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

Abstract

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.

Keywords: Effective low-strain and high-strain Young’s modulus; Mechanical vocal fold replica; Non-linear stress–strain model; Phenomenological model; Silicone composites.