Analyzing aging under oscillatory strain field through the soft glassy rheology model.

In this work, we solve the Soft Glassy Rheology (SGR) model under application of oscillatory deformation field with varying magnitudes of strain as well as frequency for different noise temperatures. In the glassy domain, the SGR model undergoes time evolution of elastic modulus. Increase in strain magnitude beyond the linear regime is observed to enhance the rate of aging as manifested by a faster evolution of elastic modulus with increase in strain amplitude due to overaging. However at higher strain magnitudes, the rejuvenation effect starts dominating over the aging, thereby reducing the rate at which elastic modulus evolves. We also plot the aging phase diagram describing an occurrence of the linear, the overaging, and the rejuvenation regimes as a function of strain and frequency for different noise temperatures. The aging phase diagram suggests that while the linear regime remains unaffected by the changes in frequency and noise temperature, the width of the overaging regime increases with increase in frequency and noise temperature. We also study the time evolution of the shapes of relaxation time spectra as a function of strain amplitude, which renders further insight into the overaging and the rejuvenation behavior. While the phenomenon of overaging is observed to be an inherent character of the SGR model, experimentally not all the materials demonstrate overaging. Such a discrepancy suggests that the energy well depths before and after a yielding event may not be completely uncorrelated as assumed in the SGR formalism.