Difference between Creep and Relaxation Poisson's Ratios: Theoretical and Practical Significance for Concrete Creep Testing

The viscoelastic Poisson's ratio is an important parameter for assessing the multiaxial creep behavior of concrete. However, its definition in viscoelasticity can generate some ambiguity: at least five different ways of defining a viscoelastic Poisson's ratio are presented in the literature. As to their difference either in theory or in practice, little is known. In this work, we focus on the most intuitive two ways of defining a viscoelastic Poisson's ratio, which we call "relaxation Poisson's ratio" and "creep Poisson's ratio". First, we derive the analytical expressions of the two Poisson's ratios and a relationship between them. We show that their initial values are identical, and that their asymptotic values when time tends towards infinity as well. We also show that such is the case for their derivatives with respect to time. Then, considering concrete as a non-aging linear viscoelastic material, the results of multiaxial basic creep tests on concrete available in the literature are analyzed to compare the relaxation and the creep Poisson's ratios. The results show that the difference between the two Poisson's ratios is rather small but does exist in some cases. In such cases, whether this difference is significant should be considered with respect to the application considered.