Comparison of viscoelastic finite element models for laminated glass beams

Abstract

Laminated glass elements, which consist of stiff elastic glass layers connected with a compliant viscoelastic polymer foil, exhibit geometrically non-linear and time/temperature-sensitive behavior. In computational modeling, the viscoelastic effects are often neglected or a detailed continuum formulation typically based on the volumetric-deviatoric elastic-viscoelastic split is used for the interlayer. Four layerwise beam theories are introduced in this paper, which differ in the non-linear beam formulation at the layer level (von Kármán/Reissner) and in constitutive assumptions for the interlayer (a viscoelastic solid with the time-independent bulk modulus/Poisson ratio). We perform detailed verification and validation studies at different temperatures and compare the accuracy of the selected formulation with simplified elastic solutions used in practice. We show that all the four formulations predict very similar responses. Therefore, our suggestion is to use the most straightforward formulation that combines the von Kármán model with the assumption of timeindependent Poisson ratio. The simplified elastic model mostly provides response in satisfactory agreement with full viscoelastic solutions. However, it can lead to unsafe or inaccurate predictions for rapid changes of loading. These findings provide a suitable basis for extensions towards laminated plates and glass layer fracture, owing to the modular format of layerwise theories.

On modal analysis of laminated glass: Usability of simplified methods and Enhanced Effective Thickness

“…The variety of interlayer materials for laminated glass is broad, ranging across the most common polyvinyl butyral (PVB), ethylene-vinyl acetate (EVA), thermoplastic polyurethane (TPU), or the stiffest ionoplast (SGP -SentryGlas(R) Plus). The density of the interlayer material is ρ 2 and we assume that its Poisson's ratio ν 2 is constant, see [37]. The viscoelastic behavior of polymers is commonly described by the generalized Maxwell model or by a fractional derivative model [14].…”

On pre- and post-fracture behaviour of laminated glass under bending

“…The details about the finite element solver developed for laminated glass and used for this numerical pre-fracture analysis can be found in [6] together with its verification. In short, the finite element model is based on a layer-wise formulation for beams including a viscoelastic constitutive law for the interalyer.…”

“…3 NUMERICAL ANALYSIS Having the material parameters of glass and interlayers, we will introduce the numerical model for laminated glass. Emphasis will be given to extension of the layer-wise finite element model from [6] towards fracture simulations. In this section, a brief introduction into a phase-field modelling of fracture is presented.…”

“…To reduce computational costs of the task, we use the refined beam elements to analyse the response of a multi-layer laminated glass structure, e.g. [6,15,16]. We follow the approach presented in [13] to obtain the tension-compression split based on the midsurface kinematic variables.…”

Evaluation of Tensile Strength of Glass From Combined Experimental and Numerical Analysis of Laminated Glass

“…The examples introduced in Section 3 were analyzed also numerically. The details about the finite element solver developed for the laminated glass can be found in [7]. It is based on a layer-wise formulation suitable for the modeling of non-linear behavior of laminated glass beams with a viscoelastic interlayer combining the von Kármán model with the assumption of time-independent Poisson ratio.…”