Fluid-particle systems with internal forces arising only from viscosity or intergranular friction represent an important special case of "purely dissipative" materials described by a 4th-rank viscosity tensor η depending on deformation history. In a recently proposed simplification [1], η is given by a tensor polynomial in a symmetric 2nd-rank structure or "fabric" tensor A, whose evolution is determined by the history of deformation. Expressing the latter as a corotational integral, with memory function involving two exponential relaxation modes, one obtains a good fit to existing data on viscosity and normal stress in steady shear reversal experiments on concentrated suspensions. A recent extension [2] gives predictions for shear and normal stress in sinsuoidal simple shear. In contrast to existing phenomenological models, the present approach provides a clear-cut distinction between instantaneous Stokesian response and non-linear effects arising from Stokesian-dynamical evolution of microstructure or from non-Stokesian friction at particle contacts. The latter serves as an essential link between the viscosity idealized suspensions ("Stokesium") and the plasticity of dry granular media ("Mohr-Coulombium"). A discussion is given of a recent extension [2] of the above model to non-homogeneous suspensions, with particle flux induced by gradients in particle concentration, deformation rate, and fabric. Also, some connections are made to elastoplastic models with evolutionary microstructure. [1] J. D. Goddard. J. Fluid Mech., 568,1–17, 2006. [2] J. D. Goddard. Phys. Fluids, 20, 040601,1-15. 2008.