## 3 Mechanical Model Establishment
### Stress in the Edge Sealing Part of VIG  
For the edge region, the atmospheric pressure taken by the glass is shared by the first row of supporting pillars and the edge sealing part, which is the direct reason of tensile stress. In this study, the glass unit corresponding to a row of supporting pillars was selected (Figure 3). Due to the symmetry, the supporting pillars within glass unit were located at the midpoint in the width direction, the width was \(b\) and the number of supporting pillars was \(n\).  
The upper surface of the glass is subjected to the uniform atmospheric pressure and the lower surface of the glass is subjected to the supporting force of the supporting pillars at  
Figure 3: Schematic diagram of the force unit, the width of force unit is \(b\), and supporting pillars are located at the midpoint in the width direction.  
Figure 2: Simplified square unit and its force diagram. Where \(a\) is the pillar separation of the square unit, \(q_{0}\) is the atmospheric pressure, \(r\) is the supporting pillar radius and \(F\) is the support force from the supporting pillar.  
equal intervals. At the edge sealing part, the glass is subjected to tensile stress by the sealing material. In this study, the tensile stress was assumed to be a linear gradient distribution, and the largest value (\(f_{4}\)) was located in the outer edge. The inner edge of the edge sealing part was selected as the origin, and the force moment at this point was deduced. Each supporting pillar and atmospheric pressure contribute half of the force moment to the long and short sides.  
The moment of force produced by atmospheric pressure on the right of origin is  
\[\begin{array}{l}2M_{1}=\frac{q_{0}e^{2}b}{2}+\frac{q_{0}(2e+a)ab}{2}+\frac{q_ {0}(2e+3a)ab}{2}+\frac{q_{0}(2e+5a)ab}{2}\\ \hskip 14.226378 pt+\cdot\cdot\cdot+\frac{q_{0}|2e+(2n-3)a|ab}{2}+\frac{q_{0}|e+ (n-1)a+\frac{1}{4}a|ab}{2}\end{array} \tag{4}\]  
where \(\varepsilon\) is distance between the first supporting pillar and the inner sealing edge (mm); \(b\) is width of the force moment unit (mm); and \(n\) is the number of supporting pillars in the force moment unit.  
The force moment produced by the supporting pillars on the right side of the origin is  
\[2M_{2}=F_{1}\varepsilon+F_{2}(\varepsilon+a)+F_{3}(\varepsilon+2a)+\cdot\cdot \cdot+F_{n}[\varepsilon+(n-1)a] \tag{5}\]  
\[F_{2}=\ldots=F_{n}=q_{0}ab \tag{6}\]  
The force moment to the left of the origin is  
\[M_{I}=\frac{f_{4}m^{2}b}{3}+\frac{q_{0}m^{2}b}{2} \tag{7}\]  
where \(f_{4}\) is the maximum line tension of the edge sealing part (MPa) and \(m\) is the edge sealing width of VIG (mm).  
According to the torque balance (\(M_{I}=M_{1}-M_{2}\)),  
\[f_{4}=(\frac{q_{0}\varepsilon^{2}}{2}+\frac{q_{0}\varepsilon a}{2}+\frac{q_{0} a^{2}}{8}-F_{1}\varepsilon-q_{0}m^{2})\frac{3}{2m^{2}} \tag{8}\]  
The mathematic model showed that the maximum line tension of the edge sealing part (\(f_{4}\)) is mainly affected by the supporting force from the outermost supporting pillar (\(F_{1}\)) and the structural parameters (\(m\) and \(\varepsilon\)). Obviously, the smaller the \(F_{1}\), the greater the \(f_{4}\). Therefore, the limit condition was considered, that is, when \(F_{1}=0,f_{4}\) is the maximal value.  
\[f_{4,\text{max}}=(\frac{\varepsilon^{2}}{2}+\frac{\varepsilon a}{2}+\frac{a^{ 2}}{8}-m^{2})\frac{3q_{0}}{2m^{2}} \tag{9}\]