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以表明异常，或者对于其功能至关重要，例如动脉中的应力。 由于材料特性的复杂性和通常未知的性质，测量组织中的这些应力具有挑战性。 最近，一种称为角度剪切波恒等式的的方法被提出，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。 我们扩展了这一方法及其基本恒等式，以包括粘性耗散，这在生物组织中可能非常重要。 为了推广该恒等式，我们考虑由广义牛顿粘性应力描述的软粘弹性固体，并考虑横向各向异性，这是肌肉组织等常见的特征。 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。 与弹性情况类似，当材料中的应力与横向各向异性共轴时，恒等式得以恢复。 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。 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 materials one would need to measure the wave attenuation as well as the wave speed.