## 2 Materials and Methods  
In this section, the constitutive law of the materials (such as masonry and FRCM) adopted for the structural analysis are defined. From the scientific literature, several stress-strain constitutive relationships can be used to describe the mechanical behavior of masonry [31]. One of the most adopted models for compressive behavior, used for the presented analyses, is suggested by CEN Eurocode 6 [32], as shown in Figure 2. This model completely neglects the post-peak softening, considering a perfectly plastic post-peak behavior. The tensile behavior, on the other hand, can be described by elastic-brittle relationship, yet for the purposes of the present work, its contribution is negligible when the strengthening system is applied. Composite materials are, by definition, made up of two or more materials known as phases. In FRCM composite materials, it is possible to differentiate exactly three phases: the fibrous phase, the mortar matrix phase, and the interface phase. Due to this mixed nature of the mortar matrix and fiber, the FRCM composite is characterized by various phenomena such as matrix cracking, slip, or debonding phenomena. However, it is possible to provide a general stress-strain relationship to simulate the behavior of the whole composite system to interpret the different factors that influence its behavior most. [PERSON] et al. [33] reported three different stress-strain relationships to simulate the behavior of composite systems in tension: linear, bilinear, and trilinear behavior. For the purposes of this work, only the linear and bilinear behaviors were compared to different behaviors between a classical FRP and FRCM with synthetic fibers, as shown in Figure 3. Moreover, the bilinear and trilinear relationships take into account several effects of the mortar matrix, such as the cracking, bond slip, or tension stiffening effect that are neglected by the linear behavior. Figure 3: Different stress–strain constitutive relationships for composite systems in tension. Figure 2: Stress–strain relationships of the masonry. The structural analysis of the strengthened cross section was performed with reference to the p-m interaction domains that allows for the evaluation of the flexural capacity (m) under a specified axial load (p) in the dimensionless format. Indeed, we evaluated the impact of mechanical parameters on the flexural capacity response. The numerical analysis of the cross section is based on the same classic assumptions used for reinforced concrete (RC) cross sections in the technical approach. * Conservation of plain sections (also referred to as the Bernoulli-Navier assumption);
* validity of the Bernoulli principle, wherein the shear deformability is neglected;
* the stress-strain relationship of the materials is known a priori;
* the stresses are dependent on the strain of the element alone, so that the effects of viscosity and shrinkage over time are neglected;
* it is assumed that the application of the load and consequent deformation take place in a monotonous way, and thus they do not explicitly consider the behavior under cyclic loads;
* it assumes the perfect bond between masonry and the strengthening system (without slip);
* the ultimate condition of the cross section is reached, either by crushing the compressed masonry or tensile failure of the composite system. As listed previously, the strengthening system was considered perfectly bonded to the masonry substrate in accordance to several experimental bond tests [34; 35], which evidenced that debonding phenomena from the substrate rarely occur for such materials. Bonding with the matrix fiber interface is included in the phenomenological constitutive relationships in tension for the composites. The construction of p-m interaction domains has considered with a completely dimensionless form. To better understand the dimensionless procedure, we started from translation and rotation equilibrium equations wherein each contribution is in dimensional form.