# Two-Dimensional Mesoscale Finite Element Modeling of Concrete Damage and Failure
## 3 Automatic Generation of Cohesive Elements
Figure 16 shows the generated concrete mesostructures with different aggregate shapes and their corresponding mean stress-strain curves are depicted in \[\delta_{m,f}=\frac{2}{K\delta_{m,0}}\Big{[}G_{C}^{I}+(G_{C}^{II}-G_{C}^{I}) \Big{(}\frac{G_{s}}{G_{n}+G_{s}}\Big{)}^{\eta}\Big{]}, \tag{22}\]0 The results show that the tensile strength and load capacity of circular, elliptical, and smoothed polyhedral aggregates are greater than those of sharp-edged polyhedral aggregates, while the difference between the tensile strength of circular, elliptical, and smoothed polyhedral aggregates is negligible. This can be explained by the high local stress concentration at the corner of the polyhedral aggregates with sharp edges [53]. The smoothed edges of circular, elliptical, and smoothed polyhedral aggregates lead to a more uniform stress distribution and, thus, delay the fracture process and thus increase the maximum tensile strength. \[\delta_{m,f}=\frac{2}{K\delta_{m,0}}\Big{[}G_{C}^{I}+(G_{C}^{II}-G_{C}^{I}) \Big{(}\frac{G_{s}}{G_{n}+G_{s}}\Big{)}^{\eta}\Big{]}, \tag{22}\]1 Concrete mesostructures with different aggregate shapes. ## 6 Conclusions

Two different effective and efficient algorithms are developed to realize the propagation of cracks and fracture of concrete specimens at the mesoscale using the finite element method. In the first algorithm, concrete mesostructures with randomly distributed circular, elliptical, or polygonal aggregate shapes and circular voids are generated. In the second algorithm, zero-thickness two-dimensional cohesive interface elements (CIEs) are generated and inserted into the interfaces of solid elements. The developed algorithm is capable of generating zero-thickness two-dimensional cohesive interface elements (i) within the elements constituting the mortar matrix, (ii) within the elements constituting the aggregates, and (iii) in the ITZ zone. In the parametric studies conducted, the effect of the volume fraction of the aggregate, the shape of the aggregate, and the total volume fraction of the porosity content is studied on the mechanical response at the structural level. In each analysis, 10 different model realizations are created for each given mesostructural parameter and the final response is determined using statistical analysis. In this way, the effect of varying the spatial distribution of the rock particles in each model realization is minimized. The results showed that:

1. The methodology developed for mesoscale simulation of concrete crack propagation and failure is capable of reproducing the concrete fracture properties observed in numerical and experimental studies in the literature [13; 53; 54; 55; 56; 57; 58]. 2. Two different macrocrack patterns are observed in the mesoscale simulation of concrete specimens under the uniaxial tension loading condition. In the first type, the microcracks merge to form a failure macrocrack. This type of macrocrack leads to a sharp decrease in the load-carrying capacity of the concrete specimen immediately after the onset of the softening zone. Thus, less energy is dissipated until complete failure. In the second type, the coalescence of microcracks leads to the formation of two or more failure macrocracks. In this condition, a more gradual softening response is observed, and, therefore, more energy is dissipated until complete failure. 3. Under tensile loading of concrete specimens, the damage starts to initiate first in the ITZ zone, which is known to be the weakest phase, and as the specimen is further loaded, the microcracks propagate through the mortar matrix, resulting in a decrease in the stiffness of the concrete. 4. The tensile strength and strain at which the softening zone begins are lower for the crushed aggregates than for the circular and elliptical aggregates. This can be

\[\delta_{m,f}=\frac{2}{K\delta_{m,0}}\Big{[}G_{C}^{I}+(G_{C}^{II}-G_{C}^{I}) \Big{(}\frac{G_{s}}{G_{n}+G_{s}}\Big{)}^{\eta}\Big{]}, \tag{22}\]2 Influence of aggregate geometrical configuration.