×

The mechanical and thermodynamical theory of plasticity. (English) Zbl 1294.74002

Boca Raton, FL: CRC Press (ISBN 978-0-8493-7230-8/hbk; 978-1-4200-0676-6/ebook). xxiv, 759 p. (2012).
The book presents a detailed introduction into plasticity theory including the fundamentals of continuum mechanics and the necessary mathematical tools like tensor calculus. It starts, like many other books in the field, with a more phenomenological description of material behaviour in one dimension. Before extending this to the fully 3-D case, an introduction to tensor algebra and analysis is given. This is followed by a detailed introduction to the kinematics of continuum mechanics. Next, one would expect the stress analysis. But, surprisingly, the author prefers to write about the decomposition of deformation gradient into elastic and plastic parts. He calls these parts also gradients, although it is known that none of them is a gradient in general. Clearly, without the concept of stresses, it is not possible to define elasticity. Neither \(F_e\) nor \(F_p\) are kinematical variables, but internal variables, which can only be (vaguely) understood based on the concepts of elasticity and plasticity, and, of course, of stresses. So, one may really doubt that the reader is able to understand this procedure.
Only after that, the stress analysis and the balance laws are presented. This gives the basis then to go into plasticity theory. This is done after the following plan: infinitesimal plasticity; elasticity and thermoelasticity; finite plasticity; thermoplasticity; viscoelasticity; crystal plasticity. The order of these topics is again cumbersome in parts, since one would expect elasticity before plasticity. Anyway, the book covers much more than the usual plasticity theory, and does it in a rather detailed, if not lengthy way. The used notations are clear and up-to-date. Many notation lists are helpful, the same as the index at the end, and the given examples and solved problems.
The book suffers from lacking of sources and discussions of different approaches. We know that plasticity is a controversial subject, so that different opinions coexist and should have been referred to and compared. Instead, quotations are almost completely suppressed, which is inadequate for scientific texts.
With this one exception, we can recommend the book as a detailed introduction into plasticity on a graduate level.

MSC:

74-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74Cxx Plastic materials, materials of stress-rate and internal-variable type
74A15 Thermodynamics in solid mechanics
74F05 Thermal effects in solid mechanics