Validation in four-point bending tests of a viscoelastic model for laminated glass based on fractional calculus

• Published in: Structures (Oxford) Vol. 80; p. 109645
• Main Authors: Santi, Lorenzo, Royer-Carfagni, Gianni
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2025
• Subjects: Finite element method; Four-point bending tests; Fractional calculus; Laminated glass; Viscoelasticity; Viscoelasticity; Finite element method; Laminated glass; Fractional calculus; Four-point bending tests
• ISSN: 2352-0124; 2352-0124
• DOI: 10.1016/j.istruc.2025.109645

We present a one-dimensional viscoelastic finite element model for laminated glass, employing fractional calculus to effectively capture the shear-coupling behavior of the polymeric viscoelastic interlayer between glass plies. The polymer relaxation curve is approximated using four power-law branches, which are sufficient to represent both the short- and long-term responses of most commercial materials. This ensures that Boltzmann’s integral aligns with Caputo’s definition of a fractional time derivative. The spatial FE discretization is incorporated into the weak formulation of the dynamic viscoelastic problem derived from Hamilton’s principle. Time integration is performed using finite differences, with fractional derivatives approximated through the L1 formula. This allows to use a variable time-step, progressing in logarithmic scale, to balance the representation across the different power-law branches of the relaxation curve. The model is validated through four-point bending experiments on laminated glass specimens, involving loading at various strain rates and relaxation tests at different temperatures. Comparisons between experimental results and model predictions show strong agreement across a wide range of loading conditions, time scales, and temperatures. This demonstrates the model’s ability to accurately simulate the coupled viscoelastic response of laminated glass under bending loads, establishing it as a valuable tool for structural analysis and design in building engineering.