Thermomechanics of Continua

1 Introduction.- 1.1 Preliminary Remarks.- 1.2 Chains of Mass Points.- 1.3 Contents of the Book.- 2 Geometry.- 2.1 Reference and Current Configurations.- Remark 2.1. On Non-material Vectors.- Remark 2.2. On Non-integrable Deformation Gradients.- 2.2 Polar Decomposition of the Deformation Gradient.- Example 2.1. Deformation of a Prism in the Homogeneous Extension.- Example 2.2. Deformation of a Prism in the Simple Shearing.- Example 2.3. A Polar Decomposition and Elastic-plastic Deformation.- 2.3 Some Other Measures of Deformation.- Remark 2.3. On Universal Solutions - Part.- 3 Kinematics.- 3.1 Description of Motion.- 3.2 Time Changes of Some Geometric Objects.- 3.3 Change of the Reference Frame.- Remark 3.1. On Objective Time Derivatives.- 4 Balance Equations.- 4.1 Preliminary Remarks.- 4.2 Global Balance Equations.- 4.3 Local Balance Equations.- 4.4 Local Conservation Laws.- 4.5 Spatial Form of Balance Equations.- 4.6 Spatial Form of the Local Conservation Laws.- Example 4.1. Stresses in the Homogeneous Extension of a Prism.- 4.7 Conservation Laws in a Non-Inertial Frame of Reference.- 5 Structure of Field Equations.- 5.1 Introductory Remarks.- Example 5.1. Isothermal Processes in a Linearly Elastic Rod.- Example 5.2. The Heat Conducting Linearly Elastic Rod.- 5.2 Isotropic Functions.- Example 5.3. Euler; the Basic Invariants and Generators for m Vector Variables.- Example 5.4. The Basic Invariants and Generators for one Vector and one Symmetric Tensor Variable.- Example 5.5. The Linearization for one Vector and one Symmetric Tensor Variable.- 5.3 Galilean Invariance of Field Equations.- Example 5.6. The Field Equations for Thirteen Fields.- Remark 5.1. On the Moments of the Boltzmann Equation.- Remark 5.2. On the Material Objectivity.- 6 Entropy Principle.- 6.1 Preliminary Remarks.- 6.2 Entropy Inequality.- Example 6.1. Eulerian Heat Conducting Fluid.- Example 6.2. Thermo-Viscoelastic Rod.- 6.3 Hyperbolicity of Field Equations.- 6.4 Thermoelastic Materials with Mechanical Constraints.- Example 6.3. Non-linear Thermoelastic Materials.- Example 6.4. Incompressible Materials.- Example 6.5. Inextensible Materials.- Example 6.6. Rigid Bodies.- Remark 6.1. On the Universal Solutions - Part II.- 6.5 Solid Interfaces.- 7 Ideal Gase.- 7.1 Introduction.- 7.2 Galilean Invariance; Material Frame Indifference.- 7.3 Entropy Inequality.- 7.4 Hyperbolicity.- 8 Maxwellian Fluids; Viscoelastic Solids Part 1: Maxwellian Fluids.- 8.1 Background of the Models of Maxwellian Fluids.- 8.1.1 Example 8.1. One-dimensional NthGrade Models.- 8.2 Constitutive Relations for a Non-Conducting Non-Newtonian Fluid; Field Equations.- 8.3 Entropy Principle.- 8.4 Thermodynamical Stability; Shear Pulses.- 8.5 Incompressibility; 2nd Grade Fluids.- 8.6 Field Equations in the Lagrangian Description.- 8.7 Second-Order Model of Isotropic Materials.- 8.8 Linear Viscoelastic Solids.- 9 Second Sound.- 9.1 Preliminary Remarks.- Remark 9.1. On the Moments of the Boltzmann-Peierls Equation.- 9.2 Thermodynamical Model of the Phonon Gas.- 9.3 Four-Field Model.- 9.4 Thermal Waves.- Example 9.1. Characteristic Speeds for the Four-Field Model.- 10 Some Multicomponent System.- 10.1 Introduction.- 10.2 Lagrangian Description.- Remark 10.1. On the Measurability of the Temperature.- Remark 10.2. On the Natural Mechanical Boundary Conditions.- 10.3 Balance Equation for Porosity.- 10.4 Second Law of Thermodynamics for a Thermoelastic Skeleton and Ideal Fluid Components.- 10.5 Small Deviations from the Thermodynamical Equilibrium.- 10.6 Propagation of Plane Waves of Small Amplitude.- 10.7 Final Remarks.- Appendix A: Thermostatics.- Appendix B: Curvilinear Coordinates.- Appendix C: Hyperbolic Systems of PDE.- C.l. Preliminaries.- C.2. Single Equation of Two Independent Variables.- C.3. Set of Equations with Two Independent Variables.- C.4. Time of Existence of Classical Solutions.- C.5. Systems with Many Independent Variables.- References.