On the viscoelastic Poisson's ratio in amorphous polymers

Poisson's ratio is defined as the ratio of the lateral contraction to the elongation in the infinitesimal uniaxial extension of a homogeneous isotropic body. In a viscoelastic material, Poisson's ratio is a function of time (or frequency). In this paper, the time-dependence of the Poisson's ratio is analytically evaluated from the bulk and shear responses using the relations between the viscoelastic functions in the Laplace domain. It has been found that, in the region of α -relaxation, Poisson's ratio may be a nonmonotonic function of time, with a weak minimum at short times, when the shear response is broader than bulk response such that the ratio τ_G / τ_K is much larger than 1, or a monotonically increasing function of time if the shear and bulk responses share similar timescales and relaxation time distributions. The latter case is verified using experimental data from the literature for a cross-linked polymer, whereas the former case is verified for two linear polymers.