Theoretical and practical differences between creep and relaxation Poisson’s ratios in linear viscoelasticity

Poisson’s ratio is a well-defined parameter in elasticity. For time-dependent materials, multiple definitions based on the ratios between lateral and axial deformations are available. Here, we focus ourselves on the two most widely used definitions in the time domain, which define time-dependent functions that we call relaxation Poisson’s ratio and creep Poisson’s ratio. Those two ratios are theoretically different, but are linked in an exact manner through an equation we derive. We show that those two functions are equal at both initial and large times and that their derivatives with respect to time also are. Based on simple rheological models for both the deviatoric and volumetric creep behaviors, we perform a parametric study and show that the difference between those two time-dependent Poisson’s ratios can be significant. However, based on creep data available in the literature, we show that, for cementitious materials, this difference can be negligible or not, depending on the case.