# Two-Dimensional Mesoscale Finite Element Modeling of Concrete Damage and Failure
## 3 Automatic Generation of Cohesive Elements
This is achieved by changing the deformation scale variable in the visualization module of Abaqus/CAE. Figure 10a (marked point A in Figure 9) shows that very few microcracks occur at low stress. As can be seen in Figure 10b (marked point B in Figure 9), as the deformation continues and the average stress value increases, more microcracks appear. Since the ITZ zone is the weakest zone within the concrete structure, the initiation and propagation of microcracks occur mainly in this zone. Figure 10c shows the marked point C, which is located in the nonlinear part of the pre-crack zone. As can be seen, the propagating microcracks have complex patterns and run approximately perpendicular to the loading direction. Furthermore, no coalescence of microcracks into a macrocrack is observed before reaching the peak stress, and a few microcracks are located within the mortar matrix. This is due to the relatively high cohesive strength of the mortar matrix compared to the ITZ zone. As can be seen from Figure 10d, with increasing displacement, some cracks located in the ITZ zone continue to propagate and merge with the newly formed microcracks in the mortar matrix. At this stage, a macrocrack is generated and the softening process in the mean stress-strain curve begins (see Figure 9). The onset of the softening process is followed by the localization of stresses. As can be seen in Figure 11, there is no localized stress in the concrete specimen before point D, but after the peak stress is reached, the localization of the stress begins. If the displacement is further increased, the specimen will fail due to the further propagation of the generated macrocrack at stage D and the generation and propagation of a new macrocrack. In the subsequent analysis, a sensitivity study is conducted to assess the influence of factors such as aggregate content, volume porosity, and aggregate shape on the mesoscale fracture behavior of concrete. \[\delta_{m}= \sqrt{<\delta_{n}>^{2}+\delta_{s}^{2}}, \tag{21}\]0 The evolution of pre-peak microcracking and post-peak macrocracking for the concrete mesoscale sample depicted at various stages. The corresponding value of each stage on the mean stress–strain curve is illustrated in \[\delta_{m}= \sqrt{<\delta_{n}>^{2}+\delta_{s}^{2}}, \tag{21}\]1 For the sake of clarity, the three phases of concrete at the mesoscale are not illustrated. ### Effect of Aggregate Content

The effect of the aggregate content is studied on concrete microstructures with polyhedral aggregates and no void content. To reduce the effects of microstructural heterogeneity, mesoscale simulations are performed on ten mesoscale specimens with the same aggregate content but with different spatial distributions of aggregates. The average stress-strain curve for each aggregate content is obtained by averaging the results of ten mesoscale simulations. The Fuller's curve is employed to determine the size distribution of aggregates in concrete specimens with 50%, 35%, and 20% coarse aggregate content. Table 3 shows the volume fraction of the individual size segments in the concrete structure with different aggregate contents. Figure 12 shows the concrete samples with three different coarse aggregate volume fractions and the corresponding mean stress-strain curve is plotted in \[\delta_{m}= \sqrt{<\delta_{n}>^{2}+\delta_{s}^{2}}, \tag{21}\]2 It can be seen that the average load capacity decreases by 8%, from 3.45 MPa to 3.2 MPa, when the volume fraction of aggregate is increased from 20% to 50%. This is due to the fact that increasing the volume fraction of coarse aggregate increases the volume of the weak aggregate-mortar interface. It can also be observed that the overall elastic modulus of the concrete structure increases due to the increase in aggregate content. This is due to the significantly higher elastic modulus of the aggregate compared to the mortar matrix [53]. \[\delta_{m}= \sqrt{<\delta_{n}>^{2}+\delta_{s}^{2}}, \tag{21}\]3 Development of von Mises stress state at different stages of tensile loading.