chapter  4
28 Pages

Rheology Fundamentals and Structural Theory of Elasticity

ByAlejandro G. Marangoni, Suresh S. Narine

The theoretical foundations for the characterization of the properties of solids were devised by Robert Hooke (1635-1703). Hooke observed that, for small elongations, the amount of elongation of a spring, L, was directly proportional

to the applied force. This observation is expressed mathematically as Hooke’s law:

F kL (1)

The range of elongation where Hooke’s law is obeyed is called the elastic region of the spring (Figure 1). Within this elastic region, spring deformations are reversible, that is, once the force is removed, the spring returns to its original length (Lo). At elongations above the elastic limit of the spring, irreversible deformations take place, and Hooke’s law is no longer applicable-no linear relationship between the applied force and the amount of spring elongation is observed. Beyond the limit of elasticity, the spring eventually reaches its breaking point (Figure 1).