# Primary Seal Deformation in Multipane Glazing Units
## 2 Methodology  
Since there are no general criteria regarding the sealant system strain-stress state for determining the serviceable IGU lifetime, it can be deduced from the abovementioned literature where PIB strain is the limiting factor. The strain state is not equal in all PIB layers and varies along the circumference of the IGU as well. It is reasonable to assume that the location of maximal strain with proportional loading from the initial state represents a critical point also for cyclic loading and thus is the decisive factor in high-performance IGU lifespan. Figure 1 shows a schematic representation of different strain modes that occur under loading conditions in a single-chamber double-glass unit (DGU). The climatic conditions, including solar radiation, influence the temperature of the glass panes and gas within the chamber. The glass panes' dimensions vary vs. the spacer due to temperature change, and the elongation differences between the panes and spacer cause shear strains, as presented by modes A and B of the elementary PIB volume. The heat-related pressure increase in the chamber generates the extension of the PIB, shown as mode D. Furthermore, the edge rotates due to the consequent glass pane bulging, which causes shear and normal strain on the inner and outer sides of the PIB, shown as mode C.  
Figure 1: Polyisobutylene (PIB) deformation modes. To summarize, in the PIB there is a complex strain state with the non-zero strain components being \(\gamma_{xx},\gamma_{xy},\varepsilon_{xx}\), and \(\varepsilon_{yy}\). It should be noted that strains due to other loading types, such as self-weight or wind-load, are of the same type and can be algebraically added to these strains. In order to estimate the critical strain state, the following approach is proposed:  
1. First, we determine the assumed quasi-steady-state temperature field of the analysed IGU structure. According to the prescribed climatic conditions (including solar radiation-induced internal heating), individual pane temperatures are determined. With all glass-pane temperatures known, the temperatures of other structural elements may be determined using linear interpolation, which is an approximation of the alternative 3D heat transfer analysis. The temperature field serves as the input data for the subsequent thermo-mechanical analysis. 2. A 3D finite element method (FEM) thermo-mechanical IGU model is built, where the mechanical influence of the PIB on the global mechanical response of the structure is neglected. Although the same assumption was also applied by [PERSON] et al. in [25], PIB notably contributes to the rigidity of the seal system when cold. However, due to the exponential growth of vapour permeation with increasing temperature, the primary longevity-related issue is the summer, when the PIB is also soft and its mechanical rigidity really becomes negligible. Additional mechanical loads, e.g., wind load and self-weight, can be optionally added. The analyses give a reliable strain-stress state for all structural components, except for the omitted PIB. However, the results include the displacements of the glass panes and spacers to which the PIB is attached. These displacements are the input data for the identification of the type and severity of the PIB deformation modes, as presented in Figure 1.
3. The extracted, numerically determined, displacements represent the boundary conditions for the shear and normal strain calculations of the PIB for all deformation modes separately. 4. In accordance with the superposition principle, the analytically calculated strains for all deformation modes are summed into a strain tensor for each point of the PIB along the unit's circumference and for all PIB layers. Lastly, an equivalent strain calculation serves for the final comparative evaluation. Each step will be described in detail in the next section, where the approach is applied to a six-pane Q-Air glazing unit [10] with a specific large-unit design, 10-18-4-18-4-18-4-18-4-18-66.4, cf.