Is the Maxwell stress tensor a physically objective Cauchy stress?
The Maxwell stress tensor (MST) TM 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 fM=def.∇⋅TM, where fM(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 TM is not uniquely defined via the preceding relationship from knowledge of fM, we point out in this paper that the interpretation of TM 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.
