  Solid polycrystalline materials undergoing diffusion creep are usually
described by Cauchy continuum models with a Newtonian viscous rheology
dependent on the grain size. Such a continuum lacks the rotational degrees of
freedom needed to describe grain rotation. Here we provide a more general
continuum description of diffusion creep that includes grain rotation, and
identifies the deformation of the material with that of a micropolar (Cosserat)
fluid. We derive expressions for the micropolar constitutive tensors by a
homogenisation of the physics describing a discrete collection of rigid grains,
demanding an equivalent dissipation between the discrete and continuum
descriptions. General constitutive laws are derived for both Coble
(grain-boundary diffusion) and Nabarro-Herring (volume diffusion) creep.
Detailed calculations are performed for a two-dimensional tiling of irregular
hexagonal grains, which illustrates a potential coupling between the rotational
and translational degrees of freedom. If only the plating out or removal of
material at grain boundaries is considered, the constitutive laws are
degenerate: modes of deformation that involve pure tangential motion at the
grain boundaries are not resisted. This degeneracy can be removed by including
the resistance to grain-boundary sliding, or by imposing additional constraints
on the deformation.
