## 4 Numerical Simulations and Modeling Based on Visualization Techniques
### Numerical Methods  
The two main types of numerical simulation methods are the DEM method and the Finite Element Method (FEM). Both methods have been mentioned several times in this manuscript, and their applications to numerical reconstruction models have been reviewed. In addition, two novel models, namely LDPM and mesoscale modelling, are introduced in this section. Meso-structure modeling methods are effective tools for understanding the mechanical behavior of stone-based materials and provide an important complement to experiments. [PERSON] [128] reconstructed the fine-structure model of stone matrix materials by building a library of realistic shape-based numerical representations of aggregates with high accuracy and time and cost savings for both discrete and finite element models. [PERSON] et al. [129] developed a full 3D mesoscopic finite element model of concrete and used an advanced finite element mesh solver to mesh the highly unstructured region. The 3D mesoscopic numerical simulations were performed on concrete specimens under different loading conditions. [PERSON] [130] performed 2D multiphase simulations of recycled aggregate concrete using the interface element technique to investigate the relative strength of old and new mortar, the amount of bond of old mortar, the performance of the transition zone between old and new interface, and the replacement rate of recycled aggregate. [PERSON] [131] developed 2D and 3D micromechanical finite element models by ABAQUS, which has strong nonlinear functions. [PERSON] [126] investigated the shear modulus of steel-reinforced recycled aggregate to solve the problem of difficult interface modeling in finite element analysis that does not allow for a proper and accurate consideration of the bonding properties. [PERSON] [132]  
Figure 11: Digital specimen of asphalt mixtures: (a) aggregate skeleton; (b) specimen assembly. conducted uniaxial static creep tests and indirect tensile fracture energy tests and combined the fracture energy test results with finite element simulations of virtual specimens to investigate the effect of the angle of the aggregate prism on the properties and characteristics of the mix. [PERSON] [133] used FEM to simulate a two-phase cubic concrete specimen containing spherical aggregates in homogeneous mortar, studied the damage of concrete from a fine viewpoint, and investigated the damage of concrete. [PERSON] [134] proposed a random aggregate structure generation method for round and angular aggregates based on the Monte Carlo random sampling principle, which was combined with nonlinear FEM for a fine-view concrete study. [PERSON] [47] developed 3D finite element models for different aggregate angles by keeping other properties of asphalt mixes constant and artificially reducing the angle of aggregates, and uniaxial compression test simulations were carried out. The relationship between the angle of the aggregate prism and the mechanical response of the asphalt mixture in terms of bearing capacity, asphalt mastic creep deformation, damage behavior and energy dissipation were investigated. The calculation results showed that the aggregate angle of inclination had a significant effect on the mechanical properties. The major theories of DEM [135] are derived from molecular dynamics and particle media mechanics, also known earlier as the particle element method, and proposed by [PERSON] to analyze the stacking behavior of bulk particles, which is considered to be a unique advantage in dealing with the fine-scale mechanisms such as displacement, rotation and contact fracture of granular materials [136]. The compaction of asphalt mixtures is actually a process of aggregate accumulation in which slip occurs between the aggregates [137]. Therefore, DEM can simulate the compaction process of the asphalt mixture. Figure 12 presents the transformation of the aggregate from images into discrete element models. Figure 13 is a flowchart of the DEM modeling of asphalt mixtures considering composition and structural characteristics.