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**Mechanics of solid materials. Transl. from the French by B. Shrivastava. Foreword to the French edition by Paul Germain, foreword to the English edition by Fred Leckie.**
*(English)*
Zbl 0743.73002

Cambridge etc.: Cambridge University Press. xxv, 556 p. (1990).

On its spirit: the writing of the book has been organized to facilitate transfer of knowledge to engineering science: fundamental knowledge oriented towards practical applications, knowledge of macroscopic properties for formulating macroscopic laws of material behaviour, and a synthesis of the knowledge of theoretical and practical aspects. The recent progress in the mechanics of solid materials has resulted from simultaneous and decisive developments in all these fields:

At the fundamental level, it is the synthesis of continuum mechanics with the method of local state in thermodynamics. At the level of applications, it is a recognition of the need to ensure higher safety and economy in the building of more sophisticated structures. It also recognizes the possibility of using faster computers to solve nonlinear problems numerically. At the level of microscopic properties, it is the theory of dislocations and the invention of electron microscopes. At the level of macroscopic phenomena, it is the technique of identification of mathematical models from experimental results. At the theoretical level, it is the development of functional analysis and variational formulations. Finally, at the experimental level, it is, of course, the introduction of electronics and microcomputers in testing machines and measurement procedures.

The first chapter is devoted to physical mechanisms of deformation and fracture of metals and alloys, polymers, concrete and wood. The second chapter reviews the elements of continuum mechanics and thermodynamics of irreversible processes which constitute the theoretical tools used in other chapters. The third chapter presents a schematic classification of the behaviour of solids based on experimentation and identification, the main methods of which are described. The fourth chapter marks the begining of the modelling of different material behaviours. All the subsequent chapters follow the same outline, namely: domain of validity defining more or less precisely the conditions for using the models, phenomenological aspects derived experimentally, general formulation based on thermodynamics, determination and identification of particular models with examples for common materials, and a concise presentation of the associated structural analyses. Within this framework, the fourth chapter presents linear elasticity, thermoelasticity, and viscoelasticity.

The fifth chapter is devoted to plasticity. Classical isotropic plasticity is formulated starting with the dissipation potential associated with the flow criterion. Above all, we insist on plasticity with anisotropic hardening which can be used to consider the cyclic behaviour so important for the prediction of fatigue failure. The sixth chapter is concerned with the same questions but this time applied to metals and alloys under loads at such intermediate or high temperatures which give rise to the phenomena of viscosity: viscoplasticity. The seventh chapter approaches the fracture of a volume element through the continuum damage mechanics. Different models have been worked out for considering and predicting the phenomena of ductile fracture, brittle fracture and fatigue fracture. The eighth chapter deals with crack mechanics of solids. The fracture mechanics of crack growth is approached by energy methods which logically introduce the concept of the energy release rate. This variable, associated with stress intensity factors, is used to formulate models of fracture by instability, of ductile fracture, and of fatigue crack growth.

The book therefore covers the whole field of the mechanics of materials, but in a highly condensed fashion. For a more detailed study, it is advisable to consult the important works listed in the bibliography at the end of each chapter. This book is therefore intended for the reader, who has a good knowledge of the basic elements of continuum mechanics or of the strength of materials, but who wishes to introduce more physics into the design and manufacture of products, with or without the help of computers, or in the safety analysis of structures.

At the fundamental level, it is the synthesis of continuum mechanics with the method of local state in thermodynamics. At the level of applications, it is a recognition of the need to ensure higher safety and economy in the building of more sophisticated structures. It also recognizes the possibility of using faster computers to solve nonlinear problems numerically. At the level of microscopic properties, it is the theory of dislocations and the invention of electron microscopes. At the level of macroscopic phenomena, it is the technique of identification of mathematical models from experimental results. At the theoretical level, it is the development of functional analysis and variational formulations. Finally, at the experimental level, it is, of course, the introduction of electronics and microcomputers in testing machines and measurement procedures.

The first chapter is devoted to physical mechanisms of deformation and fracture of metals and alloys, polymers, concrete and wood. The second chapter reviews the elements of continuum mechanics and thermodynamics of irreversible processes which constitute the theoretical tools used in other chapters. The third chapter presents a schematic classification of the behaviour of solids based on experimentation and identification, the main methods of which are described. The fourth chapter marks the begining of the modelling of different material behaviours. All the subsequent chapters follow the same outline, namely: domain of validity defining more or less precisely the conditions for using the models, phenomenological aspects derived experimentally, general formulation based on thermodynamics, determination and identification of particular models with examples for common materials, and a concise presentation of the associated structural analyses. Within this framework, the fourth chapter presents linear elasticity, thermoelasticity, and viscoelasticity.

The fifth chapter is devoted to plasticity. Classical isotropic plasticity is formulated starting with the dissipation potential associated with the flow criterion. Above all, we insist on plasticity with anisotropic hardening which can be used to consider the cyclic behaviour so important for the prediction of fatigue failure. The sixth chapter is concerned with the same questions but this time applied to metals and alloys under loads at such intermediate or high temperatures which give rise to the phenomena of viscosity: viscoplasticity. The seventh chapter approaches the fracture of a volume element through the continuum damage mechanics. Different models have been worked out for considering and predicting the phenomena of ductile fracture, brittle fracture and fatigue fracture. The eighth chapter deals with crack mechanics of solids. The fracture mechanics of crack growth is approached by energy methods which logically introduce the concept of the energy release rate. This variable, associated with stress intensity factors, is used to formulate models of fracture by instability, of ductile fracture, and of fatigue crack growth.

The book therefore covers the whole field of the mechanics of materials, but in a highly condensed fashion. For a more detailed study, it is advisable to consult the important works listed in the bibliography at the end of each chapter. This book is therefore intended for the reader, who has a good knowledge of the basic elements of continuum mechanics or of the strength of materials, but who wishes to introduce more physics into the design and manufacture of products, with or without the help of computers, or in the safety analysis of structures.

### MSC:

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

74R99 | Fracture and damage |

### Keywords:

physical mechanisms of deformation; fracture; metals; alloys; polymers; concrete; wood; thermodynamics of irreversible processes; schematic classification of the behaviour of solids; modelling of different material behaviours; linear elasticity; thermoelasticity; viscoelasticity; plasticity; anisotropic hardening; cyclic behaviour; fatigue failure; continuum damage mechanics; crack growth; energy methods
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\textit{J. Lemaitre} and \textit{J. L. Chaboche}, Mechanics of solid materials. Transl. from the French by B. Shrivastava. Foreword to the French edition by Paul Germain, foreword to the English edition by Fred Leckie. Cambridge etc.: Cambridge University Press (1990; Zbl 0743.73002)

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