The elusive and fickle viscoelastic poisson's ratio and its relation to the elastic-viscoelastic correspondence principle

Abstract

This paper is dedicated to my good friend and colleague Professor Emeritus Georges J. Simitsis. The conditions for the applicability of the elastic-viscoelastic correspondence principle (analogy) in the presence of any of the five distinct classes of viscoelastic Poisson's ratios (PR) are investigated in detail. It is shown that if Poisson's ratios are time-dependent, no analogy in terms of PRs is possible, except for two of the classes under specifically prescribed highly limited conditions. Separately, the severely restrictive conditions involving time-independent PRs are discussed in detail. Failure to observe all such restrictions leads to ill posed overdeterminate problem formulations. Similarities associated with viscoelastic Timoshenko shear coefficients are also investigated and it is shown that no analogy to equivalent elastic problems can be constructed if these coefficients are time functions. In the final analysis, the PR analogy difficulties can be entirely avoided by characterizing viscoelastic materials in terms of relaxation moduli or creep compliances or creep and relaxation functions without any appeal to PRs.