标题： 软粘性固体中角度剪切波恒等式的普遍性 显示英文标题

标题： Universality of the angled shear wave identity in soft viscous solids

摘要： 生物组织内的机械应力可能表明异常，或者对于其功能至关重要，例如动脉中的应力。由于材料性质的复杂性和通常未知的特性，测量组织中的应力具有挑战性。最近，提出了一种称为角度剪切波恒等式的的方法，通过测量两个小振幅剪切波的速度来预测应力。该方法不需要材料本构定律的先验知识，使其非常适合复杂的生物组织。我们扩展了这种方法及其基本恒等式，以包括粘性耗散，这对于生物组织可能非常重要。为了推广这个恒等式，我们考虑由广义牛顿粘性应力描述的软粘弹性固体，并考虑横观各向同性，这是肌肉组织等常见的特性。然后，我们推导出在大静态变形上叠加的小振幅剪切波的色散关系。类似于弹性情况，当材料中的应力与横观各向同性共轴时，可以恢复该恒等式。本文的一个关键结果是，为了预测粘性材料中的应力，需要测量波的衰减以及波速。还讨论了具有记忆的粘弹性材料的情况。 显示英文摘要

摘要： Mechanical stress within biological tissue can indicate an anomaly, or can be vital of its function, such as stresses in arteries. Measuring these stresses in tissue is challenging due to the complex, and often unknown, nature of the material properties. Recently, a method called the angled shear wave identity was proposed to predict the stress by measuring the speed of two small amplitude shear waves. The method does not require prior knowledge of the material's constitutive law, making it ideal for complex biological tissues. We extend this method, and the underlying identity, to include viscous dissipation, which can be significant for biological tissues. To generalise the identity, we consider soft viscoelastic solids described by a generalised Newtonian viscous stress, and account for transverse isotropy, a feature that is common in muscle tissue, for instance. We then derive the dispersion relationship for small-amplitude shear waves superimposed on a large static deformation. Similarly to the elastic case, the identity is recovered when the stress in the material is coaxial with the transverse anisotropy. A key result in this paper is that to predict the stress in a viscous material one would need to measure the wave attenuation as well as the wave speed. The case of viscoelastic materials with memory is also discussed.