The load bending capacity of laminated glass in the pre-breakage phase depends upon the shear coupling of the glass plies through the polymeric interlayers. Although the interlayer is viscoelastic, most design calculations follow the quasi-elastic approximations, in which the polymeric film is considered linear elastic, with an effective shear modulus calibrated on the duration of applied actions and operating temperature. However, when impulsive actions are applied (impact, blast waves), and even more so when the load is not monotone, the hereditary memory of viscoelasticity, neglected in the quasi-elastic approximation, may provide inaccurate results. In such cases, a full viscoelastic analysis is expected.
Here, we discuss an innovative approach, mentioned in modern Standards, which uses fractional calculus to characterize the interlayer viscoelastic properties, and compare it with the more traditional Wiechert model and Prony series. Two issues are considered: 1) the characterization of material parameters as a function of temperature; 2) the integration in time of the viscoelastic response. Concerning 1), observe that 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 geometrically visualized and described by only two material parameters, whereas Prony series requires many more coefficients, hard to calibrate. Passing to 2), we demonstrate, in the paradigmatic example of laminated glass beams, that the integration can be readily obtained via the Grünwald-Letnikov approach, which provides a convergence faster than the finite difference
