Mechanical and Aerospace Engineering Department, North Carolina State University, R3158 Engineering Building 3, Campus Box 7910, 911 Oval Drive, Raleigh, NC 27695, United States.
Mechanical and Aerospace Engineering Department, North Carolina State University, R3158 Engineering Building 3, Campus Box 7910, 911 Oval Drive, Raleigh, NC 27695, United States.
Math Biosci. 2019 Feb;308:1-7. doi: 10.1016/j.mbs.2018.12.007. Epub 2018 Dec 8.
Tendon-to-bone insertion tissues may be considered as functionally-graded connective tissues, providing a gradual transition from soft tendon to hard bone tissue, and functioning to alleviate stress concentrations at the junction of these tissues. The tendon-to-bone insertion tissues demonstrate pronounced viscoelastic behavior, like many other biological tissues, and are designed by the nature to alleviate stress at physiological load rates and strains states. In this paper we present experimental data showing that under biaxial tension tendon-to-bone insertion demonstrates rate-dependent behavior and that stress-strain curves for the in-plane components of stress and strain become less steep when strain rate is increased, contrary to a typical viscoelastic behavior, where the opposite trend is observed. Such behavior may indicate the existence of a protective viscoelastic mechanism reducing stress and strain during a sudden increase in mechanical loading, known to exist in some biological tissues. The main purpose of the paper is to show that such viscoelastic stress reduction indeed possible and is thermodynamically consistent. We, therefore, propose an anisotropic viscoelasticity model for finite strain. We identify the range of parameters for this model which yield negative viscoelastic contribution into in-plane stress under biaxial state of strain and simultaneously satisfy requirements of thermodynamics. We also find optimal parameters maximizing the observed protective viscoelastic effect for this particular state of strain. This model will be useful for testing and describing viscoelastic materials and for developing interfaces for dissimilar materials, considering rate effect and multiaxial loadings.
肌腱-骨插入组织可被视为功能梯度连接组织，提供从软肌腱到硬骨组织的逐渐过渡，并起到减轻这些组织交界处的应力集中的作用。肌腱-骨插入组织表现出明显的粘弹性行为，与许多其他生物组织一样，其设计目的是在生理负荷率和应变状态下减轻应力。在本文中，我们提出了实验数据，表明在双轴拉伸下，肌腱-骨插入表现出与速率相关的行为，并且当应变率增加时，平面内应力和应变的应力-应变曲线变得不那么陡峭，与典型的粘弹性行为相反，在典型的粘弹性行为中观察到相反的趋势。这种行为可能表明存在一种保护性粘弹性机制，可以在机械加载突然增加时降低应力和应变，这种机制存在于一些生物组织中。本文的主要目的是表明这种粘弹性的应力降低确实是可能的，并且在热力学上是一致的。因此，我们提出了一种用于有限应变的各向异性粘弹性模型。我们确定了该模型的参数范围，该参数范围在双轴应变状态下产生负粘弹性对平面内应力的贡献，同时满足热力学要求。我们还找到了使特定应变状态下观察到的保护性粘弹性效应最大化的最佳参数。该模型将有助于测试和描述粘弹性材料，并为不同材料的界面开发考虑速率效应和多轴加载。
