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
3 - KINEMATICS OF CONTINUA
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
The man who cannot occasionally imagine events and conditions of existence that are contrary to the causal principle as he knows it will never enrich his science by the addition of a new idea.
— Max Planck (1858–1947)It is through science that we prove, but through intuition that we discover.
— Henri Poincaré (1854–1912)Introduction
Material or matter is composed of discrete molecules, which in turn are made up of atoms. An atom consists of negatively charged electrons, positively charged protons, and neutrons. Electrons form chemical bonds. The study of matter at molecular or atomistic levels is very useful for understanding a variety of phenomena, but studies at these scales are not useful to solve common engineering problems. Continuum mechanics is concerned with a study of various forms of matter at the macroscopic level. Central to this study is the assumption that the discrete nature of matter can be overlooked, provided the length scales of interest are large compared to the length scales of discrete molecular structures. Thus, matter at sufficiently large length scales can be treated as a continuum, in which all physical quantities of interest, including density, are continuously differentiable almost everywhere.
Engineers and scientists undertake the study of continuous systems to understand their behavior under “working conditions,” so that the systems can be designed to function properly and to be produced economically. For example, if we were to repair or replace a damaged artery in the human body, we must understand the function of the original artery and the conditions that led to its damage.
- Type
- Chapter
- Information
- An Introduction to Continuum Mechanics , pp. 81 - 150Publisher: Cambridge University PressPrint publication year: 2013