# Numerical Study of Concrete: A Mesoscopic Scale Simulation Methodology
## 1 Introduction  
Concrete, widely employed in construction due to its cost-effectiveness, strength, and durability, has diverse applications in civil engineering. However, its highly heterogeneous microstructure complicates predictions solely based on experiments. Theoretical studies employing micromechanics analysis help deduce macroscopic constitutive behavior. Comprising different phases, concrete's behavior and properties exhibit variations across scales, from the microscopic to the macroscopic scales [1, 2]. At the microscopic level, concrete is a composition of cement particles and water, forming an intricate cement paste that envelops aggregates like sand and gravel. The microstructure of this paste is complex, featuring porosities, micro-cracks, and other defects that can significantly influence its mechanical properties [3]. Zooming into the mesoscopic level, concrete reveals itself as a material consisting of three crucial phases: the mortar, comprising cement, water, and fine aggregate; the ITZ found between the coarse aggregateand the mortar; and the coarse aggregates themselves [4; 5]. Each of these phases uniquely contributes to the overall behavior of the material. At this level, parameters like the shape, size, and distribution of coarse aggregates significantly impact concrete's mechanical behavior. This study aims to create random mesostructured models for concrete, considering the coordinates and sizes of aggregate particles and then subjecting them to finite element method (FEM) analysis to understand their effects on macroscopic responses. At the macroscopic level, concrete is simplified as a single-phase material characterized primarily by its compressive strength, modulus of elasticity, and flexural and tensile behavior. This macroscopic view is essential in the design process, where meticulous control and verification of these properties are imperative to ensure the safety and durability of constructed structures [6]. Engineers and architects rely on a thorough understanding of concrete's behavior at different scales to optimize its use in various applications, meeting the stringent demands of modern construction standards. Numerical models become valuable tools when examining concrete at the mesoscopic level, which deals with millimeter-scale dimensions. These models enable a detailed analysis of how concrete behaves at the specimen level. The material's traits are intricately influenced by the properties of its key components: coarse aggregate, mortar, and the interface between them. Utilizing numerical models at this mesoscopic scale holds significant importance, offering insights into the mechanical aspects of concrete, such as its fracture toughness and load-bearing capacity. This approach provides a nuanced understanding of concrete behavior, contributing to advancements in structural engineering and material science [7]. Several mesoscopic models have been developed, each examining how material composition influences overall behavior [8; 9; 10]. Aggregate shapes, sizes, and distributions are essential factors affecting stress distribution and crack initiation. Various approaches, including truss models, lattice models, and finite element mesh simulations, have been employed to study concrete microstructure. Notably, the choice of aggregate size distribution, often described by grading curves like the Fuller curve, plays a vital role in concrete mix design, affecting the workability, mechanical strength, permeability, and durability of the material. Different methods have been used to simulate aggregate spatial distribution, such as take-and-place, divide-and-fill, stochastic-heuristic algorithms, and distinct element methods. Meshing techniques, such as aligned and unaligned approaches, help discretize mesoscopic models for numerical analysis. The ITZ between aggregates and mortar is recognized as influential in microcrack initiation, prompting varied approaches in mesh generation considering ITZ domains [11].