of a large-scale piping system using a press-to-connect system. In this study, to determine the material properties of the STS 304, tensile tests were conducted on three specimens, as shown in Figure 2, and the stress-strain relationships of the STS 304 material are displayed in Figure 3.  
Figure 1: Experimental test of press-to-connect elbow system. Figure 2: Tensile tests of STS 304 material. Based on the tensile test results, kinematic hardening model for this material was assumed as described in Figure 3. The material parameters were constituted with kinematic hardening modulus (c), equivalent stress in accordance with yield surface \(\left(\sigma^{vM}\right)\), back-stress \(\left(\alpha\right)\), and equivalent plastic strain \(\left(\dot{\varepsilon}^{pl}\right)\), as defined in Equation (1) [12]. \[\dot{\alpha}=C\frac{1}{\sigma^{vM}}(\sigma-\alpha)\left(\dot{\varepsilon}^{ pl}\right) \tag{1}\]  
where, the kinematic hardening modulus was applied in this study regardless of temperature, the equivalent plastic strain can be explained in a similar manner based on the definition of the von Mises constitutive equation [13], and the yield surface can be defined as the stress surface that satisfied the yield condition of the yield function related to the principal stresses. In addition, the equivalent stress in accordance with von Mises stress can be expressed in Equation (2), if \(\sigma_{12}=\sigma_{23}=\sigma_{31}=0\)  
\[\sigma^{vM}=\sqrt{\frac{1}{2}\Big{\{}(\sigma_{1}-\sigma_{2})^{2}+(\sigma_{2}- \sigma_{3})^{2}+(\sigma_{3}-\sigma_{1})^{2}\Big{\}}} \tag{2}\]  
More specifically, a bilinear hardening plastic stress-strain curve corresponding to the kinematic hardening model was determined to describe the constitutive model of the elbow system, as shown in Figure 3. Finally, an FE model of the press-to-connect elbow system was constructed, and the jig condition was represented by a 2-node beam element (B31), while 4-node shell elements (S4R) were applied to establish the mechanical joint and straight pipe using the ABAQUS platform [11]. Considering the O-ring seals, the FE model of the elbow joint was simplified based on the spring element because of its extreme complexity and convergence difficulty of the simulation between the O-ring seals at the end of the pipe and mechanical pressing connectors. Figure 4 illustrates the FE model of the elbow joint and related boundary conditions. To achieve efficiency and accuracy of the FE model, a 2 mm mesh size for the elbow and straight piping system was generated, and the beam element for the jig was set to a 3 mm mesh size in this study. The reconciliation of the experimental and numerical data is shown in Figure 5. As can be seen, the load-displacement relationship of the simulation model was in good agreement with the data of the experimental test obtained using the UTM, and the initial stiffnesses of the results of the experimental test and FE simulation model were almost the same. The maximum forces corresponding to the experimental test result and FE model up to 20 mm were 5.44 kN and 5.59 kN, respectively. Furthermore, the results of the normalized energy dissipation related to the loading protocol is shown in Figure 6a. Figure 3: Stress–strain relationships of STS 304 material. Even considering that the difference between the experimental and analytical data slightly increased, the error did not exceed 5%. In addition, the overall trend of the deformation angle of the FE elbow model shown in Figure 6b up to 20 mm is considerably higher than that of the experimental test. This issue may be caused by the springback and Bauschinger effect, due to the difference between tensile strength and compressive strength at the yield position [14], of the constitutive steel material model on the press-to-connect elbow system.