Fractional viscoelastic modelling of laminated glass

This doctoral research investigates the time-dependent mechanical behavior of laminated glass, focusing on the viscoelastic response of polymeric interlayers. These materials, which play a key role in the structural performance and durability of laminated glass systems, exhibit complex relaxation phenomena that require advanced constitutive modeling beyond classical approaches. In the first part of the thesis, a comprehensive review of viscoelastic models is presented, highlighting the limitations of the traditional Prony series formulation in capturing wide-spectrum relaxation behaviors. To overcome these constraints, the research proposes an alternative interpolation framework based on fractional viscoelastic theory and power-law relaxation functions. This approach, rooted in the concept of fractional derivatives, allows a continuous and physically meaningful description of the stress–strain relationship with a reduced number of parameters and enhanced fitting accuracy. A detailed experimental campaign was conducted to characterize the relaxation behavior of different polymeric interlayers across a broad temperature and time range. The experimental data were analyzed and fitted using both Prony series and power-law formulations, providing a quantitative comparison of their predictive capabilities. The results demonstrated that the power-law approach, expressed as a piecewise fractional model, offers superior agreement with experimental observations and significantly simplifies the parameter identification process. The final part of the thesis focuses on the implementation of the proposed fractional model into finite element (FE) simulations of laminated glass structures. The developed numerical framework enables accurate prediction of structural response under realistic loading and boundary conditions, including short- and long-term behaviors. Validation against experimental bending and creep tests confirmed the reliability and robustness of the model, opening the way to efficient simulation-based design of laminated glass components. Overall, this work contributes to the advancement of viscoelastic modeling in glass engineering by integrating experimental evidence, mathematical innovation, and numerical implementation. The fractional viscoelastic approach proposed herein not only improves the predictive capability of current models but also provides a versatile and computationally efficient tool for industrial applications and further academic research in the mechanics of time-dependent materials.