Modelling and validation of the non-linear elastic stress–strain behaviour of multi-layer silicone composites

Multi-layer silicone composites are commonly used to mold deformable silicone vocal folds replicas. Nevertheless, so far the stress–strain characterisation of such composite specimens is limited to their effective Young's modulus (up to 40 kPa) characterising the elastic low-strain range, i.e. up to about 0.3. Therefore, in this work, the characterisation is extended to account for the non-linear strain range. Stress–strain curves on 6 single-layer and 34 multi-layer silicone specimens, with different layer stacking (serial, parallel, combined or arbitrary), are measured at room temperature using uni-axial tensile tests for strains up to 1.36, which amounts to about 4.5 times the extent of the linear low-strain range. Cubic polynomial and exponential two-parameter relationships are shown to provide accurate continuous fits (coefficient of determination R²≥99%) of the measured stress–strain data. It is then shown that the parameters can be a priori modelled as a constant or as a linear function of the effective low-strain Young's modulus for strains up to 1.55, i.e. 5 times the low-strain range. These a priori modelled parameter are confirmed by approximations of the best fit parameters for all assessed specimens as a function of the low-strain Young's modulus. Thus, the continuous stress–strain behaviour up to 1.55 can be predicted analytically from the effective low-strain Young's modulus either using the modelled parameters (R²≥85%) or the approximations of the best fit parameter sets (R²≥94%). Accurate stress–strain predictions are particularly useful for the design of composites with different composition and stacking. In addition, analytical expressions of the linear high-strain Young's modulus and the linear high-strain onset, again as a function of the effective low-strain Young's modulus, are formulated as well.