PMID: 11909293Mar 23, 2002Paper

Body versus surface forces in continuum mechanics: is the Maxwell stress tensor a physically objective Cauchy stress?

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
C Rinaldi, Howard Brenner

Abstract

The Maxwell stress tensor (MST) T(M) plays an important role in the dynamics of continua interacting with external fields, as in the commercially and scientifically important case of "ferrofluids." As a conceptual entity in quasistatic systems, the MST derives from the definition f(M)def=inverted Delta x T(M), where f(M)(x) is a physically objective volumetric external body-force density field at a point x of a continuum, derived from the solution of the pertinent governing equations. Beginning with the fact that T(M) is not uniquely defined via the preceding relationship from knowledge of f(M), we point out in this paper that the interpretation of T(M) as being a physical stress is not only conceptually incorrect, but that in commonly occuring situations this interpretation will result in incorrect predictions of the physical response of the system. In short, by elementary examples, this paper emphasizes the need to maintain the classical physical distinction between the notions of body forces f and stresses T. These examples include calculations of the torque on bodies, the work required to deform a fluid continuum, and the rate of interchange of energy between mechanical and other modes.

References

Aug 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·R Paul, K V Kaler
Aug 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Y Zimmels
Feb 15, 2001·Physical Review Letters·S Odenbach, M Liu

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Citations

Jul 21, 2004·The Journal of Chemical Physics·Ronald E Rosensweig
Apr 18, 2017·Proceedings. Mathematical, Physical, and Engineering Sciences·Hanxiong WangDong Liu
Feb 21, 2008·The European Physical Journal. E, Soft Matter·P Ilg
Feb 1, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tae Gon KangHan E H Meijer
Jul 9, 2020·Physical Review Letters·Michel Fruchart, Vincenzo Vitelli
Jan 16, 2019·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·Consuelo Bellver-Cebreros, Marcelo Rodriguez-Danta

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