Compliance of Pillars in a Vacuum Insulated Glass

Abstract

This paper presents an analytical framework for characterising the lateral compliance of a cylindrical column constrained between deformable elastic substrates, with direct application to the contact mechanics of pillars used in vacuum insulating glass (VIG) units; these pillars support the glass panes as a set of discrete array points over the glass surface to maintain separation under atmospheric pressure. Under combined normal and lateral loading, four physically distinct deformation mechanisms were found to contribute to total pillar (column) compliance: column bending, column shear, rigid-body rotation driven by asymmetric substrate indentation, and surface shear of the substrate at the contact interface. Using Timoshenko beam theory for a column, Fabrikant's flat-punch tilting solution for rotational compliance, and contact mechanics solutions for surface shear, the total lateral compliance is expressed as a closed-form superposition. The analytical predictions are validated against three-dimensional finite element models across column heights of 0.1 to  0.5 mm and radii of 0.15 to 0.5 mm with excellent agreement over all cases. This framework will enable rapid parametric optimisation of the pillar geometry in VIG design for any external load configurations.