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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月13日

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  • Radovan Zeman,
  • Jan Kober,
  • Marco Scalerandi

摘要

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.