Causality of strain within framework of small and large amplitude oscillatory testing

Abstract

The Small Amplitude Oscillatory Strain (SAOS) testing is commonly used to measure linear viscoelastic functions such as elastic moduli, which are denoted respectively \(G^{*}(i\omega )\) and \(E^{*}(i\omega )\) in simple shear and tension-compression. Beyond the linear regime, Large Amplitude Oscillatory Strain (LAOS) is a widely used experimental technique to investigate nonlinear phenomena. From mathematical standpoint, Fourier transform and Fourier series are used to handle SAOS and LAOS data. In general, SAOS-tests do not account a strain jump discontinuity to make easy measurement data processing. Thereby, we focus on the influence of a strain jump discontinuity (or not) on the response of the Cauchy stress. First, we investigate the problem of strain discontinuity (or not) within framework of one-dimensional isotropic linear viscoelasticity by considering both the integral approach and the fractional Maxwell constitutive model. Second, we assume that, the Large Amplitude Oscillations Strain (LAOS) is equivalent to small oscillations around a static pre-deformation. It means that, the jump at the origin is shifted to minus infinity in the time scale. Therefore, we investigate the first and third harmonics within framework of the nonlinear Kelvin-Voigt model. We conclude with some future perspectives for the present work.