This paper presents a continuum-based transverse isotropic model incorporating rate-dependency and fibre dispersion, applied to the planar biaxial deformation of aortic valve (AV) specimens under various stretch rates. The rate dependency of the mechanical behaviour of the AV tissue under biaxial deformation, the (pseudo-) invariants of the right Cauchy-Green deformation-rate tensor $\dot{\mathbf{C}}$ associated with fibre dispersion, and a new fibre orientation density function motivated by fibre kinematics are presented for the first time. It is shown that the model captures the experimentally observed deformation of the specimens, and characterises a shear-thinning behaviour associated with the dissipative (viscous) kinematics of the matrix and the fibres. The application of the model for predicting the deformation behaviour of the AV under physiological rates is illustrated and an example of the predicted $\sigma -\lambda$ curves is presented. While the development of the model was principally motivated by the AV biomechanics requisites, the comprehensive theoretical approach employed in the study renders the model suitable for application to other fibrous soft tissues that possess similar rate-dependent and structural attributes.

本文提出了一种基于连续统一的横向各向同性模型，该模型结合了速率依赖性和纤维分散性，适用于在不同拉伸速率下主动脉瓣（AV）标本的平面双轴变形。双轴变形下房室组织力学行为的速率相关性，右柯西-格林变形率张量的（伪）不变量$\dot{\mathbf{C}}$与纤维色散相关联，并首次提出了由纤维运动学驱动的新的纤维取向密度函数。结果表明，该模型捕获了实验观察到的样品变形，并表征了与基质和纤维的耗散（粘稠）运动学相关的剪切稀化行为。举例说明了该模型在生理速率下预测房室的变形行为的应用，并给出了一个预测的例子$\sigma -\lambda$曲线被呈现。虽然模型的开发主要是由AV生物力学的要求推动的，但研究中采用的综合理论方法使该模型适用于其他具有类似速率依赖性和结构属性的纤维性软组织。