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
6 - CONSTITUTIVE EQUATIONS
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 truth is, the science of Nature has been already too long made only a work of the brain and the fancy. It is now high time that it should return to the plainness and soundness of observations on material and obvious things.
— Robert Hooke (1635–1703)There are two possible outcomes: If the result confirms the hypothesis, then you've made a measurement. If the result is contrary to the hypothesis, then you've made a discovery.
— Enrico Fermi (1901–1954)Introduction
General Comments
The kinematic relations developed in Chapter 3, and the principles of conservation of mass, balance of momenta, and thermodynamic principles discussed in Chapter 5, are applicable to any continuum irrespective of its physical constitution. The kinematic variables such as strains and temperature gradient, and kinetic variables such as stresses and heat flux were introduced independently of each other. Constitutive equations are those relations that connect the primary field variables (e.g., ρ, θ, ∇θ, u, ∇u, v, and ∇v) to the secondary field variables (e.g., e, η, q, and σ), and they involve the intrinsic physical properties of a continuum. Constitutive equations are not derived from any physical principles, although they are subject to obeying certain rules and the entropy inequality. In essence, constitutive equations are mathematical models of the real behavior of materials that are validated against experimental results. The differences between theoretical predictions and experimental findings are often attributed to an inaccurate mathematical representation of the constitutive behavior.
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- An Introduction to Continuum Mechanics , pp. 221 - 264Publisher: Cambridge University PressPrint publication year: 2013
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