  The following note shows that the symmetry of various resistance formulae,
often based on Lorentz reciprocity for linearly viscous fluids, applies to a
wide class of non-linear viscoplastic fluids. This follows from Edelen's
non-linear generalization of the Onsager relation for the special case of
\emph{strongly dissipative} rheology, where constitutive equations are
derivable from his dissipation potential. For flow domains with strong
dissipation in the interior and on a portion of the boundary this implies
strong dissipation on the remaining portion of the boundary, with strongly
dissipative traction-velocity response given by a dissipation potential. This
leads to a non-linear generalization of Stokes resistance formulae for a wide
class of viscoplastic fluid problems. We consider the application to non-linear
Darcy flow and to the effective slip for viscoplastic flow over textured
surfaces.
