The significance of (an)isotropic viscoelastic Poisson ratio stress and time dependencies

Abstract

Although viscoelastic moduli may be linear, Poisson ratios (PR) are always nonlinear functions of pairs of normal strains. This is equally true for physical PR defined in the real time space and for pseudo PR differently derived in the Fourier transform (FT) domain. It is shown analytically that only if anisotropic or isotropic viscoelastic moduli and relaxation or creep functions are characterized by identical time functions in all ditections and stresses are constants or at most temporal and spatial separable functions, then corresponding PR must be time independent. Under all other conditions PR are proven to be time, stress and thermal expansion dependent through time integrals, although physical and pseudo PR are shown to be functionally unrelated. The consequences of PR nonlinearities are that their uniaxially determined values are not applicable to other uniaxial loadings with different time histories or to multiaxial loadings and thermal expansions, if the latter are present. Similarly, isotropic PR cannot generally be determined solely from viscoelastic Young's and shear moduli, even for linear materials. Consequently, viscoelastic material property characterization in terms of PR is not unique and viscoelastic responses are best described in terms of creep or relaxation functions. Anisotropic and isotropic viscoelastic PR time effects are investigated analytically and evaluated numerically.