# Introduction to Continuum Mechanics for Engineers

Written by: Ray M. Bowen (Texas A&M University)

This graduate-level continuum mechanics textbook was written by Ray M. Bowen of Texas A&M University. An introductory course but it does require students to have a “firm understanding of classical models such as the linear viscous fluids (Navier-Stokes theory) and infinitesimal elasticity. This understanding should include an appreciation for the status of the classical theories to nonlinear models is essential in light of the increasing reliance, by engineering designers and researchers, on prepackaged computer codes.” [Reviewing Bowen’s Porous Elasticity Textbook may provide a refresher but I’m not sure if it includes material on “infinitesimal elasticity”.]

Based upon the author’s preface and his introduction to Chapter 1, students may find reviewing the Introduction to Tensor Calculus and Continuum Mechanics textbook helpful.

I don’t generally like to just repost here the introductory or preface text from the books featured here on The Free Textbook List; but, this is a good time to do so – it’s quite technical and I don’t want to explain it incorrectly.

“The relationship of the classical theories to nonlinear models is essential in light of the increasing reliance, by engineering designers and researchers, on prepackaged computer codes. These codes are based upon models which have a specific and limited range of validity. Given the danger associated with the use of these computer codes in circumstances where the model is not valid, engineers have a need for an in depth understanding of continuum mechanics and the continuum models which can be formulated by use of continuum mechanics techniques. Classical continuum models and others involve a utilization of the balance equations of continuum mechanics, the second law of thermodynamics, the principles of material frame-indifference and material symmetry. In addition, they involve linearizations of various types. In this text, an effort is made to explain carefully how the governing principles, linearizations and other approximations combine to yield classical continuum models. A fundamental understanding of these models evolve is most helpful when one attempts to study models which account for a wider array of physical phenomena. ”

This textbook was originally published in 1989. The last time I reviewed this Continuum Mechanics textbook, it was the 2007 revised edition. The early versions were used as part of the curriculum at Rice University. Students at the University of Kentucky, taking Professors Donald C. Leigh’s course, have also used this textbook.

1. One-Dimensional Continuum Mechanics
1.1. Kinematics of Motion and Strain
1.2. Balance of Mass
1.3. Balance of Linear Momentum
1.4. Balance of Energy
1.5. General Balance
1.6. The Entropy Inequality
1.7. Example Constitutive Equations
1.8. Thermodynamic Restrictions
1.9. Small Departures from Thermodynamic Equilibrium
1.10. Small Departures from Static Equilibrium
1.11. Some Features of the Linear Model
2. Kinematics of Motion
2.1. Bodies and Deformations
2.2. Velocity, Acceleration and Deformation Gradients
2.3. Transformation of Linear, Surface and Volume Elements
2.4. Strain Kinematics
2.5. Infinitesimal Strain Kinematics
3. Equations of Balance

3.1. Balance of Mass
3.2. Balance of Linear Momentum
3.3. Balance of Angular Momentum
3.4. Balance of Energy
3.5. The Entropy Inequality
3.6. Jump Equations of Balance – Material Versions
4. Models of Material Behavior
4.1. Examples
4.2. Isothermal Elasticity-Thermodynamic Restrictions
4.3. Isothermal Elasticity – Material Frame – Indifference
4.4. IsothermalElasticity-Material Symmetry
4.5. IncompressibleIsothermalElasticity
4.6. Thermoelastic Material with Heat Conduction and Viscous Dissipation-Constitutive Assumptions
4.7. Thermoelastic Material with Heat Conduction and Viscous Dissipation-General Thermodynamic Restrictions
4.8. Thermoelastic Material with Heat Conduction and Viscous Dissipation-Equilibrium Thermodynamic Restrictions
4.9. Thermoelastic Material with Heat Conduction and Viscous Dissipation-Material Frame– Indifference
4.10. Thermoelastic Material with Heat Conduction and Viscous Dissipation-Material Symmetry
4.11. Constitutive Equations for a Compressible, Conducting, Viscous Fluid
4.12. Constitutive Equations for an Isotropic Linear Thermoelastic Solid with Heat Conduction
5. Materials with Internal State Variables
5.1. Constitutive Assumptions and Thermodynamic Results
5.2. Maxwell-Cattaneo Heat Conductor
5.3. Maxwellian Materials
5.4. Closing Remarks-Alternate Forms of the Entropy Inequality
Appendix A.
A.l. Vector Spaces
A.2. Linear Transformations
A.3. Inner Product Spaces
A.4. Components of Vectors and Linear Transformations
A.5. Cross Products, Determinants and the Polar Decomposition Theorem
A.6. Multilinear Functionals and Tensor Algebra
A.7. Euclidean Point Spaces, Coordinate Systems
A.8. Vector Analysis
Appendix B. Representation Theorems
Index

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Introduction to Continuum Mechanics for Engineers 