The thermomechanics of plasticity and fracture. (English) Zbl 0753.73001

Maugin, Gerard A.

Cambridge Texts in Applied Mathematics. Cambridge etc.: Cambridge University Press,. xix, 350 p. (1992).

The book, an outgrowth of lecture notes for a graduate course delivered by the author to students in Theoretical Mechanics and Applied Mathematics at the Pierre-et-Marie Curie University in Paris, is devoted to the mathematical theory of plasticity and fracture. The author, a well known specialist in the field, has succeeded here in giving a coherent presentation of the main topics of the mathematical theory of plasticity and fracture covering a large spectrum of problems and methods. The book is of high theoretical level and of real pedagogical value being an excellent guide both for professional scientists and students. The arrangement of this carefully written book, its comprehensive bibliography, and the format chosen for it by the Cambridge University Press make for highly enjoyable reading. Here is the contents of the book: Preface, Historical perspective, Notation, 1. Introduction to plasticity: experimental facts, 2. Thermomechanics of elastoviscoplastic continua, 3. Small-strain elastoplasticity, 4. Problems in perfect elastoplasticity, 5. Elastoplasticity with strain-hardening, 6. Elements of limit analysis, 7. Crack propagation and fracture mechanics, 8. Elastoplasticity with finite strains, 9. Homogenization of elastoplastic composites, 10. Coupling between plasticity and damage, 11. Numerical solution of plasticity problems, 12. Experimental study using infrared thermography, Appendix 1. Thermodynamics of continuous media, Appendix 2. Convexity, Appendix 3. Analytic solutions of some problems in elastoplasticity, Appendix 4. Analytic computation of stress-intensity factors, Further reading, Bibliography, Index.
Each chapter concludes with numerous proposed problems.

Reviewer: Gh.Gr.Ciobanu (Iaşi)

MSC:

74-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74C99	Plastic materials, materials of stress-rate and internal-variable type
74R99	Fracture and damage
74R20	Anelastic fracture and damage
74A15	Thermodynamics in solid mechanics

Keywords:

elastoviscoplastic continua; small-strain elastoplasticity; strain- hardening; crack propagation; finite strains; homogenization; elastoplastic composites; damage