Multiscale numerical model for the analysis of laminated glass structures exposed to static load
Authors:   ,   Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Grozdanić Gabrijela 
Published: September 2024

This thesis presents a multiscale numerical model for the analysis of laminated glass structures exposed to static loads, and its validation with experimental tests and analytical calculations. The first part deals with the influence of atmospheric temperatures and load duration on laminated glass structures. The aim of this research is to analyse the stiffness degradation of laminated glass members exposed to different atmospheric temperatures and different load durations. The influence of these parameters is analysed through analytical calculations and numerical models. Analytical calculations include the effective thickness approach (ETA), and different expressions taken from the literature and regulations are used to define the effective thickness of the laminated glass elements. The accuracy of prediction for deflection and stress under applied loads was tested for each expression, by varying the temperature and load duration. The obtained results from the applied analytical expressions were compared and analysed. Numerical calculations were carried out using numerical models created in the ANSYS software. These numerical models were first validated by experimental tests conducted according to EN 1288-3. A four-point bending test was used so that the obtained results could be compared with available results from the literature. In the experiments, specimens were tested until fracture, while in the numerical analysis, the fracture was not simulated due to the lack of methods that could reliably describe the nonlinear behaviour of the glass part of the member. This issue arises in the simulation of the glass’s nonlinear behaviour when exposed to static loads. Therefore, the analysis was conducted for a fixed load value (stress kept under nonlinear limits), but the temperature and load durations were varied. The results showed a significant influence of temperature and load durations, as well as the type and thickness of the interlayer, on the behaviour of laminated glass elements. In the second part of this work, the focus is on solving the problem encountered in the numerical analysis from the previous step. There are not many numerical methods that can accurately predict the nonlinear behaviour of brittle materials exposed to static loads, and those that are capable usually require input to define an initial crack. Simulation of the initial crack is not in the spirit of glass material because this type of analysis mostly observes the crack propagation, and an initial crack in glass elements implies the breakage of the whole element (especially in the case of tempered glass). The lack of methods for simulating the non-linear behaviour of laminated glass members exposed to static loads is solved here with a multiscale model that uses the embedded discontinuity method in simulations of nonlinear behaviour. The embedded discontinuity method is capable of simulating crack appearance in solids without the demand for initial cracks. By using the embedded discontinuity method, a multiscale model is developed, that can simulate the ultimate load for laminated glass elements without simulating detailed fracture pattern. The model consists of a micro model that simulates a real laminated glass cross-section and a macro model that represents a monolithic cross-section with assigned material behaviour according to the micro model. This model is further extended for plate structures using discrete Kirchhoff plate theory and a constitutive model for the principal directions of the internal forces/stresses. The basic micro model is also used to define the constitutive behaviour, but this time for the principal directions of macro plate elements. In the third part of the research, in-plane loaded laminated glass elements are analysed using a combination of a simple numerical model and “Level 2” of interlayer modelling from regulations. The “Level 2” interlayer modelling proposes the simplified engineering approach (ETA) from regulations (and literature). This approach is analysed regarding the prediction of buckling forces for in-plane loaded laminated glass members. Two numerical models are used: one discretized with beam finite elements and the other with shell finite elements. The analysis was performed for several different geometries of laminated glass specimens, with different types of interlayers and different boundary conditions. The buckling force prediction is validated by comparing the results with experimental results from the literature for different geometries, interlayers, and boundary conditions. This work presents the analysis of laminated glass elements exposed to out-of-plane and in-plane static loading.