## 1 Introduction  
Masonry is a phenomenological complex material due to the elastic and strength anisotropies, its well-marked nonlinear response in tension, compression, and shear regimes [1], and due to the potential damage-induced anisotropy. Experimentation reveals the difficulty of predicting the mechanical response of masonry [2]. Such difficulties are consistent with the substantial number of works developed during the last decades aiming the assessment of masonry structures. These can be grouped within simplified or advanced approaches [3, 4, 5]. In the scope of structural analysis for masonry buildings, the prevailing design rules or analytical approaches are the most useful for practitioners, despite the possible unrealistic or conservative outcomes [6]. Other simplified procedures, such as the story-mechanism [7] and the equivalent frame-based models [8, 9, 10], can be found; in hand with the keen development and improvement of macro-elements that constitute the geometric features of masonry structures (such as walls, piers, and spandrels) [11, 12, 13, 14, 15]. The reduced degrees-of-freedom make these suitable for the study of large-scale and regular structures. Yet, these suffer from a macro-element discretisation bias, demand proper strength criteria for each macro-element type, and hardly consider out-of-plane failure modes. More suitable and yet conceptually simple procedures, such as the rigid-body approaches [16, 17] or the kinematic methods [18, 19, 20, 21, 22], are useful to supply closed-form solutions under dynamic excitations, although are still overly complex for walls subjected to two-way bending. In this context, the need for more general methods encouraged the development of advanced numerical strategies, such as the Discrete Element Method (DEM) and the Finite Element Method (FEM) [23]. DEM presents several advantages since allows one to represent masonry as a discontinuous media, in which masonry units are considered as the ensemble of distinct bodies connected by contact surfaces (joints). Since the first DEM model proposed by [PERSON] and [PERSON] [24], and the discontinuous deformation analysis (DDA) introduced by [PERSON] and [PERSON] [25], several studies have been introduced with masonry as a specific target [26]. DEM is widely applied to simple blocky structures [5]; for instance, in the analysis of arches to assess the collapse load [27], the static and dynamic analysis of masonry walls [28; 29; 30; 31; 32; 33; 2], and the rocking motion of stone blocks [34]. Software dedicated to this formulation exists, see [35; 36]. Although DEM unfolds inherent advantages, the modelling of three-dimensional complex or large structures, with a high number of block elements, can make the computational time unacceptable. Besides, simplifications concerning the mesh discretisation may compromise the accuracy and, therefore, may be taken carefully. As stated by [PERSON] [26], the accuracy for the out-of-plane study of masonry is quite dependent on the number of contact points in the thickness direction. Regardless of the latter, DEM is still rarely applied for three-dimensional structures within a dynamic analysis. To what concerns FEM, its overall use deserves wide acceptance from the scientific community [4]. FE-based models have a broad range of applications because they can be employed either in simple or complex geometric structural configurations, and either within static or dynamic problems. These are typically classified according to the followed modelling strategy, namely: (i) direct numerical simulation or micro-modelling approach; (ii) macro-modelling approach; and (iii) multi-scale computational approach. In the direct numerical simulation, both masonry components (units and mortar joints) are explicitly represented. Both in- and out-of-plane orthotropic nonlinear behaviour can be reproduced, but long processing times are expected, hence being only recommended for limited size structural problems [26; 37; 38; 39; 40; 41; 42; 43; 44; 45].