# Short-Term Deformability of Three-Dimensional Printable EVA-Modified Cementitious Mortars
## 4 Results and Discussion  
### Stress-Strain Relationship and Modulus of Elasticity  
Stress-strain curves provide basic data for estimating the modulus of elasticity. Given that concrete is not completely elastic, however, estimating the elastic modulus based on these curves results in various issues. Strictly speaking, the modulus of elasticity only applies to the linear elastic section of the stress-strain curve. In cases where it is difficult to judge the linear elastic section from the curved part, as is the case with concrete, the secant modulus of elasticity, also known as the chord modulus, is alternatively used [23]. In extrusion-based additive construction, the modulus of elasticity is a critical factor that is used to estimate both the stress caused by drying shrinkage in layered EVA-modified cementitious mortar (\(\sigma=\varepsilon_{sh}E\)) and the stress caused by thermal expansion (\(\sigma=\alpha E\Delta T\)). In concrete, stress and strain typically have a non-linear relationship, but the relationship can be considered the linear elastic section at a lower stress level. This stress range can reach up to 40% of the ultimate strength, within which concrete can be considered an elastic material. The stress-strain diagrams of the developed EVA-modified cementitious mortars are presented in Figure 8. The shapes of these curves resemble those obtained for cementitious paste [23]. Based on these diagrams, the obtained compressive strengths were 48.3 MPa, 41.8 MPa, 38.2 MPa, 35.7 MPa, and 33.5 MPa when the EVA/cement ratios were 0, 0.05, 0.10, 0.15, and 0.20, respectively. The compressive strength decreased as the EVA/cement ratio increased. The secant modulus was calculated using Equation (1). The results were 21.6 GPa, 19.1 GPa, 18.1 GPa, 17.6 GPa, and 16.7 GPa when the EVA/cement ratios were 0, 0.05, 0.10, 0.15, and 0.20, respectively. The relationship between these elastic modulus measurements and the applied EVA/cement ratios was analyzed, as presented in Figure 9. A high correlation was found (i.e., the modulus of elasticity tended to decrease as the EVA/cement ratio was increased). Figure 7: Test setup for measuring drying shrinkage. Earlier studies showed that the modulus of elasticity in the compression of unmodified cementitious concrete was 21.1 GPa, while the value ranges were 22.4 GPa to 23.6 GPa, 20.2 GPa to 24.3 GPa, and 10.0 GPa to 19.0 GPa for polyacrylic ester (PAE)-modified cementitious concrete, styrene butadiene rubber (SBR)-modified cementitious concrete, and polyvinyl acetate (PVAC)-modified cementitious concrete, respectively [18]. The results varied depending on the polymer type and polymer/cement ratio. Overall, the modulus of elasticity tended to decrease as the polymer/cement ratio increased, and the degree of reduction increased when the polymer content was excessive. A decrease in the elastic modulus reduces the stiffness of EVA-modified cementitious mortar but also decreases the level of stress caused by drying shrinkage and temperature change. Figure 8: Stress–strain diagrams for different EVA/cement ratios. Figure 9: Relationship between the EVA/cement ratio and modulus of elasticity. It is also known that the modulus of elasticity of polymer-modified cementitious mortar is relatively low, 10 GPa to 30 GPa, because it contains polymer (elastic modulus: 0.1 GPa to 10 GPa) [24]; the elastic modulus of cementitious concrete in compression generally falls within the range of 14 GPa to 40 GPa [17]. In the present research, the maximum compressive strains were 0.00256, 0.00267, 0.00272, 0.00278, and 0.00283 when the EVA/cement ratios were 0, 0.05, 0.10, 0.15, and 0.20, respectively. These results indicate that the maximum compressive strain tended to increase as the EVA/cement ratio increased. Given that the figures were 0.002 and 0.0027 for 30 MPa cement concrete and 34 MPa cement paste [23], respectively, the measured maximum compressive strains were found to be comparable to that of cement paste. Concrete in compression shows some inelastic strain before failure.