Distribution of Time Scales Induces Slow Dynamics and Elastic Hysteresis in Sandstones: A Model of Non-equilibrium Strain

Elasticity in consolidated granular materials exhibits non-classical nonlinearity and slow dynamics. These effects are typically analyzed through separate experimental methods and theoretical models. Our research aims to unify these descriptions by introducing a model based on non-equilibrium strain, incorporating a wide range of relaxation times to account for both fast nonlinear effects and slow conditioning and relaxation of elastic properties. Utilizing observations from dynamic acoustoelastic testing of sandstone, we propose a time-delay model that accurately reflects the observed experimental behaviors, including log-time relaxation and hysteresis. Our findings indicate that the slow and fast dynamics in sandstone are intrinsically coupled, and the model provides a comprehensive framework for understanding these complex interactions. This model, which is validated by fitting experimental data including conditioning loops and relaxation curves, offers a tool for predicting the elastic behavior under various loading conditions.