Hidden jerk in universal creep and aftershocks

TL;DR

This paper reveals a physical mechanism involving jerk that explains creep memory and aftershock laws, providing a deterministic interpretation and linking parameters to material properties without relying on viscosity.

Contribution

It introduces a linear physical model based on jerk to interpret Andrade's creep law and Omori-Utsu law, connecting them to material properties and eliminating the need for fractional derivatives.

Findings

Established a physical mechanism involving jerk for creep and aftershocks.

Linked model parameters to macroscopic material properties.

Validated the model against experimental observations.

Abstract

Most materials exhibit creep memory under the action of a constant load. The memory behavior is governed by Andrade's creep law, which also has an inherent connection with the Omori-Utsu law of earthquake aftershocks. Both empirical laws lack a deterministic interpretation. Coincidentally, the Andrade law is similar to the time-varying part of the creep compliance of the fractional dashpot in anomalous viscoelastic modeling. Consequently, fractional derivatives are invoked, but since they lack a physical interpretation, the physical parameters of the two laws extracted from curve fit lack confidence. In this Letter, we establish an analogous linear physical mechanism that underlies both laws and relates its parameters with the material's macroscopic properties. Surprisingly, the explanation does not require the property of viscosity. Instead, it necessitates the existence of a rheological property that relates strain with the first order time derivative of stress, which involves jerk. Further, we justify the constant quality factor model of acoustic attenuation in complex media. The obtained results are validated in light of the established observations.