On the Origin of Delayed Elasticity in Inorganic Glasses

Delayed elasticity is a universal feature of glasses, manifesting as a recoverable deformation accompanying viscous flow across the glass-transition domain. While heuristic models have been proposed to explain its origin, the underlying mechanisms remain poorly understood. Here, the origin of delayed elasticity is investigated using a mesoscopic shear transformation (ST) model within the linear viscoelastic regime. Glasses undergo continuous, thermally activated STs that generate long-range stress fields, leading to a randomly fluctuating internal stress. In the linear viscoelastic regime, applied macroscopic stresses are much smaller than the characteristic stress fluctuations induced by interactions between shear transformation zones (STZs). The model reveals that delayed elasticity emerges from the collective behavior of STZs rather than from their individual mechanical history which cannot be preserved under such fluctuating internal stresses. When STZs have no intrinsic distribution of energy barriers, localization into shear bands mays occur, leading to faster plastic strain accumulation in certain regions and the generation of a certain counteracting "back stress." However, more realistically, when an intrinsic distribution of energy barriers exists, localization is suppressed, and delayed elasticity arises instead from the cooperative dynamics of STZs. The back stress, which drives delayed elasticity recovery, originates from these collective interactions, through long-range stress fields, rather than from individual mechanical history/memory. Thus, the memory behind delayed elasticity, often considered local, is fundamentally collective.