Clarifications of Certain Ambiguities and Failings of Poisson's Ratios in Linear Viscoelasticity

摘要

Detailed new analytical investigations are presented describing the behavior of Class I, II and III viscoelastic Poisson's ratios (PR). Their previously demonstrated dependence on stress-time histories, which lead to the inability to consider them as universal viscoelastic material properties and the incapacity to produce a general elastic-viscoelastic correspondence principle (EVCP) based, is expanded. A new Class VI PR is analytically derived from the viscoelastic constitutive relations in the Fourier transform (FT) space to achieve the proper FT form of the elastic/viscoelastic correspondence principle, i.e., the elastic-viscoelastic analogy. However, even though this PR Class is a pure universal material property function, it still fails to provide a convenient and useful path to a correspondence principle due to its inopportune constitutive form in real time space vis-a-vis a thermodynamic model with equivalent attributes. Consequently, no general EVCP involving PRs can be formulated. The derived Class VI PRs are equivalent to the defined Class HI PRs with 1-D loadings (stresses).