## 4 Mechanism Analyses  
### Rheological Analysis  
Figure 6 shows the shear stress evolution over time for 3 DPFC, while Figure 7 presents the static yield stress of the same material.  
From Figure 6, it is evident that the shear stress of 3 DPFC of different formulations exhibits an initial increase followed by a decrease over time, eventually stabilizing. The peak value of the shear stress evolution curve at a constant low shear rate over time is defined as the static yield stress [45; 46]. Figure 7 shows that the substitution rate of expanded perlite significantly affects the static yield stress of 3 DPFCs. Sample EP80S1 exhibits the highest static yield stress at 1722.374 Pa, which is 166.512 Pa higher than that of sample EP40S1. This could be due to the porous structure of expanded perlite, which absorbs free water between particles, thereby increasing interparticle friction. However, when the level of expanded perlite substitution reaches 100%, the static yield stress decreases to 1225.399 Pa, as seen for sample EP100S1. This phenomenon may be attributed to the low density and strength of expanded perlite itself, reducing the power required for rotation.  
Figure 6: Yield stress curve of 3 DPFCs over time.  
Figure 7: Static yield stress of 3 DPFCs.  
Furthermore, within a similar density range, sample EP80S1 exhibits higher static yield stress than sample EP40S2. Similarly, the static yield stress of sample EP100S1 is also higher than that of sample EP80S2. This can be explained by (1) the irregular shape and water absorption capacity of expanded perlite, which increase the interparticle friction in 3 DPFC; and (2) the higher levels of expanded perlite substitution, which reduce foam usage and thereby decrease the total porosity and the number of large pores in 3 DPFC under similar dry density conditions. However, when the substituted level of expanded perlite is the same, samples with a higher foam content exhibit lower static yield stress, which can also be explained by the development of the pore structure in the 3D-printed expanded perlite foam concrete [12; 29].  
According to Figure 8, it is evident that as the shear rate increases, the apparent viscosity of all 3 DPFCs initially decreases rapidly, then slows down, and finally stabilizes. This means that the printing slurry under various proportions exhibits noticeable shear-thinning behavior as the shear rate increases, and with a further increase in shear rate, the plastic viscosity of the cement slurry gradually reaches a steady state. This is because the internal flocculation structure of the printing concrete is disrupted during the testing process, leading to a decrease in slurry viscosity. Additionally, from Figure 8, it can be observed that with a lower foam content, the apparent viscosities of samples EP40S1, EP80S1, and EP100S1 are similar. This indicates that at low foam concentrations in 3D-printed concrete, the substitution level of expanded perlite has little effect on the apparent viscosity of 3 DPFC. In contrast, with a higher foam content, samples EP40S2, EP80S2, and EP100S2 exhibit a gradual decrease in apparent viscosity. This may be due to the reduced density of the paste around the foam at higher substitution rates of expanded perlite, which results in a better shape retention of the foam under the same compressive shear conditions, and the fact that most of the expanded perlite particles are irregularly shaped spheres, thus leading to a decrease in apparent viscosity with an increase in the expanded perlite substitution rate.