Phenomenology of Rubber-Like Materials
These lectures are devoted to an overview of the basic balance laws and constitutive requirements of continuum mechanics. Some solutions of simple boundary value problems are considered and a critical review of strain-energy density functions is proposed.
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1 Introduction These notes are about the possible application of the theory of finite elasticity to the understanding of the mechanics of rubber-like materials. There is a large literature on nonlinear elasticity and for this reason I begin with some bibliographic notices. This is also an opportunity to declare my sources of main inspiration. First of all I have to mention the book by R. W. Ogden Non-linear elastic deformations (first published in 1984 by Ellis Horwood Ltd, Chichester and then reprinted in 1997 by Dover Publications Inc., Mineola). This is a complete and meticolous account of the theory of finite and nonlinear elasticity. Another interesting textbook is the basic treatise by R. J Atkin and N. Fox: An Introduction to theory of Elasticity (1980, Longman, London). A short but very interesting text is also the introductory survey by M. F. Beatty: Introduction to Nonlinear Elasticity (first published as Topics in Finite Elasticity in Applied Mechanics Review, 40, 1987, pp 1699-1734 and then updated and reprinted in Nonlinear Effects in Fluids and Solids, edited by M. M. Carroll and M. Hayes (1986) Plenum Press, New York). This is an excellent survey of some selected topics in finite elasticity with an updated list of references. For mathematically oriented readers, in my opinion, it is not possible to skip the monograph by J. E. Marsden and T. R. J. Hughes, Mathematical Foundations of Elasticity (first published in 1983 by Prentice-Hall, Englewood Cliffs and then reprinted in 1994 by Dover, Mineola) and the monograph by S.S. Antman, Problems of Nonlinear Elasticity (1995, Springer, New-York) where also theories of elastic structures are considered. Finally, all these books have been updated in very recent years by two collections of original papers: Nonlinear Elasticity: Theory *These lecture notes are dedicated to the memory of Professor Pietro Benvenuti (1933-2002). I would never have been able to learn the little mechanics I know without the wonderful advice and the fatherly help of Pietro Benvenuti. G. Saccomandi et al. (eds.), Mechanics and Thermomechanics of Rubberlike Solids © Springer-Verlag Wien 2004
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and Applications, edited by Y. B. Fu and R. W. Ogden, LMS Lectures Note Series 283 (2001) Cambridge University Press and Topics in Finite Elasticity, edited by M. Hayes and G. Saccomandi, CISM Lectures Note Series 429 (2001) Springer, Berlin. Obviously this is only a partial list dictated by personal taste and for any aspect of continuum mechanics not covered by these books my standard references are C. Truesdell and C.A. Toupin, The Classical Fields Theories (in S. Flugge, ed., Encyclopedia of Physics, Volume III/1, Springer-Verlag Berlin, 226-793, 1960) and C. Truesdell and W. Noll, The Non-Linear Field Theories of Mechanics, 2nd edn., Springer-Verlag, 1992. I am indebted for valuable suggestions and comments to Mike Hayes, Robin Knops, Edvige Pucci, Ray Ogden and Kumbakonam Rajagopal, moreover I must particularly thank Cornelius Horgan my dear friend and collaborator because
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