# Two-Dimensional Mesoscale Finite Element Modeling of Concrete Damage and Failure
## 1 Introduction
Numerous numerical models have been developed for mesoscale concrete analysis, each with distinct strengths and limitations. The lattice model treats concrete as a discrete system, allowing simulation of failure mechanisms within different phases. Although the model is simple and it is easy to assign material properties, it struggles with complex geometries and continuum representation [15; 16; 12]. The particle model offers computational efficiency, but precise calibration of numerical parameters is time consuming, limiting accuracy at larger scales [17; 18; 19; 20]. The distinct finite element method (DEM) analyzes concrete as interacting particles, effective for granular materials but computationally intensive and challenging for highly dense systems [21; 22]. The boundary finite element method (BEM) excels in structural analysis with domain boundary focus, but faces difficulties in scenarios where interior domain information is crucial [23]. The combined finite-discrete element method (FDEM) effectively captures elastic deformation and post-failure behavior, but implementation complexities arise due to combining fundamentally different methodologies [24; 25]. Finally, the continuum finite element approach with explicit representation of the mesostructure is commonly used for concrete analysis [2; 26; 27; 14; 28]. Cohesive zone modeling (CZM) is increasingly popular for failure and fracture analysis of concrete and similar materials due to its straightforward formulation and implementation, involving cohesive elements inserted at solid interfaces [29; 30; 31; 32]. The application of CIEs within the CZM to simulate fracture behavior has great potential for the realistic simulation of crack initiation and propagation in brittle and semi-brittle materials. Interested readers are also referred to some recent publications in the field of CZM-based FE model simulation of concrete materials using CIEs [33; 34; 35; 36; 37; 38; 39]. Two common points in these publications are, first, the potential of CZM to provide realistic simulation outputs that resemble experimental ones, and second, the performance of parametric studies that pave the way for the development of concrete materials with specific properties. The objective of this research is to address the limitations of current methods used to simulate fracture in brittle materials, particularly in concrete. A significant limitation in the existing literature is the predominant use of single-mode fracture simulations for concrete materials at the mesoscale, neglecting the dependence of fracture behavior on the specific type of fracture. Additionally, many finite element implementations of concrete materials at the mesoscale assume that shear fracture energy is equal to normal fracture energy in the pre-processing step, overlooking the significant heterogeneity in concrete materials [32]. This work overcomes this limitation by considering mixed fractures calibrated against experimental data, providing a more accurate representation of concrete material behavior under mixed fracture conditions. Moreover, there is a notable gap in the field of mesoscale simulations for concrete materials concerning the generation of particulate concrete microstructures with randomly distributed aggregates of various shapes, as well as voids of different sizes and shapes, and the creation and insertion of cohesive interface elements for three-phase materials such as concrete. This work pioneers a fully described, detailed approach to generate microstructures and insert cohesive interface elements for concrete at the mesoscale level, as well as other composite materials with varying numbers of phases. To the best of the authors' knowledge, existing codes or literature lack applicability for three-phase materials, especially when dealing with varying void sizes and shapes. The proposed algorithms significantly contribute to enabling the creation of cohesive interface elements applicable to diverse element types in both two and three dimensions, accommodating any given microstructure.