Continuum thermodynamics, Part I, Foundations - Wilmański, Krzysztof (World Scientific, 2008)
Includes bibliographical references (pages 373-395) and index
1. Introduction -- 2. Geometry. 2.1. Deformation gradient, material vectors. 2.2. Measures of deformation. 2.3. Extension, dilatation, shear. 2.4. Displacement. 2.5. Geometrical compatibility conditions. 2.6. Geometrical compatibility condition for singular surfaces -- 3. Kinematics. 3.1. Basic notions. 3.2. Objective time derivatives. 3.3. Boundaries, kinematical compatibility condition for singular surfaces -- 4. Balance equations. 4.1. Balance laws in Lagrangian description. 4.2. Balance laws in Eulerian description. 4.3. Extension on membranes and interfaces -- 5. Second law of thermodynamics. 5.1. Entropy inequality, thermodynamical admissibility. 5.2. Isotropy, material objectivity. 5.3. Materials with constraints. 5.4. Constitutive relations for various thermoelastic materials. 5.5. Proportionality theorem -- 6. Equilibrium Gibbs thermodynamics. 6.1. Thermostatics of gases. 6.2. Thermostatic theory of homogeneous mixtures --
- 7. Kinetic theories. 7.1. Liouville equation. 7.2. BBGKY-hierarchy. 7.3. Boltzmann equation -- 8. Extended thermodynamics. 8.1. General structure. 8.2. Nonrelativistic ideal gases. 8.3. A few remarks on boundary conditions -- 9. Thermodynamical model of viscoelastic materials. 9.1. Foundations. 9.2. Thermodynamical admissibility. 9.3. Viscous fluids, linear viscoelastic solids. 9.4. Maxwell fluid, Rivlin-Ericksen fluids -- 10. Elasto-viscoplastic materials. 10.1. Preliminaries. 10.2. Local configurations. 10.3. Crystal plasticity of monocrystals. 10.4. Polycrystals and orientation distribution function. 10.5. Thermodynamical admissibility. 10.6. Two particular classes of models -- 11. Thermodynamics of miscible mixtures. 11.1. General structure and field equations. 11.2. Thermodynamical admissibility -- 12. Thermodynamics of immiscible mixtures: introduction and models without the field of porosity --
- 13. Thermodynamics of poroelastic materials with the balance equation of porosity. 13.1. General structure. 13.2. Two-component poroelastic materials. 13.3. Linear models of saturated poroelastic materials. 13.4. Waves in poroelastic materials. 13.5. On adsorption in porous materials -- 14. Final remarks
This book is a unique presentation of thermodynamic methods of construction of continuous models. It is based on a uniform approach following from the entropy inequality and using Lagrange multipliers as auxiliary quantities in its evaluation. It covers a wide range of models - ideal gases, thermoviscoelastic fluids, thermoelastic and thermoviscoelastic solids, plastic polycrystals, miscible and immiscible mixtures, and many others. The structure of phenomenological thermodynamics is justified by a systematic derivation from the Liouville equation, through the BBGKY-hierarchy-derived Boltzmann equation, to an extended thermodynamics. In order to simplify the reading, an extensive introduction to classical continuum mechanics and thermostatics is included. As a complementary volume to Part II, which will contain applications and examples, and to Part III, which will cover numerical methods, only a few simple examples are presented in this first Part. One exception is an extensive example of a linear poroelastic material because it will not appear in future Parts