Can the definition of mechanical stress tensor be applied to a dielectric fluid in an electrostatic or magnetostatic field?

Summary It is proved that, for an uncharged and linear dielectric fluid at rest and in local equilibrium in an electrostatic or magnetostatic field, the definition of stress tensor employed in continuum mechanics is inconsistent with the assumption that the stress tensor depends only on the local values of mass density, temperature, electric- or magnetic-field components and the derivatives of these quantities with respect to space and time.