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**An introduction to thermomechanics. 2nd, rev. ed.**
*(English)*
Zbl 0531.73080

North-Holland Series in Applied Mathematics and Mechanics, Vol. 21. Amsterdam-New York-Oxford: North-Holland Publishing Company. XIII, 355 p. $ 68.00; Dfl. 160.00 (1983).

[For a review of the first edition (1977) see Zbl 0358.73001.]

As we have seen, yet from the preface, the purpose of this book is to elaborate a general modern theory of continuum thermomechanics. The author observes that the early concepts of continuum mechanics and thermodynamics cannot be separated, if we want to describe any general bodies, i.e. bodies for which (for example) the viscosity is to be taken into account, or if we must employ the complet set of different equations of motion (which contains the energy balance), and so on.

The exposition is based on a modern treatment of this subject, in other words: one conceives the thermodynamics as a field theory (and not as a theory of infinitely slow processes that lead, generally, to a theory of reversible processes). The book is conceived as an introduction to this theory and for that, is based on the simplest possible approach.

The elements of vector algebra and analysis, the basic laws of mechanics and thermodynamics, some elements of geometry in n-dimensional spaces and of the theory of functions are supposed to be known. Each section includes, at the end, a number of problems, in order to provide the reader with a means of testing his grasp of the matter.

The first three chapters of the book are concerned with some mathematical preliminaries concerning the theory of Cartesian tensors and with the mechanical laws governing the motion of a continuum.

In Chapter 4 the author deals with thermodynamics, showing how the fundamental laws can be formulated in terms of a field theory. In the present treatment the author introduces the stress as a sum of a quasiconservative stress (a state function dependent on the free energy) and a dissipative one (a term connected with the dissipation function). In chapter 5 the characteristic properties of some general materials, such as fluids and elastic solids are presented.

Chapters 6 through 11 deal with the application of the theory to various types of continua, such as: ideal fluids, crystals, inviscid gases, viscous fluids, plastic bodies,.... In chapters 12 and 13 the author presents a short outline of general tensors and their application in the study of large displacements. In chapter 14 we return to the basis of thermodynamics and the author shows that the exclusion of gyroscopic forces, in the irreversible case, is achivable by assuming that the dissipative stresses are determined by the dissipation function; this connection having the form of an orthogonality condition. In chapter 15 the author shows that the orthogonality condition is equivalent to a number of extremum principles and chapters 16 through 18 are concerned with applications of the orthogonality condition and principle to various types of continua, such as: non-Newtonian fluids, plastic materials and viscoelastic bodies.

The bibliography which we can find at the end of this book is very restrictive and for that is far to be at the level of the content of the book.

This book will be of interest to students, engineers and research workers.

As we have seen, yet from the preface, the purpose of this book is to elaborate a general modern theory of continuum thermomechanics. The author observes that the early concepts of continuum mechanics and thermodynamics cannot be separated, if we want to describe any general bodies, i.e. bodies for which (for example) the viscosity is to be taken into account, or if we must employ the complet set of different equations of motion (which contains the energy balance), and so on.

The exposition is based on a modern treatment of this subject, in other words: one conceives the thermodynamics as a field theory (and not as a theory of infinitely slow processes that lead, generally, to a theory of reversible processes). The book is conceived as an introduction to this theory and for that, is based on the simplest possible approach.

The elements of vector algebra and analysis, the basic laws of mechanics and thermodynamics, some elements of geometry in n-dimensional spaces and of the theory of functions are supposed to be known. Each section includes, at the end, a number of problems, in order to provide the reader with a means of testing his grasp of the matter.

The first three chapters of the book are concerned with some mathematical preliminaries concerning the theory of Cartesian tensors and with the mechanical laws governing the motion of a continuum.

In Chapter 4 the author deals with thermodynamics, showing how the fundamental laws can be formulated in terms of a field theory. In the present treatment the author introduces the stress as a sum of a quasiconservative stress (a state function dependent on the free energy) and a dissipative one (a term connected with the dissipation function). In chapter 5 the characteristic properties of some general materials, such as fluids and elastic solids are presented.

Chapters 6 through 11 deal with the application of the theory to various types of continua, such as: ideal fluids, crystals, inviscid gases, viscous fluids, plastic bodies,.... In chapters 12 and 13 the author presents a short outline of general tensors and their application in the study of large displacements. In chapter 14 we return to the basis of thermodynamics and the author shows that the exclusion of gyroscopic forces, in the irreversible case, is achivable by assuming that the dissipative stresses are determined by the dissipation function; this connection having the form of an orthogonality condition. In chapter 15 the author shows that the orthogonality condition is equivalent to a number of extremum principles and chapters 16 through 18 are concerned with applications of the orthogonality condition and principle to various types of continua, such as: non-Newtonian fluids, plastic materials and viscoelastic bodies.

The bibliography which we can find at the end of this book is very restrictive and for that is far to be at the level of the content of the book.

This book will be of interest to students, engineers and research workers.

Reviewer: V.Tigoiu

### MSC:

74A15 | Thermodynamics in solid mechanics |

74-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids |

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |

76-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics |

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

80-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to classical thermodynamics |