Book contents
- Frontmatter
- Dedication
- Contents
- List of Symbols
- Preface to the Second Edition
- Preface to the First Edition
- About the Author
- 1 INTRODUCTION
- 2 VECTORS AND TENSORS
- 3 KINEMATICS OF CONTINUA
- 4 STRESS MEASURES
- 5 CONSERVATION AND BALANCE LAWS
- 6 CONSTITUTIVE EQUATIONS
- 7 LINEARIZED ELASTICITY
- 8 FLUID MECHANICS AND HEAT TRANSFER
- 9 LINEARIZED VISCOELASTICITY
- References for Additional Reading
- Answers to Selected Problems
- Index
4 - STRESS MEASURES
Published online by Cambridge University Press: 05 July 2013
- Frontmatter
- Dedication
- Contents
- List of Symbols
- Preface to the Second Edition
- Preface to the First Edition
- About the Author
- 1 INTRODUCTION
- 2 VECTORS AND TENSORS
- 3 KINEMATICS OF CONTINUA
- 4 STRESS MEASURES
- 5 CONSERVATION AND BALANCE LAWS
- 6 CONSTITUTIVE EQUATIONS
- 7 LINEARIZED ELASTICITY
- 8 FLUID MECHANICS AND HEAT TRANSFER
- 9 LINEARIZED VISCOELASTICITY
- References for Additional Reading
- Answers to Selected Problems
- Index
Summary
Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone.
— Albert Einstein (1879–1955)Introduction
In the beginning of Chapter 3, we briefly discussed the need for studying deformations and stresses in material systems that we may design for engineering applications. All materials have certain thresholds to withstand forces, beyond which they “fail” to perform their intended function. The force per unit area, called stress, is a measure of the capacity of the material to carry loads, and all designs are based on the criterion that the materials used have the capacity to carry the working loads of the system. Thus, it is necessary to determine the state of stress in a material.
In this chapter we study the concept of stress and its various measures. For instance, stress can be measured per unit deformed area or undeformed area. As we shall see shortly, stress at a point in a three-dimensional continuum can be measured in terms of nine quantities, three per plane, on three mutually perpendicular planes at the point. These nine quantities may be viewed as the components of a second-order tensor, called a stress tensor. Coordinate transformations and principal values associated with the stress tensor and stress equilibrium equations are also discussed.
- Type
- Chapter
- Information
- An Introduction to Continuum Mechanics , pp. 151 - 180Publisher: Cambridge University PressPrint publication year: 2013