# Short-Term Deformability of Three-Dimensional Printable EVA-Modified Cementitious Mortars
## 4 Results and Discussion
### Coefficient of Thermal Expansion  
The coefficient of thermal expansion is defined as the change in the unit length of a material for a unit change in temperature. Thermal shrinkage strain is determined by the degree of temperature drop in concrete and its coefficient of linear thermal expansion [17]. The coefficient of the thermal expansion of concrete is determined by the combined values of the dissimilar thermal coefficients of its two main constituents (i.e., cement paste and aggregates) [23]. Concrete structures are deformed by temperature variations resulting from the hydration reaction of cement or atmospheric temperature changes. When this temperature variation causes the tensile stress of concrete to exceed its tensile stress, cracking is initiated. Layered cementitious materials built through extrusion-based additive construction are expected to undergo cracking and delamination due to temperature change.  
In the present study, thermal strain tests were conducted, and the results are presented in Figure 13. The thermal strains were \(437\times 10^{-6}\), \(530\times 10^{-6}\), \(643\times 10^{-6}\), \(812\times 10^{-6}\), and \(997\times 10^{-6}\) when the EVA/cement ratios were 0, 0.05, 0.10, 0.015, and 0.020, respectively. It was found that in all cases, the thermal strain was reached within about two hours. The coefficient of thermal expansion was estimated by dividing each thermal strain measurement by the corresponding temperature rise. Once calculated, its relationship with the EVA/cement ratio was analyzed, as shown in Figure 14. Here, the coefficients of thermal expansion were \(7.9\times 10^{-6}\)/C, \(9.6\times 10^{-6}\)/C, \(11.7\times 10^{-6}\)/C, \(14.8\times 10^{-6}\)/C, and \(18.1\times 10^{-6}\)/C when the EVA/cement ratios were 0, 0.05, 0.10, 0.15, and 0.20, respectively. This indicates that the thermal expansion coefficient tended to increase as the EVA/cement ratio increased, and the correlation between the two factors was high.  
Previous studies have reported that the coefficient of thermal expansion of polymer-modified cementitious mortar ranged from \(9\times 10^{-6}\)/C to \(10\times 10^{-6}\)/C [24]. Notably, however, when the polymer/cement ratio ranged from 0.10 to 0.20, the coefficient of thermal expansion of SBR latex-modified cementitious mortar was reported to be between \(7.7\times 10^{-6}\)/C and \(8.6\times 10^{-6}\)/C, which was not significantly different from that of unmodified mortar at \(7.9\times 10^{-6}\)/C [18]. For ordinary cementitious  
Figure 12: Relationship between EVA/cement ratio and drying shrinkage.  
concrete, [PERSON] [23] reported that the coefficient of linear thermal expansion of hydrated cementitious paste varied from \(11\times 10^{-6}/^{\circ}\)C to \(20\times 10^{-6}/^{\circ}\)C. [PERSON] et al. [17] presented that the coefficient of linear thermal expansion of cementitious mortars was approximately \(18\times 10^{-6}/^{\circ}\)C for cementitious paste, \(12\times 10^{-6}/^{\circ}\)C for mortar, and between \(6\times 10^{-6}/^{\circ}\)C and \(12\times 10^{-6}/^{\circ}\)C for concrete. As explained above, the measured coefficient of thermal expansion was determined to be significantly higher in the present study when compared to the results reported by previous studies on polymer-modified cementitious mortars. At the same time, the coefficient of thermal expansion of ordinary cementitious concrete and mortars measured in the present study was largely comparable to those reported in similar previous research.