Stress-Strain Relationships (Rheology)

Stress-Strain Relationships (Rheology)

Introduction

The goal of rheology is to relate, by laboratory testing, each component of stress to each component of strain while, in the process, introducing as few material prop-erties as is necessary to capture the fundamental behavior with sufficient accuracy for engineering purposes. Such 'constitutive relationships' for engineering anal-ysis and design are only a small part of material science which, using chemistry and physics, tries to answer the question 'why' in addition to 'how' materials behave. As yet, material science is not capable of deriving with sufficient accuracy for engineers the load-deformation response of any 'solid' material from funda-mental principles (such as bond strength, crystal structure, etc). Thus, while such considerations can often lead to a better understanding of the behavior of materi-als under load, decisions as to what might be done to make materials better, or even the design of new materials for special uses, the material properties from standard tests remain the basis for engineering analysis and design.

   Linear Elastic Behavior

A material specimen put under load deforms and with sensitive instruments we can measure, at a given time and temperature, its new shape. The first and sim-plest response idealization is linear-elastic behavior. If, in our test, we increase the load and the deformations increase proportionately, the material is linear. If we unload the specimen and it returns to its original shape, it is also elastic. Hooke was the first to do experiments of this sort and to recognize that this fun-damental concept, now called Hooke's Law,* defining a linear load-deformation relationship could lead to revolution in structural mechanics.