Rheological Origin of Aging

Abstract: Most materials of practical applications age, and their properties change with time. The aging of materials is reflected in their mechanical responses to external stress and strain, which exhibit ubiquity in the form of logarithms and power laws, respectively. Such responses are usually described using complicated phenomenological models, including fractional viscoelastic models, but they lack physical insights. In this Letter, we postulate a linear time-varying rheological property whose constitutive relations are motivated from thermodynamic principles and experimental observations of the stick-slip-induced friction. The property satisfyingly explains the logarithmic relaxation and the three stages of universal creep behavior. Consequently, the fractional Maxwell model and the Mittag-Leffler function gain physical interpretation. Lastly, we show that viscosity emerges as a special case of the proposed property.