## 3 Modelling Strategies
### Strategies for Numerical Models  
The analysis of URM buildings can be performed by adopting four numerical modelling approaches, namely the finite element method (FEM), discrete element method (DEM), rigid macroblocks, and equivalent frame model (Figure 3). A general description is given in the following. Modelling strategies for URM buildings are treated in more detail in [11; 54; 55; 56; 57; 58; 59; 60].  
In FEM models, the continuous domain is discretized into small and simpler subdomains called elements, which are connected by nodes to form a mesh. These models represent structural problems using various types of elements, such as 1D, 2D, 3D, springs, interfaces, etc. [11]. FEM models are versatile and can solve both static and dynamic problems with linear or non-linear solutions. While implicit methods are commonly used for solving nonlinear problems, explicit solutions can also be applied when needed. Currently, FEM models, combined with a macro-modelling approach, are extensively used for the overall seismic assessment of unreinforced masonry (URM) buildings [36].  
DEM is a collection of numerical techniques used to analyse the dynamics of a set of particles or bodies treated as a discontinuous material. In the seismic evaluation of unreinforced masonry (URM) buildings, DEM models typically consist of blocks representing individual units or larger portions of the structure, and their interactions are defined through contact points with specific contact properties [11; 36]. These blocks in DEM models can be treated as either rigid or deformable bodies [61]. DEM models employ explicit solutions to address highly nonlinear geometric problems, enabling the simulation of collapse mechanisms with large displacements [36]. For more comprehensive details, refer to [PERSON] [62].  
The equivalent frame method consists of the simplification of the building by identifying its main load-bearing components, such as piers and spandrels. The discretization process becomes a challenging task when the building has a complex geometry where openings are irregularly distributed [11]. Subsequently, these components are typically replaced with nonlinear columns, beams, or blocks, which are connected using rigid nodes,  
Figure 3: Numerical models: (**a**) finite element method (FEM); (**b**) discrete element method (DEM); (**c**) equivalent frame method; (**d**) rigid macroblocks [36].  
Figure 2: Modelling strategies for material (adapted from [12]): (**a**) detailed micro-modelling; (**b**) simplified micro-modelling; (**c**) macro-modelling.  
plastic hinges, interfaces, or springs [63]. The formulation captures the shear-diagonal deformation, flexural response, and shear sliding of the components [64]. The global response is only related to the IP behaviour of the walls and floors, and no information is provided regarding the OOP performance [11].  
In the last strategy, the building is idealized as a structure composed of rigid macroblocks, which are delimited by the expected collapse mechanisms. These mechanisms can be defined according to the observed damage in similar structures during an earthquake, experimental campaigns, or experience [36]. It is noted that the adopted discretisation dominates the response and can be overestimated if the mechanism with the lowest capacity is neglected. The limit analysis is generally used to evaluate the seismic response.