The Phenomenological Theory of Linear Viscoelastic Behavior

When a stress or a strain is impressed upon a body, rearrangements take place inside the material by which it responds to the imposed excitation. In any real material these rearrangements necessarily require a finite time. The time required, however, may be very short or very long. When the changes take place so rapidly that the time is negligible compared with the time scale of the experiment, we regard the material as purely viscous. In a purely viscous material, all the energy required to produce the deformation is dissipated as heat. When the material rearrangements take virtually infinite time, we speak of a purely elastic material. In a purely elastic material the energy of deformation is stored and may be recovered completely upon release of the forces acting on it. Water comes close to being a purely viscous material; and steel, if deformed to no more than a percent or two, behaves in an almost completely elastic fashion. In principle, however, all real materials are viscoelastic. Some energy may always be stored during the deformation of a material under appropriate conditions, and energy storage is always accompanied by dissipation of some energy.

The representations discussed in the preceding three chapters are all related to the Boltzmann superposition principle which forms the analytic basis of the theory of linear viscoelastic behavior. In this chapter we discuss the representation of such behavior by empirical mathematical models which bear no relationship to the superposition principle. These models are useful when it is desired to describe linear viscoelastic behavior qualitatively by a small, easily manageable, number of parameters. The standard linear solid and liquid models satisfy the latter requirement but they do not model the distribution of respondance times so characteristic of viscoelastic behavior.