Introduction to Continuum Mechanics, 3rd ed.

Rating:
Summary: Excellent Book!
Review: I have used this book in Dr. Lai's into to elasticity class at Columbia University. It is chock full of well written text and many example problems that are worth looking at! I finally understand what eigenvalues and eigenvectors are good for!

Rating:
Summary: Disservice to students and insult to experts
Review: It's understandable and forgivable when the first or even second-edition of a technical book has some errors. However, when a book has reached its third edition, one should expect a relatively error-free and comprehensive reference. This book is an insult to the scientific method and to the tenets of decent technical writing. Considering only the part of this text that would be covered in a first course in continuum mechanics, even a cursory inspection reveals major theory errors as well as lazy typesetting, grammar, and editing issues that simply aren't acceptable for books in this price range. For instance...

* The index is only five pages long! It's missing absolutely essential entries like: coordinates, e-delta identity, invariants, gradient, velocity, velocity gradient, Stoke's theorem, and thermodynamics. The index is also missing several other terms (such as pseudo stress vector) that students would need to look up because they appear in the exercises.

* The reference list is anemic -- a rich and well-developed field like continuum mechanics deserves more than just 19 supplemental resources. Omission of Mase and Mase is unfortunate because those authors have greatly contributed to continuum mechanics texts for beginners.

Naturally, any introductory book on a complicated topic will, at times, provide the reader with some key equations without providing a proof. However, whenever a proof is omitted, the reader should AT LEAST be told where the proof can be found. For example, this textbook cites the conditions of compatibility for finite deformation without stating any reference book or journal article where the advanced reader (who, by this point, has learned to doubt the typesetting skills of these authors) can go to double check the equations.

* Discussion of the physical meanings of various strain measures is inexcusably fouled up. In the paragraph above eq 3.24.4, the cross-reference to eq. 3.25.2 should instead point to 3.24.2. Two equations below eq 3.26.8, the denominator is missing a factor of 2 and wrongly uses S instead of s). One equation above eq 3.26.9a, there should NOT be a 1 in the first term on the right hand side. Incidentally, the fact that these authors give equation numbers only for the equations that THEY themselves cross-reference is frustrating. OTHER PEOPLE might want to point to equations in this book -- having to say "the equation two lines below the authors' numbered equation" is awkward.

* In the section on transformation laws, eq. iii should NOT have a prime on b.

* The solution to exercise 7.8 (b) is missing a factor of 3 (probably other solutions are wrong too).

* The authors understanding of rotation and their proof of the polar decomposition theorem are seriously flawed. Their formula for the rotation expressed in terms of an angle and axis (in exercise 2B29) is wrong - it doesn't even give R=I when the rotation angle is zero. They claim in numerous locations (e.g., end of section 2B10) that improper orthogonal tensors are reflections (this is a common error - any proper rotation followed by a reflection will be an improper orthogonal tensor that is NOT a reflection). The authors clearly do not understand that symmetry and positive definiteness are requirements that must be IMPOSED in the polar decomposition - neither property is a consequence. They don't explain that a symmetric positive definite tensor has an INFINITE number of square roots, of which eight are symmetric, and only one is also positive definite. They prove that R is orthogonal, but fail to prove the theorem's assertion that it is PROPER orthogonal. Earlier in the text, the authors state that they will use the notation U for any deformation gradient that is symmetric; subsequent text clearly shows that they are presuming that a symmetric deformation gradient a stretch, which is false. To be a stretch, U must be additionally positive definite (a deformation gradient diagonal with components 1, -1, -1 is symmetric, but certainly not a stretch, and this example has negative eigenvalues, invalidating the authors claim immediately following their eq 3.20.2c)

* At the beginning of section 2B18, the authors state that a real symmetric tensor has "at least" three real eigenvalues. At least?? Are there more? They should have said "exactly three" (for a 3D space, of course).

* In the section on the rate of deformation tensor, the authors fail to prove that this tensor is not really a true rate. Here is a fact that lots of people know, but don't really understand and certainly don't know how to prove. Modern books in continuum mechanics need to discuss it.

* The authors present conservation of mass in the kinematics section, which is not correct. Kinematics is the mathematics of motion. Conservation of mass is a physical principle of Newtonian physics.

* Above eq 5.3.2: Cross reference to Problem 5.1 should be to Problem 5.2

* Eq. 3.28.6: Authors fail to give the proper name of this important relationship (Nanson's relation).

* Exercise 2B40: uses the word "principle" where "principal" is needed.

* After Eq. 3.30.7: Subject verb agreement ("The components... is called)"

* In example 3.1.2: Straightforward is ONE word, not two.

* Exercise 4.12: period and comma in a row ("For any stress state T., we define...")

* Eq 4.10.8a: Misplaced tilde in typesetting, and indistinguishable tilde in subsequent text. Same problem preceding eq 3.4.3.

* Eq 4.10.6b: "jm" needs to be a SUBSCRIPT.

* Exercise 3.31: typesetting is so juvenile that the authors used a superscripted lower case "o" to denote degrees instead of using the professional choice: the degree symbol. Professional typesetting conventions (e.g., italics for variables) are inconsistently enforced throughout this book.

* Exercises 2D4 and 2D5: missing plurals on "coordinates"

* Example 2B3.1: "Given that" should be replaced by "Given"

Granted, the comments in the above list transition from egregious errors to minor oversights, but the scientific community should DEMAND technical and editing perfection from a book on a classic subject that is in its third edition. Either that, or the purchase price should be set at a value that is consistent with this book's sloppy execution.

Note: this review covers ISBN 0750628944 paperback version.

Rating:
Summary: Excellent Book
Review: This is the best text that I have found for introducing continnuum mechanics and tensor notation to students. I have used this text in both Continuum Mechanics and Elasticity courses. Very clear explanations and examples to make the student proficient in conntinuum mechanics. I would love to see it expanded to include metric tensors and Christoffel symbols.