Memory materials without characteristic time and their relation to the rheology of certain particle suspensions

It is shown that the lack of a characteristic time and the associated time-scale invariance serve to plac e severe restrictions on the rheology of a simple material. i.e. on the general form of the functional relating stress to deformation history.The rate-independent material proposed by Pipkin and Rivlin in 1965 as a model of plasticity in solids is found to arise as an important special case of a time-scale invariant material, and it is shown how their idea of rate-independent functionals can be used to construct rheological representations for more general materials, including fluids without charcateristic time. It is also demonstrated that such idealized fluids, which exhibit mathematically singular viscometric behavior, should provide a faithful continuum model for the rheology of rigid particle suspensions in Newtonian liquids (the generalized Einstein problem) and, as such, may provide asymptotic models for real particle susension, such as colloids, in the “flow-dominated” limit of large Deborah number.