## 3 Material and Numerical Models  
### General Comments and Strategy Employed for Masonry Modelling  
Numerical analysis by FEM is used to observe the behaviour of the structure in the linear stage, through cracking until complete loss of strength [31]. Non-linear material models are mainly used in numerical analyses. Models based on empirical observations differ in constitutive laws. Strength parameters can be defined for components of the masonry or the equivalent material by averaging properties. Hence, a few modelling methods can be identified for the numerical analysis of masonry structures by FEM. They are:  
1. The macro-model, which treats the masonry structure as a material having identical mechanical parameters. Such a model is applied in practical computations for large masonry structures (finite elements can include two or more masonry units) [31; 32; 33; 34];
2. The mezzo-model--a variant of the macro-model that is similar to the periodic micro-structure, which includes non-linear relations between mean stresses and mean deformations of the element, composed of masonry units and mortar layers equivalent to a given medium \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Element Name** & **Model Drawing** & **Model** & **Number of Models** \\ \hline \(1\) & \(2\) & \(3\) & \(4\) \\ \hline
**MMSO** & & & \\
**MSO** & & & \\
**M2 SO** & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Research programme for full-scale walls (dimensions in cm). (of the same dimensions). Its basic element (representative volume element [35]) contains the required geometrical and physical information about any type of component for the masonry elements [36; 37];
* The micro-model, which identifies the masonry structure as a heterogeneous material. Classification into finite elements is made for each material (mortar, masonry unit). Different non-linear behaviour is assumed for bricks and mortar, including potential interaction forces between them. This type of model is usually used to analyse small constructions or to perform in-depth analysis. Its description requires information about the characteristics of components and the contact between them [38; 39; 40; 22; 32; 33; 34; 35; 36; 38]. Taking into account the purpose of this paper--that is, observation of conditions in the masonry and the lintel and their interactions--the masonry wall (Figure 1a) was replaced by the masonry micro-model. In this case, there were a few methods of modelling. [PERSON] et al. [41] demonstrated that micro-models of walls can be prepared using 3D (Figure 1b) and 2D techniques for analysis of plane stress (e.g., plane deformations; connections between walls are less frequently used), as illustrated in Figure 1c-f. The main principle of micro-models, as illustrated in Figure 1d-f, is adding contact (interface) elements, which represent delamination at the interface between masonry units and mortar, to bed joints. We assumed that this type of modelling was the most adequate for the effects observed in our studies. Micro-modelling by the 3D technique was abandoned due the size of tested elements (Figure 1b). The second aspect taken into account when choosing the technique of micro-modelling was a series of cracks that developed in the masonry units during the tests, and the non-linear relationship between stress and deformation. Therefore, the authors decided not to use the model with linear and elastic masonry units (Figure 1d). The 2D micro-model, shown in Figure 1f [40], was chosen. Its masonry units took the mean mechanical parameters of the wall, then contact elements representing the behaviour of bed and head joints were placed at the interface of masonry units. All elements were modelled under conditions of plane stress. The reinforcement micro-model was also used for AAC lintels. Rebars were modelled as elements of non-linear parameters. Rebars were bonded with the surrounding AAC material, neglecting adhesion aspects.