Numerical modeling of laminated glass structures

Abstract

Laminated glass structures are formed by stiff layers of glass connected with a compliant polymer foil. Due to their slenderness, heterogeneity, and time- and temperature-dependent properties of the interlayer, they exhibit a complex mechanical response that is difficult to capture by single-layer models. The main aim of this work is to develop a finite element model that can describe the behavior of laminated glass units without the need for fully resolved three-dimensional simulations, which lead to unnecessarily expensive calculations. For a geometrically nonlinear description of the behavior of units, each layer is considered to behave according to the Reissner finite-strain beam theory or the Reissner-Mindlin plate theory, complemented with membrane effects and the von Kármán assumptions. The compatibility of independent layers is enforced by the Lagrange multipliers, which proceeds from a refined plate theory due to Mau. The time- and temperature-dependent behavior of the interlayer is accounted for by the generalized Maxwell model and by the time-temperature superposition principle due to the Williams-Landel-Ferry equation. The resulting system is solved by the Newton method with consistent linearization and the viscoelastic response is determined incrementally by the exponential algorithm. By comparing the model predictions against available experimental data, analytical methods and two-dimensional finite element simulations, it is demonstrated that the proposed formulation is reliable and accurately reproduces the behavior of the laminated glass units. As such, it offers a convenient basis to incorporate additional phenomena, such as delamination of glass layers.

Laminated glass structures are formed by stiff layers of glass connected with a compliant polymer foil. Due to their slenderness, heterogeneity, and time- and temperature-dependent properties of the interlayer, they exhibit a complex mechanical response that is difficult to capture by single-layer models. The main aim of this work is to develop a finite element model that can describe the behavior of laminated glass units without the need for fully resolved three-dimensional simulations, which lead to unnecessarily expensive calculations. For a geometrically nonlinear description of the behavior of units, each layer is considered to behave according to the Reissner finite-strain beam theory or the Reissner-Mindlin plate theory, complemented with membrane effects and the von Kármán assumptions. The compatibility of independent layers is enforced by the Lagrange multipliers, which proceeds from a refined plate theory due to Mau. The time- and temperature-dependent behavior of the interlayer is accounted for by the generalized Maxwell model and by the time-temperature superposition principle due to the Williams-Landel-Ferry equation. The resulting system is solved by the Newton method with consistent linearization and the viscoelastic response is determined incrementally by the exponential algorithm. By comparing the model predictions against available experimental data, analytical methods and two-dimensional finite element simulations, it is demonstrated that the proposed formulation is reliable and accurately reproduces the behavior of the laminated glass units. As such, it offers a convenient basis to incorporate additional phenomena, such as delamination of glass layers.