Stiff resistant inclusions in a deforming rock generate local stress concentrations and stress gradients. The resulting diffusive mass transfer is partly along grain interfaces and partly through grain interiors. For the latter effect, two different sets of fundamental ideas are in use. In either version, the effect of diffusion is to enhance strain rates and to moderate stress concentrations. In the first version, local diffusive loss is isotropic and can change an infinitesimal spherical element only to a smaller sphere whereas in the second, local diffusive loss can be anisotropic and can change a sphere to an ellipsoid.

The problem used as illustration is that of a highly viscous embedded cylinder in pure shear. Each version yields predictions of diminished stress concentrations and enhanced strain rates, and invites further development. The second version is favored; by extension, a material component’s chemical potential at a point is seen as being like the normal stress at a point, i.e. multivalued, every planar element through the point having its own associated value.