## 4 Discussion  
In this study, we successfully the performed finite element analysis to explore the influences of vacuum extractors fabricated from different materials and under different vacuum pressures on the fetal head during the delivery process. To date, there is no detailed mechanical basis for investigating the influences of using vacuum extractors made from different materials in clinical practice. The results of this study could provide a reliable reference basis for clinical obstetricians for choosing the material and magnitude of pressure of the vacuum extractor when they are needed for operative delivery. In addition, based on these results, the complications, including head deformation, scalp abrasion, even cephalohematoma, and intracerebral hemorrhage caused by the vacuum extractor during operative vaginal deliveries, could also be reduced and alleviated. According to the observation of reaction force herein, when the vacuum extractor was made of stainless steel, the fixed end of the fetal head neck was subjected to a relatively large reaction force. The main reason can be explained by the content put forward in the textbook, _Mechanics of Materials_[19]. F = \(\sigma\)A and \(\sigma\) = E\(\varepsilon\), where \(\sigma\) is the stress, F is the external force, A is the cross-sectional area, E is the [PERSON]'s modulus, and \(\varepsilon\) is the strain. Therefore, it can also be expressed as F = E\(\varepsilon\)A. When the displacement changes given are consistent and the stressed section is the same, the external force is proportional to [PERSON]'s modulus. Therefore, as [PERSON]'s modulus of the stainless steel used in this study was 200,000 MPa and that of the silicone rubber was 10.3 MPa, stainless-steel vacuum extractors made the fixed end of fetal head neck subject to a relatively large reaction force. In addition, by observing the influences of different vacuum pressures on the reaction force on the fixed end of fetal head neck, when a greater vacuum pressure was applied, the reaction force on the fixed end of the fetal head neck increased slightly. According to the textbook, _Mechanics of Materials_[19], the mechanical analysis description for spherical shells indicates that F = \(\sigma\)(2\(\pi\)rt) = p(\(\pi\)r2), where \(\sigma\) is the stress on the spherical shell, r is the inner radius of spherical shell, p is the vacuum pressure, and t is the wall thickness on the vacuum extractor. Hence, the reaction force on the fixed end of fetal head neck is proportional to the vacuum pressure. The greater the vacuum pressure, the greater the reaction force on the fixed end of the fetal head neck. By observing the stress on the vacuum extractor, the greater the vacuum pressure, the greater the von Mises stress on the vacuum extractor. Because \(\sigma\)(2\(\pi\)rt) = p(\(\pi\)r2), the stress on the spherical shell of vacuum extractor was \(\sigma\) = pr/2t. Therefore, when the vacuum extractor had a fixed shape, r and t in the formula were fixed values, so the stress on the vacuum extractor was proportional to the vacuum pressure. Hence, the greater the vacuum pressure applied, the greater the von Mises stress on the vacuum extractor. In addition, when different materials were used for the vacuum extractor, the von Mises stress on the vacuum extractor was based on \(\sigma\) = E\(\varepsilon\); when the given displacement was the same, stress (\(\sigma\)) was proportional to Young's modulus (E). Therefore, using stainless steel as the material of vacuum extractor caused relatively high stress (47.517-48.385 MPa) on the vacuum extractor. Although using stainless steel had higher stress, compared with using silicone rubber, the yield stress value of stainless steel was approximately 700 MPa [20]. In this study, when stainless steel was used as the material of vacuum extractor, the result of stress value on the vacuum extractor was much lower than 700 MPa.