Recoverable strain in amorphous materials: The role of ongoing plastic events following initial elastic recoil

Recoverable strain is the strain recovered once a stress is removed from a body, in the direction opposite to that in which the stress had acted. To date, the phenomenon has been understood as being elastic in origin: polymer chains stretched in the direction of an imposed stress will recoil after the stress is removed, for example. Any unrecoverable strain is instead attributed to irreversible plastic deformations. Here we study theoretically strain recovery within the soft glassy rheology (SGR) model, aimed at describing the rheology of elastoplastic yield stress fluids and amorphous soft solids. We consider a material subject to the switch-on of a shear stress that is held constant before later being set back to zero, after which the strain recovery is observed. After an initially fast recoil that is indeed elastic in nature, significant further strain recovery then occurs more slowly via the plastic yielding of elements with negative local stresses, opposite to that of the original shear. We elucidate the mechanism that underlies this behavior, in terms of the evolution of the SGR model’s population of elastoplastic elements. In particular, we show that the initial fast elastic recoil brings to a state of negative local stress those elements that had yielded during the forward straining while the load was applied. The subsequent delayed plastic yielding of these elements with negative stress is the origin of the slow ongoing strain recovery. In this way, counterintuitively, elements that had yielded plastically while the load was applied still contribute significantly to strain recovery after the sample is unloaded. This finding has important consequences for constitutive modeling, because such behavior can only arise in a constitutive model that evolves a full distribution of local stresses (or multiple moments of such a distribution), rather than a single average stress. Unexpectedly, although in rare parameter regimes, this slow ongoing strain recovery post switch-off does not always in fact recover in the negative direction, counter to that of the previously imposed stress, but can sometimes continue to accumulate in the forward direction. The recovery is then non-monotonic overall, reminiscent of observations of non-monotonic stress relaxation after straining.