All-polymer syntactic foams: Linking large strain cyclic experiments to Quasilinear Viscoelastic modelling for materials characterisation

The time-dependent behaviour of polymeric composites is critical in a broad range of applications, including those in marine, aerospace, and automotive environments. In the present study, we assess the validity of the quasi-linear viscoelastic (QLV) model to fit the stress–strain behaviour of all-polymer syntactic foams under large cyclic compressional strain in a novel experimental configuration. These syntactic foams were manufactured by adding hollow polymer microspheres of various sizes and wall thicknesses into a polyurethane matrix. These materials are known for their relatively large initial stiffness, and strong recoverability after large strains. In the QLV model, several strain energy functions (SEFs) were employed, including neo-Hookean, Ogden type I, and type II. The bulk and shear moduli are presented in the form of a Prony series. By estimating these experimental data using optimisation, the natural viscoelastic material properties and coefficients associated with the SEF were determined. The influence of the microsphere filling fraction was also explored. We show that at the strain rate considered here of 0.013 s${}^{-1}$, the compressible QLV model coupled with the Ogden-I SEF is capable of providing an excellent fit to experimental data. Critically, this fit can be achieved over a range of cycles via model optimisation to the first cyclic response only.