Consequences of Linear Time-Variant Rheology for Aging, Relaxation, and Creep

TL;DR

This paper introduces jerk-elasticity, a linear time-variant rheological model based on thermodynamics, which explains aging, relaxation, and creep phenomena without complex nonlinearities, unifying various rheological behaviors.

Contribution

The paper presents a novel linear rheological model, jerk-elasticity, that links material aging and creep behaviors to thermodynamic principles, providing a unified and physically interpretable framework.

Findings

Reproduces logarithmic stress relaxation and power-law creep

Links rheological parameters to thermodynamic variables

Unifies fractional and viscous rheological responses

Abstract

Most materials age, and their properties change over time. The aging of materials is reflected in their mechanical responses to external stress and strain, which exhibit logarithmic relaxation and universal power-law creep. Those responses are typically described using complex phenomenological models, including fractional viscoelastic models. While successful at reproducing experimental trends, such approaches often obscure the underlying rheological mechanism and its connection to material parameters. Their physical interpretation remains debated. We introduce jerk-elasticity, a linear time-variant model whose constitutive relations are motivated by thermodynamic principles and experimental observations of the stick-slip-induced friction. The model reproduces the Guiu-Pratt law of logarithmic stress relaxation, Andrade's power-law creep, and a unified description of the three stages of creep, without invoking distributed relaxation times or nonlinear constitutive laws. The rheological parameters of jerk-elasticity are linked with the thermodynamic variables and activation volume. The evolution of activation volume emerges as a physically interpretable measure of aging. Interestingly, viscous and fractional Maxwell responses appear as limiting cases of the jerk-elastic response, thereby offering a unified constitutive interpretation of fractional rheology. Besides, the Mittag-Leffler function gains physical interpretation. The findings are validated by established experimental observations.