Implications and Constraints of Time-Independent Poisson Ratios in Linear Isotropic and Anisotropic Viscoelasticity

Abstract

It is proven that time-independent viscoelastic Poisson ratios (PR) can only exist under separation of variable solutions which severely limits the class of applicable problems to quasi-static ones with incompressible homogeneous materials and non-moving boundaries under separable stress or displacement boundary conditions without any thermal expansions. Therefore, composites which are inherently anisotropic and sandwich structures which are nonhomogeneous and anisotropic are generally precluded from having time-independent PRs. Equal time variations for material properties in all directions are shown to be another simultaneous requirement instead of the incompressibility condition for achieving time-independent PRs. However, such restricted models lead to physically unrealistic bulk moduli responses when compared to experimentally determined relaxation moduli and are not generally achievable in current real materials. Consequently, viscoelastic materials are best characterized in terms of relaxation or creep functions, moduli or compliances rather than combinations of the latter with Poisson's ratios. Additionally, the assumption of constant PRs in problems involving thermal and chemical expansions, such as curing and manufacture of viscoelastic composites, is shown to be unjustified and insupportable. The distinct viscoelastic PR definitions, as found in the literature, are examined and classified into five categories. It is further shown that each is inherently unrelated to the others and all are always time-dependent, unless the above extremely limiting conditions are imposed. An extensive literature review indicates that experimental results overwhelmingly confirm the time dependent nature of viscoelastic PRs as no constant experimentally observed PRs were reported.