## 5 Numerical Validation of the Model
### Dynamic Analysis of a Masonry House
#### 5.2.4 Numerical Modeling  
The representation of the house using the DFM is shown in Figure 20. This mesh corresponds to the DFM\({}_{-}\)1 mesh used in the modal analysis, consisting of 126 macro-elements and 840 DOF. In this figure, the beam elements and the mass distribution are color-coded for clarity. The roof was treated as a dead load, and it was represented by additional masses at the nodes atop the east and west walls to simulate its weight and impact on structural behavior during an earthquake. The timber frames around the openings were modeled as elastic beams, with their contribution to the overall structural mass calculated using the standard approach for defining the mass matrix of beam elements. For this study, it was considered that all the dissipative phenomena that occur during an earthquake are modeled thanks to the nonlinear constitutive behavior of the DFM. As a result, there was no additional damping in the dynamic analysis. The mechanical properties for the numerical analysis are presented in Table 2. These material properties have been identified from the quasi-static tests conducted by [PERSON] [35] on a wall constructed with the same material. The five primary modes calculated for the X direction of excitation (Figure 16) correspond to the following frequencies and effective masses (the ratio of modal mass to total  
Figure 19: Positions of the cable sensors on the north wall of the reduced scale house. Figure 20: Modeling of the URM house: (**a**) the timber frames around openings, and (**b**) mass distribution. mass): Mode 1 (14.2 Hz, 49.6%); Mode 2 (25.3 Hz, 24.6%); Mode 3 (30.3 Hz, 2.3%); Mode 4 (64.1 Hz, 4%); and Mode 5 (66.3 Hz, 3.1%). Note that Modes 1 and 2 correspond to the OOP displacements of the walls perpendicular to the excitation direction (Figure 21). The parameters governing the hysteresis behavior are not included in Table 2 as they are derived from the material properties listed in the table and empirical relations outlined in [23]. Their values depend on the location of each macro-element within the structure and are locally determined using Equations (10)-(12). No DFM material properties were calibrated using the shake table test results, ensuring that the DFM serves as a fully predictive model. The displacement corresponding to the ground acceleration shown in Figure 18 was applied to the shake table on which the house model was mounted. Figure 22 displays the average of the measured displacements at Points 6 and 7 alongside the displacement calculated at Point 6 using the DFM (the calculated displacements at Points 6 and 7 are identical due to symmetry). Focusing on the time interval between 4 s and 12 s, when displacements reach their peak values, they provide insights into the numerical model's performance relative to the actual behavior of the tested house. Despite the overall accuracy, noticeable deviations exist between the model predictions and the experimental observations, particularly around the 7 s mark, where the model fails to accurately capture the measured oscillations. The most significant discrepancy occurs at the peak displacement at 9 s, where the model underestimates the experimentally recorded displacement. This limitation can be attributed to the model's inability to accurately reproduce the OOP displacement, as shown in Table 4, where the OOP displacement value is only half of the experimentally measured value. Furthermore, Table 4 presents the maximum displacements captured by the DFM alongside those experimentally recorded during the shake table test at Points 6 and 7 (d\({}_{IP}\)) and at Point 2 (d\({}_{OOP}\)). These results highlight the model's performance in replicating the IP wall movements in both negative and positive directions, achieving a maximum error of around 10%. However, the model's accuracy declined for displacements in the positive direction, with errors reaching up to 27% at the peak displacement around the 9-second mark.