Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Vectors and Tensors
- 3 Kinematics of a Continuum
- 4 Stress Vector and Stress Tensor
- 5 Conservation of Mass, Momentum, and Energy
- 6 Constitutive Equations
- 7 Applications in Heat Transfer, Fluid Mechanics, and Solid Mechanics
- Answers to Selected Problems
- References and Additional Readings
- Subject Index
6 - Constitutive Equations
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Vectors and Tensors
- 3 Kinematics of a Continuum
- 4 Stress Vector and Stress Tensor
- 5 Conservation of Mass, Momentum, and Energy
- 6 Constitutive Equations
- 7 Applications in Heat Transfer, Fluid Mechanics, and Solid Mechanics
- Answers to Selected Problems
- References and Additional Readings
- Subject 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 HookeIntroduction
The kinematic relations developed in Chapter 3, and the principles of conservation of mass and momenta and thermodynamic principles discussed in Chapter 5, are applicable to any continuum irrespective of its physical constitution. The kinematic variables such as the strains and temperature gradient, and kinetic variables such as the stresses and heat flux were introduced independently of each other. Constitutive equations are those relations that connect the primary field variables (e.g., ρ, T, x, and u or v) to the secondary field variables (e.g., e, q, and σ). In essence, constitutive equations are mathematical models of the behavior of materials that are validated against experimental results. The differences between theoretical predictions and experimental findings are often attributed to inaccurate representation of the constitutive behavior.
A material body is said to be homogeneous if the material properties are the same throughout the body (i.e., independent of position). In a heterogeneous body, the material properties are a function of position. An anisotropic body is one that has different values of a material property in different directions at a point, that is, material properties are direction-dependent.
- Type
- Chapter
- Information
- Principles of Continuum MechanicsA Study of Conservation Principles with Applications, pp. 149 - 161Publisher: Cambridge University PressPrint publication year: 2010