Linear Viscoelasticity

Abstract

Measurements of load-displacement relationships show that the theory of linear elasticity holds for most metals under small strains. However, the simple fact that the vibrations of metal systems decay even in vacuo indicates that there is some energy dissipation. Hooke's law is insufficient, and we need to consider others. This need has become more evident since the development of polymeric materials. These materials possess a capacity to store some and dissipate the rest of the energy input. While the theory of elasticity accounts for materials which are capable of storing energy without any dissipation, the theory of Newtonian viscous fluids governs those which dissipate the whole energy input. Deformed elastic bodies return to a natural or undeformed state upon removal of applied loads. Viscous fluids, however, possess no capacity at all for deformational recovery. In an elastic solid, stress is related directly to deformation; in a viscous fluid, stress depends (except for its hydrostatic component) upon the rate of deformation. Hookean elastic solids and Newtonian viscous fluids represent the ends of a spectrum. Between these extremes there are materials which incorporate a blend of both linear elastic and (Newtonian) viscous characteristics. Appropriately, such materials are named linearly viscoelastic.