Explicit enriched plate model for laminated glass

Abstract

This abstract relates to the recent publication [Viverge K., Boutin C., Sallet F. : Model of highly contrasted plates versus experiments on laminated glass, IJSS, 102-103, 238-258 (2016)]. This contribution provides a synthetic analytic formulation describing the behaviour of laminated glass under static and dynamic loadings, that is validated by experiments. We only give here a synoptic overview and for in depth reading one may refer to the above mentioned publication.

As the laminated glass is made of stiff glass layers pasted with soft viscoelastic interlayers a specific model is established to account for the high contrast of mechanical properties. The effective plate model is derived from (i) the constitutive laws of the materials combined with (ii) an asymptotic expansion formulation and (iii) the appropriate scaling of the stiffness contrast.  The different regimes of behaviour are clearly specified, according to the mechanical and geometrical parameters of the layers, and to the loading. The analysis evidences the enriched kinematics of highly contrasted plates and yields to an analytic bi-torsor representation that encompasses (i) the shear related to the sliding within the PVB, (ii) the local  bending of each glass layer, and (iii) global bending of the whole laminate. Hence, the model can degenerate in either Reissner–Mindlin plate or shear-bending plate model, depending on the parameters of the constituents. In general it results in a tri-Laplacian formulation that help in understanding the behaviour and enables to derive analytical solutions under basic loadings. Furthermore, the theory applies to viscoelastic layers as PVB in laminated glass. This enriched plate model is validated through experiments conducted on two layers laminated glass with viscoelastic PVB interlayers. The theoretical result stating that the principle of time-temperature superposition of the PVB also applies, with the same time factor to the laminated glass, is observed experimentally. In addition, bending creep tests evidence the theoretically predicted transition from the (quasi-) monolithic behaviour at short time to the (quasi-) bi-layers behaviour at long time. The theoretical results describing the influence of both the temperature and frequency are also in good agreement with the experimental data. To conclude, the proposed model provides a simple easy-to-use theoretical framework for engineering purposes. For instance, it allows simple comparisons of the performances - in time and temperature - of laminated glasses made with different polymeric layers. In addition, the presented analytical results are suitable for determining the optimal design of structural elements made of laminated glass. Applications to the assessment or the improvement of the sound attenuation by laminated glass may also be considered.