Hidden jerk in universal creep and aftershocks

Abstract

Most materials exhibit creep-memory under the action of a constant load. The memory behavior is governed by Andrade's power-law of creep. The creep law has an inherent connection with the Omori-Utsu law that describes the frequency of earthquake aftershocks. Both the laws are empirical and they lack a deterministic interpretation. Interestingly, the creep response of a fractional dashpot in anomalous viscoelastic modeling is given by Andrade's law. Consequently, fractional derivatives are invoked but they are plagued by curve-fits. Here we establish an analogous physical mechanism that underlies both the laws. In this Letter, we relate the parameters of the two laws with the macroscopic properties of the material. Surprisingly, the derivation necessitates the existence of a rheological property that relates strain with the first-order time-derivative of stress. The obtained results are validated in light of the established observations.Comment: 12 pages, 1 figur