Multi-Material Polymeric Interlayers (MMPI) combine different polymers between two or more glass plies. Typically, a soft polymer sheet is used as the core layer, while two stiffer sheets encase this core. MMPIs are widely used in various industries, such as construction and automotive, for their ability to impart hybrid characteristics to laminated glass structures. For instance, an acoustic monolayer PVB can be used as the core layer to enhance sound insulation, while a stiff PVB is applied as the outer layer to increase structural stiffness. Modelling the mechanical behaviour of MMPIs is challenging due to their time- and temperature-dependent rheological properties. Accurately predicting the relaxation function of a stacked interlayer requires combining the relaxation functions of each material through a comprehensive viscoelastic analysis, where the current strain depends not only on the actual stress but also on the entire stress history.
A novel approach involving fractional calculus is here used for a comprehensive viscoelastic characterization of MMPIs. The fractional derivatives are numerically approximated using the L1 formula, which allows a variable time-step in the computations. The basic assumption is that the relaxation functions are represented by continuously connected power-law branches. This is a faithful representation for the response of many commercial polymers, which simplifies parameter determination from experimental data and enables easier and more computationally efficient numerical implementation. The fractional approach offers significant advantages in accuracy, efficiency, and simplicity compared to the traditional method using Prony series of exponential functions, making it a promising method of analysis.
In this study, we combine the single relaxation functions of the interlayers in a laminated glass package to obtain the MMPI’s, comparing model predictions with experimental data. We also highlight potential differences from the quasi-elastic approach, which models the polymers as linear-elastic materials with a temperature- and time-dependent secant shear modulus.