# Two-Dimensional Mesoscale Finite Element Modeling of Concrete Damage and Failure
## 3 Automatic Generation of Cohesive Elements
All mesoscale samples are subjected to a uniform displacement of 0.15 mm in the x-direction. Strain is determined by dividing the displacement at each step frame by the initial length of the specimen. explained by the local stress concentration at the sharp edges of the crushed aggregates. Therefore, the strength of the concrete may be overestimated in the mesoscale simulation with circular and elliptical aggregates. 5. It is found that the modulus of elasticity of concrete is linearly proportional to the total volume fraction of aggregate particles, whereas the ductility of concrete is inversely proportional to the volume fraction of aggregates. 6. An increase in the volume fraction of coarse aggregate leads to a reduction in the maximum tensile strength and the load-carrying capacity of the concrete specimens. This can be explained, on the one hand, by the increase in the weak aggregate-mortar interface and, on the other hand, by enhanced crack bridging mechanisms, especially in zones where a higher concentration of aggregates is observed. 7. An increase in the total volume fraction of porosity leads to a reduction in the maximum tensile strength and load-bearing capacity. This is attributed to the fact that a higher content of voids facilitates the initiation and propagation of cracks. This case shows the importance of considering voids in the mechanical and fracture modeling of concretes with high void content. It is worth mentioning that all the above conclusions were obtained by finite element simulations of concrete specimens under tensile loading. The algorithms for cohesive interface elements and concrete microstructures exhibit broad applicability in practical engineering, regardless of the concrete's design, composition, or aggregate materials. They can accommodate multiple material composites, model dynamic loading conditions, and facilitate coupled multiphysics analysis for environmental exposures. Additionally, the algorithms have no constraints on aggregate selection or material properties, allowing for flexible applications, such as studying aggregate grading impacts, extension to 3D simulations and complex geometries, or integration into multiscale modeling approaches. Furthermore, the algorithms' flexibility enables crack propagation within aggregates when their material properties are equivalent or inferior to those of the mortar matrix. This adaptability allows the investigation of concrete behavior under diverse conditions, material design optimization, and connection of microstructural details with macroscopic performance, advancing concrete engineering practices. This conclusion emphasizes the robustness and versatility of the proposed algorithms, aligning with the feedback provided. Explicitly considering specific strength and toughness parameters in the mesostructural optimization of concrete materials, including the design and placement of microscopic components such as aggregates, cement paste, and potential admixtures, is crucial for enhancing the durability and performance of structures. This approach allows tailoring concrete materials to their intended applications, ranging from high-strength mixes for skyscrapers to earthquake-resistant configurations. Furthermore, mesoscale simulations in this research have proven to be effective tools for comprehending the intricate behavior of concrete materials under various conditions. The results establish a direct relationship between mesostructural properties, such as aggregate size, volume fraction, porosity, and shape, and macroscopic performance characteristics, including tensile strength, ductility, and load-bearing capacity. These findings emphasize the significant role of mesostructural optimization in advancing concrete construction methods and enhancing the performance and safety of concrete structures. An intrinsic problem in modeling crack propagation using the cohesive zone model is its mesh dependency. One way to address this problem is to implement a finer level of discretization, which leads to higher computational costs.