预应力粘弹性固体的增量动力学及其在剪切波弹性成像中的应用
Incremental dynamics of prestressed viscoelastic solids and its applications in shear wave elastography
AI总结：
提出有限应变粘弹性固体的广义增量动力学理论，兼容GOH和KVFD模型，经实验与仿真验证，可准确预测色散曲线并实现无需本构参数的预应力量化，适用于高频高分辨率剪切波弹性成像。
摘要：
剪切波弹性成像（SWE）是一种极具前景的成像模态，可用于组织的力学表征，提供的生物标志物具有早期精准诊断的潜力。尽管已有多种方法从剪切波特性中提取力学参数，但它们在预应力下粘弹性材料中的关系仍知之甚少。在此，我们提出了一种适用于有限应变粘弹性固体的广义增量动力学理论。该理论推导了静态预应力下材料中的小振幅粘弹性波动。该形式体系与一系列现有的本构模型兼容，包括超弹性和粘弹性——例如本研究中使用的 Gasser-Ogden-Holzapfel (GOH) 和 Kelvin-Voigt 分数导数 (KVFD) 模型的组合。我们通过对预应力软材料和生物组织进行实验和数值模拟，利用光学相干弹性成像和超声弹性成像验证了该理论。理论预测与宽频范围内的实验色散曲线高度吻合，并准确捕捉了预应力效应。此外，该框架揭示了剪切波相速度、衰减和主应力之间的关系，能够在无需预先了解本构参数的情况下实现粘弹性固体中的预应力量化。这种广义声-粘弹性形式体系特别适用于预应力组织的高频、高分辨率 SWE。
英文摘要：
Shear wave elastography (SWE) is a promising imaging modality for mechanical characterization of tissues, offering biomarkers with potential for early and precise diagnosis. While various methods have been developed to extract mechanical parameters from shear wave characteristics, their relationships in viscoelastic materials under prestress remain poorly understood. Here, we present a generalized incremental dynamics theory for finite-strain viscoelastic solids. The theory derives small-amplitude viscoelastic wave motions in a material under static pre-stress. The formalism is compatible with a range of existing constitutive models, including both hyperelasticity and viscoelasticity--such as the combination of Gasser-Ogden-Holzapfel (GOH) and Kelvin-Voigt fractional derivative (KVFD) models used in this study. We validate the theory through experiments and numerical simulations on prestressed soft materials and biological tissues, using both optical coherence elastography and ultrasound elastography. The theoretical predictions closely match experimental dispersion curves over a broad frequency range and accurately capture the effect of prestress. Furthermore, the framework reveals the relationships among shear wave phase velocity, attenuation, and principal stresses, enabling prestress quantification in viscoelastic solids without prior knowledge of constitutive parameters. This generalized acousto-viscoelastic formalism is particularly well-suited for high-frequency, high-resolution SWE in tissues under prestress.
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