The Non-Linear Field Theories of Mechanics

1. Front Matter

   Pages I-X

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2. The Non-Linear Field Theories of Mechanics

   • C. Truesdell, W. Noll

   Pages 1-579

3. Back Matter

   Pages 580-591

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This volume is a second, corrected edition of The Non-Linear Field Theories of Mechanics, which first appeared as Volume IIII3 of the Encyclopaedia of Physics, 1965. Its principal aims were to replace the conceptural, terminological, and notational chaos that existed in the literature of the field by at least a modicum of order and coherence, and second, to describe, or at least to summarize, everything that was both known and worth knowing in the field at the time. Inspecting the literature that has appeared since then, we conclude that the first aim was achieved to some degree. Many of the concepts, terms, and notations we introduced have become more or less standard, and thus communication among researchers in the field has been eased. On the other hand, some ill-chosen terms are still current. Examples are the use of "configuration" and "deformation" for what we should have called, and now call, "placement" and "transplacement", respectively. (To classify translations and rotations as deformations clashes too severely with the dictionary meaning of the latter.) We believe that the second aim was largely achieved also. We have found little published before 1965 that should have been included in the treatise but was not. However, a large amount of relevant literature has appeared since 1965, some of it important. As a result, were the treatise to be written today, it should be very different.

• Fluide, elastische und hyperelastische Materialien
• chaos
• coherence
• deformation
• fluidity, elastic materials, hyperelastic materials
• mechanics
• physics
• translation

From the reviews of the third edition:

"As there is hardly anyone in the continuum mechanics community who does not know, use and appreciate Truesdell and Noll’s ‘Nonlinear field theories of mechanics’, there is surely no need to review this masterpiece again … . What is interesting to note is that Springer Verlag released a third edition … ." (Albrecht Bertram, Zentralblatt MATH, Vol. 1068, 2005)

"The Springer-Verlag now published the third edition of the historical Volume III/3 of the Encyclopedia of Physics … . This text gives interesting insights into the genesis of their work. … It is interesting to note that their system of notation, symbols, and terminology has been widely adopted, even by scientific descendants of critics of their enterprise. … No doubt, these arguments justify the reprint of the The Non-Linear Field Theories of Mechanics." (Technische Mechanik, Vol. 25 (3-4), 2005)

• Baltimore, USA

  Clifford Truesdell

• Carnegie-Mellon University, Pittsburgh, USA

  Walter Noll

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