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SIMPLE FLUIDS WITH FADING MEMORY,
MELLON INST PITTSBURGH PA
Aspects of the mathematical theory of fluid behavior developed by the authors during the last four years are summarized. A simpled fluid with a fading memory is a fluid in which a recent deformation would effect stress more than a much older deformation. The theory of a simple fluid with fading memory is explained, and various classical linear theories of fluid and viscoelastic behavior are shown to arise naturally as first-order approximations to the theory. The circumstances are described in which the classical theories can be expected to lose their physical applicability and are able to exhibit complete second-order extensions of the classical theories within the framework of the theory. The theory is general enough to cover a wide range of mechanical phenomena, yet it is specific enough to have content. The goal seeks to find that constitutive assumption which expresses, in mathematical language, the essence of certain intuitive prejudices about fluidity. Most of the nonclassical theories of fluids studied in the past may be reinterpreted to fall as special cases within the framework of the theory. Exceptions are Ericksens theory of anisotropic fluids and Truesdells theory of Maxwellian fluids.
Prepared in cooperation with Carnegie Inst. of Tech., Pittsburgh, Pa., under Grant NSF G5250. See also PB-143 029, PB-148 527, and PB-149 810.