Lie Derivative, Deformation Rate, Velocity Gradient
Submitted by John Craighead on Fri, 2010-07-09 20:08.
I'm trying to understand elastic deformation using the Lie derivative. I've read a good summary on Wiki but want other sources to review. Can anyone offer any sources &/or explanations. I need something fairly basic. Thanks, John.
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Re: Lie Derivative, Deformation Rate, Velocity Gradient
You may want to have a look at "Computational Inelasticity" by Simo and Hughes.
Regards,
Arash
Lie Derivative, Deformation Rate, Velocity Gradient
Arash,
Thanks, I tried Simo & Hughes but found a bit too advanced for me. Have you seen Nonlinear Solid Mechanics by Holzapfel ? Only short section on Lie derivative & deformation but found helpful. Thanks again, John.
Elasto-Plasticity Theory (by Lubarda)
may be the chapter on kinematics in the book "Elastoplasticity Theory" (by V Lubarda) can help you.
Mubeen, Thanks very
Mubeen,
Thanks very much, I'll try Lubarda. Have you seen Nonlinear Solid Mechanics by Holzapfel ? Only short
section on Lie derivative & deformation but found helpful. Thanks
again, John.
Hello John, I have
Hello John,
I have recently seen your blog, and I would like to respond.
I think Lie derivative is not an easy topic at all, so I think there is no simple explanation (or the simple explanation is not exhaustive).
My suggestion would be to look at Frankel: The Geometry of Physics, for the mathematical background, and then Marsden-Hughes: Mathematical Foundations of Elasticity for the role of Lie derivative in elasticity.
I know that they are a bit advanced, but the insight thees books give is worth it.
Andras
Your Suggested Books
Andras,
Thanks very much for suggesting the books & also kind words about Lie derivative being challenging. I have been using Marsden/Hughes &, with some time, have begun to understand (some of) it. I'll try Frankel.
In the meantime, I have found some lecture notes from Prof. Pandolfi at Milano Tech. which have been a good starting point. Also, some papers on geometric kinematics by Marsden, Hughes et al. If any of this of interest, I'm pleased to share.
Thanks, John.
Lie Derivative, elastic deformation
John take a look at these links:
1) 3 papers related to elasticity and Lie derivative
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VJS-482GP1M-5T&_user=83473&_coverDate=12%2F31%2F1993&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1434903127&_rerunOrigin=google&_acct=C000059671&_version=1&_urlVersion=0&_userid=83473&md5=58122dfcbccfddeeea776d9909e5fb5c
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6X42-4FPHTWY-14&_user=83473&_coverDate=12%2F31%2F1956&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1434903287&_rerunOrigin=google&_acct=C000059671&_version=1&_urlVersion=0&_userid=83473&md5=5d7720d6fee667d3af573440a64754a9
http://onlinelibrary.wiley.com/doi/10.1002/nme.1620290304/pdf
b) 3 books:
http://www.emis.de/monographs/KSM/kmsbookh.pdf
http://openlibrary.org/books/OL3427193M/Gauge_theory_and_variational_principles
http://www.scribd.com/doc/18077688/Foundations-of-Mechanics
I hope I helped you.
Best regards,
George Papazafeiropoulos
________________________
Second Lieutenant, Hellenic Air Force
Civil Engineer (M.Sc), Ph.D. Candidate
Papers requested
Dear John,
Unfortunately I don't remember the details of the paper you want. When I have time I will re-search for it in scholar.google. Wait a little because I have a lot of work to do these days ok?
Best regards,
George Papazafeiropoulos
________________________
Second Lieutenant, Hellenic Air Force
Civil Engineer (M.Sc), Ph.D. Candidate
Paper
George,
No problem, just let me know when convenient. Thanks again, John.