# Numerical Study of Concrete: A Mesoscopic Scale Simulation Methodology
## 4 Conclusions  
The proposed model lays the foundation for a methodology aimed at numerically simulating compression tests, a common practice in laboratory settings. From the experimental and numerical perspectives of this research, the following conclusions can be drawn:  
1. The code generated in MATLAB proves to be a powerful tool for easily reproducing different Representative Volume Elements (RVEs). These RVEs correspond to the dimensions of the specimens tested in the laboratory, including the mass percentage of each considered coarse aggregate particle size, which is randomly distributed to accurately represent real conditions. 2. Regarding the numerical FEM model, more than 1 million nodes and elements are necessary to mesh an ITZ size small enough for a 50 \(\times\) 10\({}^{-3}\) m cubic specimen, considering one-fourth of the prismatic specimen with appropriate symmetry boundary conditions. Additionally, a body-fitted Cartesian algorithm for the mortar and ITZ components is adopted to efficiently develop a tetrahedral finite element mesh. 3. The Concrete Damage Plasticity (CDP) model, using a nonlinear combined mathematical model of concrete based on the Drucker-Prager material model for compressive stresses and the Willam and Warnke model for tensile stresses, effectively predicts both material failure modes: cracking and crushing of concrete. 4. There is a good agreement between the experimental results and those obtained from numerical simulation, with similar compressive strengths observed both experimentally and numerically. Notably, the stress-strain curve from the laboratory tests closely aligns with the simulation data. 5. The detailed analysis of the failure mechanisms in the specimen reveals the critical importance of the interaction between the aggregate and the mortar, particularly in the ITZ. The initial failure occurs due to crushing at the top and bottom of the aggregate and, in some cases, propagates from the ITZ of one aggregate to another and through the mortar, demonstrating the complex nature of concrete failures. Additionally, a significant number of ITZ elements are primarily affected by crushing. These findings underscore the necessity of accurately modeling the ITZ to predict material behavior under stress. On the other hand, several key points emerge in the discussion:
* Detailed Insights into Mesoscopic Behavior: The model promises to provide comprehensive insights into the mesoscopic-scale behavior of concrete. This detailed  
Figure 11: Mean stress–strain curves leading to failure obtained through laboratory experimentation and numerical simulation. information is crucial for understanding deformation and fracture mechanisms, ultimately contributing to more informed and effective material design. * Cost-Effective and Rapid Evaluation: Mesoscopic numerical simulations offer a cost-effective and time-efficient alternative for assessing concrete behavior. While they offer significant advantages, it is important to acknowledge that they cannot entirely replace experimental methods. Both approaches complement each other, each with its unique strengths and limitations. * Identification of Failure-Prone Areas: Through these simulations, it becomes possible to identify areas within the material that are more susceptible to failure. This insight is invaluable for targeted improvements and reinforcement in structural design. The aim of this work is to compare numerical results with those obtained in the laboratory; thus, we have not compared our numerical results with others obtained in a similar way or with theoretical methods. In summary, the proposed mesoscopic model not only opens avenues for efficient simulation of compression tests but also holds the potential to deepen our understanding of concrete behavior, paving the way for advancements in material science and engineering. The authors aim to soon employ this methodology as a substitute for extensive experimental testing campaigns, which generate significant waste, by utilizing numerical simulations that yield comparable results.