## 3 Material and Numerical Models
### Material Models
#### 3.2.5 Numerical Models of Whole Walls and Their Parts  
Numerical models were developed for each test model of the parts of full-scale walls using ATENA software [50]. The symmetry of the test models was used to model a half of the test model with steel elements of the test stand. The elastic-plastic model of the M-W-3 materials was assigned to masonry units and AAC intels. Material parameters are shown in Table 4 (Section 3.2.2). The contact elements, with parameters shown in Table 5 (Section 3.2.3), were used in the bed and head joints, and between the wall and the tie beam. The elastic-based degradation material, with parameters specified in Table 2 (Section 3.2.1), was used for reinforced concrete elements. The Huber-Mises-Hencky (H-M-H) models, with parameters shown in Table 7 (Section 3.2.4), was used for steel reinforcement placed in the lintel. Four-node finite elements, with two degrees of freedom for each node and the plane stress state, were used to model the wall and the lintels. The side of each finite element had a maximum length of 20 mm. Reinforcement in AAC intels, confining elements and tie beams was modelled using bar finite elements with one degree of freedom for each node. Total adhesion of reinforcement to adjacent concrete was applied. The models of wall parts were loaded in sequences during three phases corresponding to loading phases of the laboratory models. The load applied in phase I resulted from the self-weight of the model and elements of the test stand. The first loading stage was realized in the subsequent stage, that is, horizontal loads were transmitted through the prestressing tendon system on the models of wall parts, or vertical load was transmitted to the full-scale walls through tendons. In phase III, the models were loaded, that is, load from the spreader beams was applied. Loading was divided into steps in each phase: three steps in phase I, ten steps in phase II and an increase in the load  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type of Reinforcement** & & & & **Parameter** & & \\
**and Dimensions of Rebar** & \(\mathbf{E_{\rm s}}\) & \(\mathbf{\
u}\) & \(R_{\rm p0,2}\) & \(\mathbf{E_{\rm T}}\) & \(R_{\rm t}\) & \(\varepsilon_{\rm lim}\) \\
**Cross-Section, mm** & \(\mathbf{N/mm^{2}}\) & & \(\mathbf{N/mm^{2}}\) & \(\mathbf{N/mm^{2}}\) & \(\mathbf{N/mm^{2}}\) & \% \\ \hline Longitudinal reinforcement in lintels & 198,000 & & 520 & 245 & 544 & 9.9 \\ (round rebars with a diameter of 8 mm) & 201,000 & 0.3 & 479 & 233 & 501 & 9.6 \\ Longitudinal reinforcement in confining elements and tie beams & 179,330 & & 616 & 242 & 644 & 11.9 \\ (round rebars with a diameter of 12 mm) & 178,500 & & 685 & 261 & 716 & 12.3 \\ (round rebars with a diameter of 10 mm) & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 7: Mechanical parameters of concrete steel used in the numerical model.  
by 1 kN until the complete loss of strength was brought about in the final phase. The numerical models of wall parts are shown in Figure 16, whereas the models of full-scale walls are illustrated in Figure 17.  
Figure 16: Numerical models of wall parts used in finite element method (FEM) calculations for the following series: (**a**) model of elements of the numeral model I (NI) series, (**b**) model of elements of the NII series, (**c**) model of elements of the NIII series: 1—masnorry units with the elastic-plastic based M-W-3 model, 2—reinforced concrete elements with the brittle model, 3—contact elements in bed joints, 4—contact elements in head joints, 5—finite elements representing reinforcement with the Huber–Mises–Hencky (H-M-H) model.  
Figure 17: Numerical models of walls used in FEM calculations for the following series: (**a**) model of MNSO wall, (**b**) model of MSO wall, (**c**) model of M2 SO wall: 1—masnorry units with the elastic-plastic based M-W-3 model, 2—reinforced concrete elements with the elastic-brittle based model, 3—contact elements in bed joints, 4—contact elements in head joints, 5—finite elements representing reinforcement with the H-M-H model.