Book on the mathematical theory of continuum mechanics

[epr2008]

I was wondering if anyone knows of a good book on the mathematical theory of continuum mechanics.

I have looked online, and the only ones I can seem to find are like your average physics or applied mathematics book. I want something with rigorous theoretical formulation of the subject. It does not have to be concise, just straightforward and logically assembled. Preferably, it would also provide physical intuition on the subject, although this is not necessary since I can find other books for that.

Also, if you can, please list recommended prerequisites for tackling the book.

Any help would be greatly appreciated.

Thank you

 

[kevinferreira]

The Landau Lifschitz collection on theoretical physics has one volume or two ln continuum mechanics. The collection is a bit strange, at least on my view, when compared to other books, but it is worth a try, they are very good.

 

[afreiden]

What kind of continuum mechanics?
There are two great websites for solid mechanics:
1) http://utsv.net/solid-mechanics
2) http://solidmechanics.org/

I would also recommend the Malvern textbook. Again, that is if solid mechanics is your interest.

 

[jasonRF]

This is a nice set of chapters on classical physics, including elasticity:
http://www.pma.caltech.edu/Courses/ph136/yr2011/

If it isn't what you are looking for, at least the price is right!

 

[rezeew]

for your question. The mathematical theory of continuum mechanics is a complex and important subject in physics and engineering. I would recommend the book "An Introduction to Continuum Mechanics" by Morton E. Gurtin. This book provides a rigorous mathematical treatment of continuum mechanics, including the fundamental principles and equations governing the behavior of continuous materials. It also includes physical examples and applications to help develop intuition for the subject.

As for prerequisites, a strong background in calculus, linear algebra, and differential equations is essential. Some knowledge of mechanics and basic physics concepts would also be beneficial. I would also recommend having a solid understanding of mathematical analysis and functional analysis, as they are important tools in the study of continuum mechanics.

I hope this recommendation helps in your search for a suitable book on the mathematical theory of continuum mechanics. Best of luck in your studies.