An alternative approach to the linear theory of viscoelasticity and some characteristic effects being distinctive of the type of material

Abstract

In the introduction some postulates on which the linear theory of viscoelasticity is based are recalled, and the postulate of passivity is substituted by a stronger postulate called detailed passivity.

Next, a symmetric formulation of this theory is presented which is founded in a well-balanced way on the limiting properties of elasticity and viscosity. This leads to the introduction of the basic functions of creep compliance J ⁺(t) and stressing viscosity η⁺(t) associated to one another, whereas the basic functions retardation fluidity ϕ⁺(t) and relaxation modulus G ⁺(t) emerge as their time derivatives. Correspondingly, four complex basic functions are defined as their Carson transforms.

In addition to the proper retardation and relaxation terms, these basic functions contain the non-disappearing constants of either instantaneous compliance J ₀ or instantaneous viscosity η₀ and also of either ultimate fluidity ϕ_∞ or ultimate modulus G _∞. Therefrom ensues a classification of linear viscoelastic materials into four types: instantaneous elasticity or viscosity is allowed to combine with ultimate viscosity or elasticity. The latter alternative, signifying fluidlike or solidlike materials, leads, of course, to a quite different behavior in many situations; however, remarkable distinctive features are associated to the first one as well.

A few respective examples are outlined: 1) propagation of shear waves in a half-space with periodic and step-shaped excitation, 2) dissipation of work in a torsional vibration damper, and 3) shear flow between two parallel porous plates with injection and suction.

Finally, materials with viscous initial behavior are defended against the notion that they be of no or almost no real significance.