Body versus surface forces in continuum mechanics: is the Maxwell stress tensor a physically objective Cauchy stress?
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.
Rinaldi
Carlos
C
Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
Brenner
Howard
H