Laminated beams with viscoelastic interlayer

Abstract

a b s t r a c tWe analytically solve the time-dependent problem of a simply-supported laminated beam, composed of two elastic layers connected by a viscoelastic interlayer, whose response is modeled by a Prony's series of Maxwell elements. This case applies in particular to laminated glass, a composite made of glass plies bonded together by polymeric films. A practical way to calculate the response of such a package is to consider also the interlayer to be linear elastic, assuming its equivalent elastic moduli to be the relaxed moduli under constant strain, after a time equal to the duration of the design action. The obtained results, that are confirmed by a full 3-D viscoelastic finite-element numerical analysis, emphasize that there is a noteworthy difference between the state of strain and stress calculated in the full-viscoelastic case or in the aforementioned ''equivalent'' elastic problem.

Buckling of multilayered laminated glass beams: Validation of the effective thickness concept

“…Norville [16] and Galuppi and Royer-Carfagni [5,6] pointed out that the response of laminated glass beams presents two borderlines: 1) The layered limit corresponding to the case when the beam consists of free-sliding glass plies and 2) the monolithic limit, when the Euler-Bernoulli assumptions hold for the entire section of the laminate glass element. Hereafter we will denote the monolithic critical load as P crit 0 and the layered limit as P crit ∞ .…”

“…The concept of effective thickness has been proposed in recent years [4,5,6] based on the quasi-elastic solution. This method consists of calculating the thickness (time and temperature dependent) of a monolithic element with bending properties equivalent to those of the laminated one, that is to say, the deflections provided by the equivalent monolithic beam are equal to those of the layered model with viscoelastic core.…”

An experiment-based method for parameter identification of a reduced multiscale parametric viscoelastic model of a laminated composite beam

“…But their benefits go far beyond these characteristics because it is also possible to obtain mechanical properties on demand, this means that it is possible to obtain a desired strength defining a given stacking sequence of layers whose maximum strength is oriented towards strategic directions. Further, due to the resin used as matrix and transferring the stresses to the fibers, these materials also exhibit a higher damping characteristics than the observed on metals, which results on a better capacity to dissipate vibrations (Galuppi and Royer-Carfagni 2012). These, and many other characteristics besides the mechanical ones, make laminated composites attractive to very critical structures where simulations are very important to predict their mechanical behaviors; however, the mismatch of properties between fibers and resin-producing localized strains makes important to be able to develop simulations not only at the highest scales to account for global deformations, but also in lower scales to develop advanced and optimized material properties or to understand the feasibility to develop a failure.…”

Natural frequencies and damping ratios of multi-layered laminated glass beams using a dynamic effective thickness

“…A fundamental characteristic of viscoelastic materials is that the mechanical properties are frequency (or time) and temperature dependent [12,13,14,15]. The mechanical behavior of laminated glass is not elastic and the sections do not behave according to the Euler-Bernoulli Beam theory assumptions (plane sections remain plane) due to the shear effect of the interlayers [1,2].…”

“…Galuppi and Royer-Carfagni [1] concluded that a full viscoelastic analysis is only recommended when one is interested in a precise design of a laminated glass structures. Bennisson et al [3,4] proposed the concept of effective thickness for simplifying calculations of laminated glass elements under static loading, based on a previous work developed by Wölfel [17].…”