A fractional viscoelastic model for laminated glass sandwich plates under blast actions

Abstract

A model is proposed to evaluate the effects of explosions on laminated glass plates, made of glass plies bonded by thin polymeric interlayers, in the pre-glass-breakage phase. The novelty consists in the description of the viscoelastic properties of the interlayer, based on fractional calculus. This has noteworthy advantages because the relaxation function of most commercial polymers can be well approximated by power laws in the time interval of interest: in the fractional approach, this trend can be directly described by only two material parameters, whereas the traditional Prony series requires many more coefficients to be calibrated. Modelling of the plate is layerwise and the coupling with an elastic supporting back structure is considered. The glass plies are Kirchhoff–Love plates, whereas the impinging pressure from the explosion follows Friedlander equation. The governing equations, found via Hamilton’s principle, are solved à la Galerkin through a spatial expansion in Fourier series and a step-by-step integration in time using the Grünwald–Letnikov operators. Numerical experiments aim at describing how the fractional parameters of the interlayer, as well the compliance/mass of the back structure, affect the stress and deflection of the laminated plate. Comparisons are made with the commonly used quasi-elastic approximation, which considers the interlayer as linear elastic. The results show that the viscosity of the interlayer cannot in general be neglected and how a compliant back structure can help to safeguard the glass, although its displacement may exceed the serviceability limits. The optimal design shall thus represent a compromise between different effects: despite its limitation, the proposed model can represent a tool to make a correct choice.