Customer Reviews

The Thermomechanics of Plasticity and Fracture (Cambridge Texts in Applied Mathematics)

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This book is very hard to understand particularly because of the strange notaion used. The subject of the book is very good, and I couldnt find a parallel book anywhere else, so I am still diggning hard to get few ideas across.

Mechanician Gerard Maugin goes about describing the thermodynamic basis of continuum mechanics, focusing on small-strain elasto-plasticity and fracture, and taking a mathematical viewpoint. You would do well to have a background in continuum mechanics and possibly some functional analysis; Maugin makes heavy use of tensors and their accompanying indicial notation, and there are proofs that enlist the help of variational principles. That being said, I found this book to be an enlightening and thorough introduction to the topic. I would rate the prose somewhere on the above-average level of readability and reader engagement, but it isn't spectacular (so read this one with a cup of coffee close by). I enjoyed the brief history of each topic discussed, complete with references to the original papers (Hill, Rice, Woehler, E. Lee, Westergaard, von Mises, Prandtl, Barre de Saint-Venant, etc etc).

Those pesky laws of thermodynamics always apply, and so Maugin goes about explaining elasto-plasticity (mostly in metals) by using work and energy and the conservation thereof. Most of the time you can get away without due diligence for the first and second laws, but not all the time. For example, you will find a heat source at a crack tip, which is coupled to the work done by opening the crack itself. Plastic behavior (at the continuum/macroscale level) is defined to obey the laws of thermodynamics in the absence of better theories, and Maugin reviews the analysis behind such treatments. The link to thermal behavior is with some energy potential (usually Helmholtz free energy), which leads to a discussion of coupled thermo-mechanical problems. Given the nature of such a coupled beast, the discussion is rather terse compared to other topics. The largest shortcoming here is the treatment of numerical solutions of thermo-mechanical problems, but this is likely due to the book being nearly 20 years old. If you're on the market for information about thermomechanics, this book is right up your alley (even though it is a few years old)...but be aware that the audience is graduate-level engineers and applied mathematicians.