A micropolar continuum model of diffusion creep

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