3D Elasticity Theory 1

[ThetaJC]

Hello,

I am looking for a book that has a good foundation on mechanics of materials of orthotropic and anisotropic materials. Specifically I am looking for a book which introduces characteristic matrices, stress tensors, strain tensors, etc. of anisotropic materials. My limited understanding is that some materials may require up to 21 constants to properly define their elastic behavior. I understand that most likely there is not one book which can be the end all resource for rigourously introducing this topic, however, does anyone know of a book which can start with the definition of poisson's ratio, hooks law, etc. and develop matrix correlation of material behavior in 3D of materials as complicated as being anisotropic? I don't mind spending up to $200 for a good book if it contains a well ordered, logical, and rigorous development of the 3D theory of elasticity. Or if someone knows of a set of books to accomplish this please let me know. I am studying fiber reinforced composite materials and need to fill in a gap between elementary mechanics of materials (isotropic only) taught at an undergraduate level back many years ago to full out 3D elasticity theory of anisotropic materials. Thank you for any advice and recommendations you may be able to supply.

 

[mloew]

ThetaJ,

Start here: Books on Finite Element Method (faq727-384).

Best regards,

Matthew Ian Loew


Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[sdm919]

Do you really need a book on 3D aniotropic elasticity, or would a composite mechanics book be enough? Most composite books give a brief discussion of 3D anisotropic materials, then quickly specialize to the 2D case since most applications involve thin plate and shell structures. If this is sufficient, I would recommend:

"Mechanics of Composite Materials" by Robert M. Jones

On the other hand, most elasticity books give a good foundation of 3D stress and strain theory, but do not devote much (if any) attention to anisotropic problems. However, you may find it useful to read a little about elasticity if you've only studied mechanics of materials before. A very good elasticity book that is available as an inexpensive Dover paperback is:

"Elasticity: Tensor, Dyadic, and Engineering Approaches" by P.C. Chou & N.J. Pagano

If you want to get more advanced, you could read about continuum mechanics, which considers stresses and strains from a more general viewpoint, and covers fluids as well as solids. Schaum's has a inexpensive outline for this:

"Schaum's Outline of Continuum Mechanics" by George Mase.

You could say that mechanics of materials is a simplification of elasticity and elasticity is a specialization of continuum mechanics.

If you REALLY want anisotropic elasticity, here is a book which I have not seen, and therefore cannot recommend, but may be of interest to you:

"Anisotropic Elasticity: Theory and Applications" by C.T. Ting

Good Luck!

 

[imagitec]

I use Ansel Ugural and Saul Fenster's Advanced Strength and Applied Elasticity as a 3D strength of materials reference. Anisotropic materials are in that domain, but this is not a book about them. For example, referring to the constants you mentioned, the section on the generalized Hooke's Law notes, "Strain energy considerations can be used to show that for fully anisotropic crystalline materials the number of independent material constants can be as large as 21 (see Sec. 2.10)" Section 2.10 then goes into detail.

The reviews on Amazon aren't flattering, but I learned from it.

Rob Campbell, PE
Finite Monkeys -

http://www.livejournal.com/users/robcampbell

 

[ThetaJC]

Thanks so much for all your responses. I went ahead and purchased Advanced Strength and Applied Elasticity through Amazon. The previews looked good.