Aging and rheology in soft materials

We study theoretically the role of aging in the rheology of soft materials. We define several generalized rheological response functions suited to agi ng samples tin which time translation se invariance is lost). These are the n used to study aging effects within a simple scalar model (the "soft glass y theology" or SGR model) whose constitutive equations relate shear stress to shear strain among a set of elastic elements, with distributed yield thr esholds, undergoing activated dynamics governed by a "noise temperature," x . (Between yields, each element follows affinely the applied shear.) For 1 < x < 2 there is a power-law fluid regime in which transients occur, but no aging. For x < 1, the model has a macroscopic yield stress. So long as thi s yield stress is not exceeded, aging occurs, with a sample's apparent rela xation time being of order its own age. The (age-dependent) linear viscoela stic loss modulus G "(w,t) rises as frequency is lowered, but falls with ag e t, so as to always remain less than G'(w,t) (which is nearly constant). S ignificant aging is also predicted for the stress overshoot in nonlinear sh ear startup and for the creep compliance. Though obviously oversimplified, the SGR model may provide a valuable paradigm for the experimental and theo retical study of rheological aging phenomena in soft solids. (C) 2000 The S ociety of Rheology. [S0148-6055(00)00102-4].