## 5 Final Remarks  
A formal description and validation of a macro-element has been presented for the three-dimensional analysis of masonry structures. The macro-element is based on the FE method, but several simplifications have been developed to supply faster results than conventional continuous FE models, such as those retrieved from smeared crack approaches. It is aimed for the macro-scale analysis of structures, and based on a discrete approach; specifically, quadrilateral rigid plates are connected at its interfaces by a set of FE trusses. These one-dimensional elements govern the in-plane and out-of-plane deformations. The constitutive response can be based on any plasticity model; however, the so-called concrete damage plasticity model was assumed as it can reproduce well homogenised material data provided from experimentation or numerical homogenisation of concrete-like materials. A regularisation step corrects the fracture energy of the stress-strain input curves according to the defined macro-mesh dimensions, thus guaranteeing the well-posedness of the solution. Validation and convergence tests have been performed to evaluate if the macro-element fulfils the requirements for (i) elastic problems; (ii) eigenvalue problems; and (iii) nonlinear problems for monotonic and cyclic loading cases. The tests have shown that the discrete model provides good results in both static and dynamic ranges. Likewise, it has been concluded that a refinement level given by L/15 (L is the length of the wall side being meshed) seems a reasonable choice for the mesh size when performing a structural analysis; at least in the case that a mesh sensitivity test is disregarded. Computational recommendations have been also briefly addressed, as the use of an implicit solver scheme, the use of the arc-length method for nonlinear quasi-static tests, and the use of a FE node renumbering algorithm. Although the application of discrete systems may be questionable in cases where multiphase couplings can occur, as when thermal or hydro-mechanical effects exist, the latter macro-element proved to be suitable for structural-oriented problems such as the broader range of quasi-static and the seismic assessment of masonry structures. A decoupled characterisation for the admissible in- and out-of-plane deformations--that is certainly an approximation--proved to be reliable (at least for levels of pre-compression lower than the masonry compressive strength). Nonetheless, the macro-element is robust and can be implemented in any FE software, to any structural application, and perhaps more importantly, to be used by both professionals and academics. As future research streamlines, one can state that the reduced computational cost of the macro-element can be explored: (a) within larger-scale structures [122; 123]; (b) within a structural health monitoring sys \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**Material Properties**} \\ \hline  & \(\mathbf{E_{xx}}\) & \(\mathbf{E_{yy}}\) & \(\boldsymbol{v}\) & \(\boldsymbol{f_{t}}\) & \(\boldsymbol{Gf_{tension}}\) & \(\boldsymbol{f_{c}}\) & \(\boldsymbol{Gf_{compression}}\) & \(\boldsymbol{f_{shear}}\) & \(\boldsymbol{Gf_{shear}}\) \\  & **(MPa)** & **(MPa)** & **(-)** & **(MPa)** & **(N/mm)** & **(MPa)** & **(N/mm)** & **(MPa)** & **(N/mm)** \\ \hline Macro–element (discrete) model & 6400 & 3600 & & & & & & & 0.20 & 0.50 \\ Smeared crack model & 5170 & 5170 & 0.200 & 0.105 & 0.012 & 2.480 & 3.970 & – & – \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Material properties adopted for the LNEC brick house benchmark performance test. tem [124; 125] following the so-called digital twin framework; and (c) it can be accounted within a probabilistic-based features for reliability and robustness-based analysis. Conceptualisation, L.C.M.d.S. and G.M. ; methodology, L.C.M.d.S. and G.M. ; software, L.C.M.d.S. and G.M. ; validation, L.C.M.d.S. ; formal analysis, L.C.M.d.S. ; resources, L.C.M.d.S. and G.M. ; writing--original draft preparation, L.C.M.d.S.