On Poisson’s Ratio in Linearly Viscoelastic Solids

Abstract

Poisson's ratio in viscoelastic solids is in general a time dependent (in the time domain) or a complex frequency dependent quantity (in the frequency domain). We show that the viscoelastic Poisson's ratio has a different time dependence depending on the test modality chosen; interrelations are developed between Poisson's ratios in creep and relaxation. The difference, for a moderate degree of viscoelasticity, is minor. Correspondence principles are derived for the Poisson's ratio in transient and dynamic contexts. The viscoelastic Poisson's ratio need not increase with time, and it need not be monotonic with time. Examples are given of material microstructures which give rise to designed time dependent Poisson's ratios.

Broadband control of the viscoelasticity of ferroelectrics via domain switching

“…21 An electric field e is applied across the beam thickness, resulting in a macroscopic polarization p in the same direction (being accommodated by a mixture of differently polarized domains, and varying between 6p s , where p s is the saturated polarization) and an axial strain Àe s jpj/p s with a corresponding spontaneous strain e s , as shown in Fig. 4.…”

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

“…Of those two equations, the former involves a convolution, whereas the latter does not, which shows that the correspondence principle is not applicable to the creep Poisson's ratio ν c , as already noted by Hilton (2001Hilton ( , 2009Hilton ( , 2011 and Tschoegl et al (2002). Note that Lakes and Wineman (2006) found a relationship between the two Poisson's ratios ν r and ν c that differs from that given in Eq. (11).…”

“…The tests here considered characterize the so-called "basic" creep of the cementitious materials (Neville 1995), which is measured in absence of any hydric transfer and to which any time-dependent deformation observed on a nonloaded specimen (i.e., autogenous shrinkage) is subtracted.…”

“…By extension, for linear viscoelastic materials, we can aim at defining a time-dependent Poisson's ratio ( Van der Varst and Kortsmit 1992;Hilton 2001Hilton , 2011Tschoegl et al 2002;Lakes and Wineman 2006). However, such an aim can generate some ambiguity since Hilton (2001) enumerated five different ways of defining a time-dependent Poisson's ratio.…”

“…These two Poisson's ratios are not equal (Tschoegl et al 2002;Lakes and Wineman 2006). However, little is known on how significant the difference between them is.…”