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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.
Aerospace Engineering Department
(AE) and Technology Research, Education and Commercialization
Center (TRECC)
National Center for Supercomputing Applications (NCSA)
University of Illinois at Urbana–Champaign
104 South Wright Street, MC-236
Urbana, IL 61801-2935
United States
