Abstract Originating in the field of biomechanics, Fung’s model of quasi-linear viscoelasticity (QLV) is one of the most popular constitutive theories employed to compute the time-dependent relationship between stress and deformation in soft solids. It is one of the simplest models of nonlinear viscoelasticity, based on a time-domain integral formulation. In the present study, we consider the QLV model incorporating a single scalar relaxation function. We provide natural internal variables of state, as well as a consistent expression of the free energy to illustrate the thermodynamic consistency of this version of the QLV model. The thermodynamic formulation highlights striking similarities between QLV and the internal-variable models introduced by Holzapfel and Simo. Finally, the dissipative features of compressible QLV materials are illustrated in simple tension.

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关于软固体拟线性粘弹性模型的热力学一致性

摘要 Fung 的准线性粘弹性 (QLV) 模型起源于生物力学领域，是最流行的本构理论之一，用于计算软固体中应力与变形之间的时间依赖关系。它是基于时域积分公式的最简单的非线性粘弹性模型之一。在本研究中，我们考虑包含单个标量松弛函数的 QLV 模型。我们提供了状态的自然内部变量，以及自由能的一致表达式，以说明此版本 QLV 模型的热力学一致性。热力学公式突出了 QLV 与 Holzapfel 和 Simo 引入的内部变量模型之间的惊人相似之处。最后，