具有热力相容性的广义Jeffreys模型

A Generalized Jeffreys Model with Thermodynamic Compatibility

摘要: 分数阶流变本构方程因其在刻画复杂黏弹性流体行为方面的优势而受到广泛关注。然而，现有相关研究多侧重于本构关系的数学推广，对模型所对应的力学结构及其热力学相容性缺乏系统分析，物理合理性有待进一步解释。基于经典Jeffreys模型，本文从力学结构的角度出发，构建了一种修正的五参数Jeffreys本构方程。进一步对该模型的热力学相容性进行了系统研究，给出了满足热力学第二定律的充分条件，验证了模型的物理合理性。这项研究为黏弹性本构方程的构建提供了有价值的理论参考。

Abstract: Fractional rheological constitutive equations have attracted considerable attention due to their ability to describe complex viscoelastic fluid behaviors. However, most existing studies primarily focus on the mathematical generalization of constitutive relations, while the corresponding mechanical analogues and thermodynamic compatibility have not been systematically examined, leaving the physical rationality of such models insufficiently clarified. Based on the classical Jeffreys model, a modified five-parameter Jeffreys constitutive equation is constructed from the perspective of mechanical modelling. Furthermore, the thermodynamic compatibility of the proposed model is systematically investigated, and sufficient conditions ensuring compliance with the second law of thermodynamics are established, thereby verifying its physical admissibility. This study provides valuable theoretical insight into the construction of viscoelastic constitutive models.