The Non-Linear Field Theories of Mechanics

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.