# Meso-Scale Simulation of Concrete Based on Fracture and Interaction Behavior
## 7 Conclusions  
The application range of the cohesive zone model for simulation of three-phase concrete (i.e., aggregate, mortar, and ITZs) has been extended. Through the definition of mixed-mode fracture and interaction behavior, the model is suitable for simulation both under tension and compression. The modeling method and relevant material parameters are discussed based on the simulation technique and previous material experiment results. A balance between mesh sensitivity and computing efficiency has been achieved through the calibration of mesh precision. The simulation results have good agreement with the experiments in both mechanical characteristics and failure modes. The whole process analyses and parametric studies are conducted to investigate the failure mechanism of concrete under tension and compression. The following conclusions can be drawn from this study.  
The ITZ and MII elements modeled by cohesive elements are appropriate to simulate concrete meso-scale fracture behavior and damage accumulation at a smaller scale. The mesh precision level in which the approximate element size is 1/150 of the size of the model can provide a relatively high simulation accuracy and calculation efficiency.  
The discreteness of compressive behavior caused by aggregate distribution on the stress-strain curve is larger than that of tension behavior. In the tension simulation, the specimens with different aggregate distributions have similar damage evolution rates at the same global deformation level. The failure modes of concrete can be separated into two types: one or two dominant cracks perpendicular to the tension direction.  
In the concrete compression simulation, the inclination angles of shear bands range from 5 to 15 degrees. A valley in the standard deviation coefficient curve is formed, which symbolizes a relatively steady state in the softening stage when main shear bands form.  
In the parametric study, it is found that the mixed-mode fracture accounts for a considerable proportion both in tension and compression failure. The fracture energy caused by the difference of the two pure-mode fracture energy occupies 48.2% and 82.2% of the total fracture energy under tension and compression, respectively. Mode II fracture energy has a significant impact on both ultimate and residual compressive strength of concrete. In the case that mode II fracture energy is equal to mode I fracture energy, the ultimate compressive strength reduces by 44.7%.  
The mixed-mode fracture criterion mainly affects concrete performance in the softening stage under both tension and compression, while the effects on failure mode, tensile and compressive strength are negligible.  
Frictional behavior mainly affects concrete compressive performance. In the case that there is no internal frictional behavior, the ultimate compressive strength and energy dissipation reduce by 35.9% and 77.1%, respectively. The frictional stress can constrain crack propagation at the beginning of damage and reestablish the loading path in the softening stage.  
If the influence of aggregates' geometrical shapes and ITZ properties are subtracted, aggregates' mechanical characteristics affect concrete's mechanical characteristics and failure modes, mainly concentrated in the mid-and-late softening stage.  
Conceptualization, X.X. and Q.X.; methodology, X.X. and Q.X.; software, Q.X.; validation, X.X.; formal analysis, Q.X.; investigation, X.X. and Q.X.; resources, X.X.; data curation, Q.X.; writing--original draft preparation, Q.X.; writing--review and editing, X.X. and Q.X.; visualization, X.X. and Q.X; supervision, X.X.; project administration, X.X.; funding acquisition, X.X.  
This research was funded by the National Natural Science Foundation of China (Grant Nos. 51578400, 51178328), Project of Science and Technology Commission of Shanghai Municipality (Grant No. 16 DZ1201602).  
The authors declare no conflict of interest.