Non-linearity in rheological properties of polymers and composites under large amplitude oscillatory shear

Various approaches to the calculation of the components of the dynamic modulus measured at large amplitude oscillatory shear are compared. The method of Fourier analysis using Chebyshev polynomials, the determination of moduli via the differentiation of stress at the points of zero and maximum deformations, and the integration of the Lissajous figures are considered. A comparative analysis of material-nonlinearity measures obtained through various methods is performed. The measures of viscous and elastic nonlinearities, the mechanical-loss tangent of the material, and the power of its response are compared. The investigation is conducted for model samples of polyisobutylene in viscous-flow and high-elastic relaxation states and polyisoprene filled with nanoparticles of silicon oxide.