Fractional viscoelastic characterization of laminated glass

Fractional viscoelastic characterization of laminated glass

Luca Viviani, Mario Di Paola, Gianni Royer-Carfagni

download PDF

Abstract. Glass façades are often required to withstand against explosive events due to premeditated or accidental causes. Laminates made by glass plies bonded by thin polymeric foils (laminated glass) need to be used to avoid catastrophic breakage. The paradigmatic case study considered is that of a rectangular three-layer laminate, made of two glass plies, modelled as Kirchhoff-Love plates, sandwiching a thin viscoelastic polymeric interlayer. Its time-dependent response under the action of a blast wave is described via fractional calculus operators, whose main advantage is that only two material constants are needed for an exhaustive characterization. The dynamic equations are treated à la Galёrkin and their integration in time relies on the Grünwald-Letnikov approach. The fractional characterization presents noteworthy advantages from a computational point of view. We find that the maximum stress peak is mildly affected by the viscosity of the interlayer, which instead dictates the subsequent rebounding oscillations.

Laminated Glass, Fractional Viscoelastic Modelling, Blast Loading

Published online 3/17/2022, 6 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Luca Viviani, Mario Di Paola, Gianni Royer-Carfagni, Fractional viscoelastic characterization of laminated glass, Materials Research Proceedings, Vol. 26, pp 109-114, 2023


The article was published as article 18 of the book Theoretical and Applied Mechanics

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

[1] L. Galuppi G. Royer-Carfagni, “The post-breakage response of laminated heat-treated glass under in plane and out of plane loading,” Composites Part B: Engineering, vol. 147, pp. 227-239, 2018.
[2] I. V. Ivanov, “Analysis, modelling, and optimization of laminated glasses as plane beam,” International Journal of Solids and Structures, vol. 43, pp. 6887-6907, 2’006.
[3] M. López-Aenlle A. Noriega F. Pelayo, “Mechanical characterization of polyvinil butyral from static and modal tests on laminated glass beams,” Composites Part B: Engineering, vol. 169, pp. 9-18, 2019.
[4] X. Centelles F. Pelayo M. J. Lamela-Rey A. I. Fernandez R. Salgrado-Pizarro J. R. Castro L. F. Cabeza, “Viscoelastic characterization of seven laminated glass interlayer materials from static tests,” Construction and Building Materials, vol. 279, p. 122503, 2021.
[5] M. L. Williams R. F. Landel J. D. Ferry, “The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” Journal of the American Chemical society, vol. 77, pp. 3701-3707, 1955.
[6] L. Viviani M. Di Paola G. Royer-Carfagni, “A fractional viscoelastic model for laminated glass sandwich plates under blast actions,” International Journal of Mechanical Sciences, vol. 222, p. 107204, 2022.
[7] P. S. Bulson, Explosive loading of engineering structures, CRC Press, 1997.
[8] Iintenrational Organization of Standards (ISO 16933:2007), Glass in building—Explosion-resistant security glazing—Test and classification for arena air-blast loading, 2007.
[9] I. Podlubny, Fractional Differential Equations, Academic Press, 1998.
[10] L. Biolzi S. Cattaneo M. Orlando L. Ruggero Piscitelli P. Spinelli, “Constitutive relationships of different interlayer materials for laminated glass,” Composite Structures, vol. 244, p. 112221, 2020.