Ray M. Bowen

Introduction to continuum mechanics for engineers

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.- References.- 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.- References.- 4. Models of Material Behavior.- 4.1. Examples.- 4.2. Isothermal Elasticity-Thermodynamic Restrictions.- 4.3. Isothermal Elasticity-Material Frame Indifference.- 4.4. Isothermal Elasticity-Material Symmetry.- 4.5. Incompressible Isothermal Elasticity.- 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.- References.- 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.- References.- Appendix A. Mathematical Preliminaries.- A.1. 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.