Thermomechanics of Continua

The notion of continuum thermodynamics, adopted in this book, is primarily understood as a strategy for development of continuous models of various physical systems. The examples of such a strategy presented in the book have both the classical character (e. g. thermoelastic materials, viscous fluids, mixtures) and the extended one (ideal gases, Maxwellian fluids, thermoviscoelastic solids etc. ). The latter has been limited intentionally to non-relativistic models; many important relativistic applications of the true extended thermodynamics will not be considered but can be found in the other sources. The notion of extended thermodynamics is also adopted in a less strict sense than suggested by the founders. For instance, in some cases we allow the constitutive dependence not only on the fields themselves but also on some derivatives. In this way, the new thermodynamical models may have some features of the usual nonequilibrium models and some of those of the extended models. This deviation from the strategy of extended thermodynamics is motivated by practical aspects; frequently the technical considerations of extended thermodynamics are so involved that one can no longer see important physical properties of the systems. This book has a different form from that usually found in books on continuum mechanics and continuum thermodynamics. The presentation of the formal structure of continuum thermodynamics is not always as rigorous as a mathematician might anticipate and the choice of physical subjects is too disperse to make a physicist happy.

The book is an unusual, comprehensive review of modern nonlinear thermodynamics giving also numerous examples for the practitioners.

Klappentext

The book contains, in a concise form, the foundations of both continuum mechanics and modern continuum thermodynamics. It originates from numerous courses delivered by the author during the last 25 years on both subjects at various universities. In contrast to other books on these subjects, it is reasonably self-contained. In addition, examples and remarks scattered throughout the text illustrate the chosen procedures or definitions. Simultaneously, they help to understand the applicability and the limitations of thermodynamical models. The book is an excellent introduction to more advanced monographs on the so-called rational extended thermodynamics.

Zusammenfassung
From the reviews
"The subjects presented in this book are treated accurately and specific results are derived which have appeared in the recent literature. Hence the book is recommended both for basic notions of thermomechanics of continua and for updated developments of some topics such as hyperbolicity of field equations, Maxwellian fluids, second sound, porous materials. The book is certainly useful for students and researchers in mathematics, physics and engineering." (Meccanica, 1999)

Inhalt
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.- 2.2 Polar Decomposition of the Deformation Gradient.- 2.3 Some Other Measures of Deformation.- 3 Kinematics.- 3.1 Description of Motion.- 3.2 Time Changes of Some Geometric Objects.- 3.3 Change of the Reference Frame.- 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.- 4.7 Conservation Laws in a Non-Inertial Frame of Reference.- 5 Structure of Field Equations.- 5.1 Introductory Remarks.- 5.2 Isotropic Functions.- 5.3 Galilean Invariance of Field Equations.- 6 Entropy Principle.- 6.1 Preliminary Remarks.- 6.2 Entropy Inequality.- 6.3 Hyperbolicity of Field Equations.- 6.4 Thermoelastic Materials with Mechanical Constraints.- 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.- 8.2 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.- 9.2 Thermodynamical Model of the Phonon Gas.- 9.3 Four-Field Model.- 9.4 Thermal Waves.- 10 Some Multicomponent System.- 10.1 Introduction.- 10.2 Lagrangian Description.- 10.3 BalanceEquation 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.