Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Tensor based mechanics of materials books

  1. Jul 12, 2012 #1
    I was seaching mechanics of materials books, but i need them to be tensor based. Any sugestions?
  2. jcsd
  3. Jul 12, 2012 #2
    What kinds of material behaviour are you looking for? A very good starting point covering balance principles, stress and strain tensors, hyperplasticity and some thermodynamics (but no plasticity) is Holzapfel's Nonlinear Solid Mechanics: A Continuum Approach for Engineering. Really one of the best books I know. Ogden's Nonlinear Elastic Deformations might be good as well, but I have never used it. There are a number of other books, really depends on what you're looking for.
  4. Jul 12, 2012 #3
    sorry, that was meant to say "hyperELASTICTY," not "hyperPLASTICITY"
  5. Jul 12, 2012 #4
    Thanks, i'll check it out now!! i'm mainy looking for elastic bahaviour and some (just a little) thermodynamics, so Holzapfel's sounds good!!
  6. Jul 31, 2012 #5
    I'm a little late, but I'm going to post anyways in case you are still looking or anyone else is wondering. I am an undergraduate student, but I did a ton of reading on linear elasticity for a research project, and a little non-linear elasticity for fun. If you give me details on what specific topics you would like to cover, and let me know whether you are most interested in general elasticity, linear elasticity, or mechanics of materials, I can point you in a more specific direction. For what follows, I'm assuming you are new to the subject, with maybe an undergrad mechanics of materials engineering course - let me know if this isn't the case.

    In case you don't know the difference between the following (skip to dotted line if you do):
    -- Linear Elasticity - This is generally what is being referred to in undergrad mechanics of materials textbooks when they say "Elasticity", "Theory of Elasticity", etc. The main assumption that separates it from general elasticity is the omission of the last term in the equation for the strain tensor at the top of this page (link is to amazon preview of Landau and Lifgarbagez' Theory of Elasticity), which is valid if there is a small-deformation assumption. This assumption is reasonably valid in many real-life applications, and the theory that follows is very well-developed.
    -- Mechanics of Materials - This subject is heavily utilized by engineers. The line kind of blurs between mechanics of materials and linear elasticity for many models, as many mechanics of materials models use linear elasticity equations as a starting point. Additional simplifying assumptions are made (such as shape, thickness, material properties, etc) to allow analytical approximations or numerical analysis to be made for frequently-encountered problems, when the additional accuracy gained by solving the complete elasticity equations is unnecessary. It is pretty rare that a complete solution to the linear elasticity equations for a 3D object will have an easily obtainable (or even manageable) analytical solution. Additionally, mechanics of materials models may be made for cases where the deformations are too large for linear elasticity to be applied accurately. Mechanics of materials also studies yielding, failure, [usually simplified] plasticity, etc.
    -- General Elasticity - Again, it does not make the small deformation assumption that linear elasticity does. This leads to non-linear differential equations. There is overlap with plasticity. It is necessary in situations where there are large deformations (ie: a rubber band). I can't help you much with this, but I have done a little with it and may be able to point you in the right direction.


    Green and Zerna - Theoretical Elasticity
    If you like dense, dry books where you fill in a lot of the gaps yourself and are given no practice problems, you will like this book (no sarcasm - I loved it). There are some example problems, but expect to be supplementing the book to get practice. The beginning of the book has a detailed review of tensor math and a brief review of the other requirements (I believe the math review is about 50 pages total). Complex analysis is also used pretty heavily when appropriate, and in conjunction with tensor notation as much as is possible.

    It's a great book - which I recommend getting - and is useful as a reference, if for nothing else. It is probably not a good intro/stand alone book due to the lack of exercises, but the amount of information is astounding and you will probably benefit from reading it alongside a more user-friendly book. It does present a lot of the standard problem solving methods in elasticity. The way the book is set up is: tensor math review, general elasticity, a few specific cases of general elasticity, linear elasticity, specific cases of linear elasticity.

    This is probably the most advanced book I'm going to mention, and requires a good deal of mathematical maturity. It also has a ton of info on shells and 2D elasticity.


    Barber - 'Elasticity'
    This is an awesome book, and much more geared towards a student (has problems and much more examples than Green and Zerna). This book may be available for free as an e-book if you access springerlink.com through your university. You can still use it as a reference book, although it is not as efficient as using Green and Zerna (a lot of the chapters carry over from the previous chapters without explicitly mentioning it, so you will be flipping back and forth a lot). It has a lot of info on standard methods of solving problems, and is a good book if you want to learn to solve problems. It probably has more 3D stuff than Green and Zerna (if I remember correctly)


    Landau and Lifgarbagez - 'Theory of Elasticity'
    This is a good read, and has the typical straight-to-the-point approach of the Landau and Lifgarbagez series (which I like a lot). I think this is a really good starting book, personally; others may disagree. If you do go that route, I would just check it out from a library, read the first two chapters (about 90 pages - skip the part on crystals for now), and then find a more in-depth book. It will give you a good intuition, though. Landau and Lifgarbagez has problems (much better, think-outside-the-box type problems than other elasticity books that I've read), but not nearly as many as a book like Barber's. It is much more of an understand-the-subject book than a solve-problems-in-the-subject book.


    Timoshenko - 'Theory of Elasticity' and 'The Theory of Plates and Shells'
    The first is a linear elasticity book - theory and problem solving, with some good examples. The second is kind of an elasticity/mechanics of materials hybrid focused on plates and shells (lots and lots of special cases). These books are more engineering-type books than physics-type books IMO, but are good if they are what you are looking for.

    I don't really remember if they use tensors or not, sorry.


    Armenàkas - 'Advanced Mechanics of Materials and Applied Elasticity'

    I referenced this a few times, but didn't utilize it as much as others. My advisor thinks highly of it. If you are more interested in mechanics of materials than elasticity, this is the best option out of the books that I have listed. It devotes about 1/3 of the chapters to elasticity and the remaining 2/3 to mechanics of materials. It includes numerical methods as well. A much more engineering-type book than physics-type.


    Chao, Pagano - 'Elasticity: Tensor, Dyadic, and Engineering Approaches'
    This book is neat. It is very concise, and gives you an overview of linear elasticity from 3 different approaches: vector calculus, tensors, and dyadics. That being said, I didn't read it through; my advisor, however, thinks highly of it. It does have lots of nice reference tables for equations and lots of nice flowcharts for seeing the connections between different solution methods. Its also cheap.


    Lurie - 'Theory of Elasticity' - possibly free through springerlink.com if your library gives access.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook