The Mechanics and Thermodynamics of Continuous Media

1. Front Matter

   Pages I-XIV

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2. Synopsis

   1. Synopsis

      • Miroslav Šilhavý

      Pages 1-6

3. Balance Equations

   1. Front Matter

      Pages 7-7

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   2. Elements of Tensor Algebra and Analysis

      • Miroslav Šilhavý

      Pages 9-28

   3. Geometry and Kinematics of Continuous Bodies

      • Miroslav Šilhavý

      Pages 29-60

   4. Balance Equations

      • Miroslav Šilhavý

      Pages 61-86

4. Foundations

   1. Front Matter

      Pages 87-87

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   2. Material Bodies

      • Miroslav Šilhavý

      Pages 89-94

   3. The First Law of Thermodynamics

      • Miroslav Šilhavý

      Pages 95-100

   4. The Principle of Material Frame Indifference

      • Miroslav Šilhavý

      Pages 101-108

   5. The Second Law of Thermodynamics

      • Miroslav Šilhavý

      Pages 109-134

5. Constitutive Theory

   1. Front Matter

      Pages 135-135

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   2. Isotropic Functions

      • Miroslav Šilhavý

      Pages 137-150

   3. Constitutive Equations

      • Miroslav Šilhavý

      Pages 151-166

   4. The Equilibrium Response

      • Miroslav Šilhavý

      Pages 167-184

   5. The Equilibrium Response of Isotropic Bodies

      • Miroslav Šilhavý

      Pages 185-196

   6. The Dynamic Response

      • Miroslav Šilhavý

      Pages 197-206

6. Thermodynamic Equilibrium

   1. Front Matter

      Pages 207-207

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   2. The Environment

      • Miroslav Šilhavý

      Pages 209-228

   3. Equilibrium States

      • Miroslav Šilhavý

      Pages 229-242

This book presents the nonlinear theories of continuum thermomechanics. Through­ out 1 emphasize issues that are foundational in nature, and seek results common to materials of arbitrary symmetry. The central part of the book deals with thermoelastic bodies with heat conduction and viscosity, including the inviscid or ideal dissipation­ less bodies. A surprising variety of phenomena can be modeled within this frame­ work. Moreover, the main ideas can be transferred into more complicated theories. At present, the major challenge to the non linear thermoelasticity is posed by phase transformations with changes in symmetry. 1. W. Gibbs' immensely inftuen­ tiaI treatise On the equilibrium of heterogeneous substances has provided a highly successful theory of phase transitions in ftuids. Gibbs brought the view that the ther­ modynamics is not only the theory of heat, but also a theory of equilibrium, with the of the book is an extension of main tool the minimum principles. A large portion Gibbs' ideas to bodies of general symmetry by the methods of the calculus of varia­ tions. The interplay between the convexity properties of the stored energy functions, the resulting equations, and the physics of the phenomena is a leading theme.

• Classical Field Theory
• Continuum Mechanics
• Dissipation
• Kontinuummechanik
• Thermodynamik
• Variational Principles
• thermodynamics

From the reviews
"The book is excellent, and covers a very broad area (usually treated as separate topics) from a unified perspective. The author has clearly tried to reduce the mathematical tools to a minimium so as to make the book accessible to readers from the physics community (a more mathematical treatment can be found in his papers). It will be very useful for both mathematicians and physicists." (EMS Newsletter, 1999)

• Mathematical Institute, Academy of Sciences of the Czech Republic, Prague 1, Czech Republic

  Miroslav Šilhavý

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