# Numerical Modeling Technique of Damage Behavior of
## 4 Numerical Verification
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **Specimen** & \(\mathbf{D_{mn}}\)**, GPa/m** & \(\mathbf{D_{tt}}\)**, GPa/m** & \(\mathbf{s_{0}(f)}\)**, MPa** & \(\mathbf{\mu_{0}}\) & \(\mathbf{\mu_{r}}\) & \(\mathbf{r_{0}}\)**, MPa** & \(\mathbf{r_{r}}\)**, MPa** \\ \hline \multirow{2}{*}{Concrete cracks} & Bare frame & \multirow{2}{*}{2100} & \multirow{2}{*}{2700} & \multirow{2}{*}{2.75} & \multirow{2}{*}{0.95} & \multirow{2}{*}{0.75} & \multirow{2}{*}{0.14} & \multirow{2}{*}{0.035} \\  & Infilled frame & & & & & & & \\ Bed joints & Infilled frame & & & & & & & \\ Head joints & Infilled frame & & & & & & \\ Frame/infill & Infilled frame & & & & & & \\ \hline \multirow{2}{*}{Masonry cracks} & \multirow{2}{*}{Infilled frame} & \multirow{2}{*}{85} & \multirow{2}{*}{80} & \multirow{2}{*}{0.13} & \multirow{2}{*}{0.7} & \multirow{2}{*}{0.6} & \multirow{2}{*}{0.12} & \multirow{2}{*}{0.025} \\  & Infilled frame & & & & & & & \\ \hline \multirow{2}{*}{Masonry cracks} & **Specimen** & \(\mathbf{G_{f}^{I}}\)**, N/m** & \(\mathbf{\eta}\) & \(\mathbf{\alpha}\)**, m/kN** & \(\mathbf{\beta}\)**, m/kN** & \(\mathbf{\zeta_{dill,0}}\) & \(\mathbf{\zeta_{dill,r}}\) & \(\mathbf{d_{0}}\)**, m** \\ \hline \multirow{2}{*}{Concrete cracks} & Bare frame & \multirow{2}{*}{190} & \multirow{2}{*}{300} & \multirow{2}{*}{11.5} & \multirow{2}{*}{12.5} & \multirow{2}{*}{0.63} & \multirow{2}{*}{0.1} & \multirow{2}{*}{0.002} \\  & Infilled frame & & & & & & & \\ Bed joints & Infilled frame & & & & & & & \\ Head joints & Infilled frame & & & & & & & \\ Frame/infill & & & & & & & & \\ interface & & & & & & & & \\ Masonry cracks & Infilled frame & & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters for discrete constitutive relations of lightweight masonry-infilled frames. The bare frame is firstly analyzed to verify the capability of the proposed modeling with regard to bare RC frames, and the analytical lateral load-bearing capacity curve for the bare frame, are compared with the envelope curve of hysteresis loops in the experiment, as shown in Figure 9. It is concluded that the analysis predicts the experimental curve very well, with only the initial stiffness being overestimated. Figure 10 displays the lateral load-bearing capacity curve of the infilled frame for the analytical and experimental results. It is shown that the relation at the ascend stage till the ultimate lateral load is well captured by the analysis, whereas a rapid decline from the post-peak point is not precisely predicted. This is because an out-of-plane failure at the upper part of the infill panel was observed at the post peak stage in the experiment, while it is not considered in the 2D finite element analysis. More specifically, the differences of peak load, initial stiffness, and displacement corresponding to the peak load for the numerical and experimental results of two specimens are presented in Table 3. It can be seen that the comparison of three parameters also confirms the results observed in the curves. Figure 10: Lateral load-bearing capacity curves for the infilled frame. Figure 9: Lateral load-bearing capacity curves for the bare frame. Next, the damage patterns for two specimens are discussed. For the bare frame specimen, the numerical result exhibits the damage pattern very well, successfully showing the flexural yielding at the ends of columns and beam, as well as the plastic hinges at the bottom of columns and at the two ends of the beam in the late stage of the test. For conciseness, the deformed mesh is not exhibited. The damage patterns of the infilled frame for analytical and experimental results are compared in Figure 11, and a reasonable prediction result is obtained by the numerical analysis. In both results, the damage to the columns and the beam is characterized by a series of flexural cracks, and the inflection point of columns derived from the crack distribution is located at the middle height.