# Numerical Study of Concrete: A Mesoscopic Scale Simulation Methodology
## 2 Materials and Methods  
The fact that concrete is brittle in tension but relatively strong in compression, that the strength of the mortar is higher than that of the concrete itself, and that this strength decreases as the size of the coarse aggregate increases, as well as the permeability of high-density coarse aggregate concrete is higher than that of the cement paste, are questionsabout the behavior of concrete that are answered by the existence of the ITZ between the large aggregate particles and the hydrated cement paste [12]. Although composed of the same elements as the hydrated cement paste, the microstructure and properties of the ITZ differ from the bulk hydrated cement paste. Therefore, it is treated as a separate phase in the concrete microstructure.  
[PERSON] and his team [9] have delved into key aspects related to the ITZ and the behavior of concrete at the mesoscopic level. They have crafted both 2D and 3D models, meticulously considering the interplay between mortar and aggregates, along with the geometric and mechanical characteristics inherent to each phase.  
The mesoscopic model developed by [PERSON] is based on the concept that concrete can be considered a composite material formed by aggregates dispersed in a matrix of cement paste. In this model, concrete is divided into discrete elements called particles, representing the aggregates and the cement paste. Each particle is individually modeled, considering its geometric and mechanical properties. For instance, aggregates can be represented as spherical or ellipsoidal particles with specific size and strength properties, while the cement paste can be modeled as a continuous matrix with elastic or viscoelastic properties. [PERSON]'s mesoscopic model allows for the simulation of the mechanical behavior of concrete by considering the interaction between particles [13,14]. External loads can be applied to study how forces are transmitted through the particles and the paste matrix. This allows the analysis of phenomena such as deformation, strength, fracture, and the long-term behavior of concrete. The model provides a more realistic representation of concrete behavior by considering the distribution and interaction of aggregates and allows the study of the influence of different parameters, such as the water-cement ratio, aggregate size, and material properties, on the mechanical properties of concrete. It is also useful for investigating the impact of defects and heterogeneities on material behavior. However, it is important to note that [PERSON]'s mesoscopic model simplifies reality and requires careful selection of parameters and properties for accurate results, and its application can require significant computational resources.  
In this work, a detailed mesoscopic model has been devised to represent concrete, consisting of three distinct phases: mortar, coarse aggregate, and the transition zone (Figure 1).  
To carry out a successful numerical approximation, experimental tests were conducted on cubic specimens measuring 50 \(\times\) 50 \(\times\) 50 mm made of concrete dosed with a water-to-cement ratio (w/c) of 0.5 and with CEM I 52.5 cement. All manufactured specimens incorporated the same number of coarse limestone aggregates corresponding to the particle size fractions 8/10 mm, 6/8 mm, and 4/6 mm to ensure, as much as possible, the best reproducibility among tests and the production of specimens very similar to those simulated numerically. Before the tests, the manufactured specimens were cured for 28 days in a humidity chamber with a relative humidity of 95% and a temperature of 20 \({}^{\circ}\)C.  
Figure 1: RVE. Mesoscopic model section detail.  
The modeling was carried out in two stages: geometrical models are generated using our own MATLAB code, and the numerical model is analyzed using FEM with the Ansys-Workbench program.