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Finite plastic deformation of crystalline solids. (English) Zbl 0774.73001
Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge: Cambridge University Press. xiv, 235 p. (1992).
This book deals with finite plastic deformations of single crystals (chapters 1-5) and polycrystalline solids (chapters 6 and 7). It consists of seven chapters and one appendix. Chapters 1 and 2 have an introductory character and present fundamental notions and concepts needed for understanding the remaining chapters of the book. The major part of the book contains the results obtained by the author himself (there are over 30 papers by the author cited in the bibliography). The most important are chapters 3, 4 and 5. Chapter 3 (A general theory of elastoplastic crystals) contains a highly compensated theoretical knowledge, based on the previous results by the author. However, this chapter is too hard to read without any special preparatory study. Chapter 4 (Axial-load experiments and latent hardening in single crystal) and chapter 5 (Analysis of crystals in channel die compression) are well written and they exhibit a good correlation between the theory and the applications. In chapter 6 (Theoretical connections between crystal and aggregate behavior) the author reveals connections between crystal and aggregate behavior. The most important numerical methods for solving theoretical models discussed in the book are collected in the last chapter (Approximate polycrystal models). The author focusses on mechanic aspects of plastic deformation of crystalline solids. However, the problem studied may also be of interest to applied mathematicians since rigorous study remains as yet open.

MSC:
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74C99 Plastic materials, materials of stress-rate and internal-variable type
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74C20 Large-strain, rate-dependent theories of plasticity
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