# Meso-Scale Simulation of Concrete Based on Fracture and Interaction Behavior
## 2 Finite Element Modeling Method  
The explicit method in the Abaqus/Explicit module is used in this paper to simulate concrete tension and the compression loading process. Since friction and collision of particles play a significant role in concrete's compression softening stage, interaction behavior is defined to describe the contact behavior. The general contact algorithm in Abaqus/Explicit can only be used with three-dimensional surfaces [31], so three-dimensional models are used for simulation.  
The models are built to simulate concrete uniaxial tension and compression experiments conducted by [PERSON] et al. [32]. The specimens used for experiments are cuboids with dimensions of \(150\times 150\)\(\times\)\(50\) mm, which were cut from large plate specimens with dimensions of \(500\times 500\times 50\) mm. The mean tension and compression elastic modules are 42.0 GPa and 37.5 GPa, respectively. The mean tension and compression strengths are 3.24 MPa and 37.5 MPa, respectively. The volume proportion of aggregates calculated by the mixture ratio is 45.1%. For computing efficiency, aggregates whose particle diameters are greater than 2.5 mm are modeled. The fine aggregates and cement matrix are treated as mortar whose mechanical behavior is simulated by mortar particle elements and internal interface elements.  
As incomputable microcracks occur during the fracture process, it is difficult to apply the fracture criterion to simulate concrete fracture at the micro-scale. However, it is appropriate to use the traction-separation law to describe the meso-scale damage and fracture caused by the microcracks. For this reason, cohesive elements are used to simulate damage evolution and energy dissipation of concrete. In the main study of this paper (Section 6.4), the cohesive elements are only inserted between the elements of aggregates and mortar (interfacial transitional zones, ITZs), and inside the mortar elements (mortar internal interface, MII), as shown in Figure 1. In the study of Section 6.4, the cohesive elements are also inserted inside the aggregate elements (aggregate internal interface, AII), to study the effects of aggregates' mechanical characteristics. In this paper, the study adopts the simplifying assumption that the interface properties of ITZs, MII, AII are the same.  
The models are meshed by irregular triangle elements in the plane (Figure 1). Compared with other polygon elements, triangle elements provide the maximum number of interfaces with the same nodes in the plane. Cohesive elements are inserted into the interfaces to simulate damage and fracture behaviors.  
The displacement loading control is adopted to obtain the complete tension and compression process data. The vertical motions of the nodes at the bottom boundary are constrained. The load is applied by controlling the motions of the nodes at the top boundary. All nodes' motions in the direction normal to the plane are constrained. In the tension and compression simulations, the final vertical displacements of the top nodes are 0.09 mm and 0.9 mm, respectively. The total time of loading is 100 s. In the first 20 s and last 80 s, the vertical motions of the top nodes are uniformly accelerated and uniform, respectively.