I turned to this book for information on a very specific problem among the many facets of anisotropic elasticity theory addressed by the author: the interaction of a dislocation with a free surface, or with a planar boundary for a layer of different mechanical stiffness. I had read about the treatment of this problem using Stroh's 2-dimensional dislocation model and analytical continuation in the complex plane in numerous journal articles. Prior to reading Hwu's rigorous treatment of this problem, however, I did not understand how the authors of these articles used analytic continuation to extract the boundary conditions from the continuity of displacement and stress at the interface.
Instead of presenting the boundary conditions as "obvious" or as the result of "standard analytic continuation arguments" (as indifferently observed by the authors of various journal articles), Hwu clearly explains how Liouville's Theorem (a concept found in all complex analysis books) is used to arrive at the result. Liouville's Theorem states that a function which is analytic in a given region of the complex plane must also be constant in that region. Therefore, if a function in a given region is analytic, that region would necessarily be free of singularities/dislocations. By invoking Liouville's Theorem (p.102, Ch.4), Hwu makes it clear that each side of the interface (i.e. each half-space) may only be represented by a sum of functions that are devoid of singularities. Thus, if the dislocation is contained in the lower half-space (i.e. half space#1, which is situated below the interface), half-space#1 cannot include the Green's function G(z) corresponding to the dislocation/singularity. The sum of functions representing the upper half-space (i.e. half-space#2, the which is above the interface), however, may include the Green's function for the dislocation/singularity because the Green's function is finite within half-space#2. Similarly, the sum of functions representing half-space#2 may not include the Green's function corresponding to the reflection of the singularity/dislocation (i.e (G(z*))*, according the Schwarz reflection principle for harmonic functions). On the other hand, the sum of functions representing half-space#1 may include (G(z*))*, because (G(z*))* is finite within half-space#2. For a good treatment of the Schwarz reflection principle see Dennery (pp.80-82) Mathematics for Physicists (Dover Books on Physics).
Almost everything you need to know about calculating the strain field or Peach-Koehler force on a dislocation near an interface or surface is contained in Chapter 4 "Infinite Space, Half-Space, and Bimaterials" on pp.87-114. What I have learned from reading this chapter in Hwu's book is vitally important in my research work. Only the level of understanding achieved by reading a book of this caliber is sufficient for the dedicated research scientist or engineer to have confidence in his calculations.
The brilliant treatment that I have described above, however, only takes the reader up to the first four chapters (pp.1-113) of this outstanding book! In addition to the laying the groundwork for the treatment of half-spaces, the author addresses wedges and interface corners (Ch.5: pp.115-158); elliptical and polygonal holes/voids (Ch.6: pp.159-186); interfacial cracks and delimitation (Ch.6: pp.187-23; inclusions and their interactions with dislocations (Ch.8: pp.239-275); surface indentation and the elastic theory of contact between two adjacent bodies (Ch.9: pp.277-332); thermoelastic effects on voids, cracks, and wedges (Ch.10, pp.333-367); piezoelectric materials (pp.369-410); and plate bending (Ch.12: 411-434). Chapters 13-14 (pp.435-543 address stretching, voids, and inclusions in laminates: Chapter 15 (pp.545-588) is devoted to boundary element analysis. The remaining pages of this book (pp.589-673) are devoted to its extensive appendices, tables, references, and indices.
For those who find this book as fully informative and enjoyable as I have, I recommend the book authored by Professor Hwu's Ph.D. advisor, Professor Thomas Chi-Tsai (T. C. T.) Ting: Anisotropic Elasticity: Theory and Applications (Oxford Engineering Science Series).
- 语种： 英语
- ISBN: 1489985328
- 条形码: 9781489985323
- 商品尺寸: 15.5 x 4 x 23.5 cm
- 商品重量: 1.04 Kg
- ASIN: 1489985328
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