粘弹性层动态球形压痕厚度效应的解释：在关节软骨无损检测中的应用
Accounting for the thickness effect in dynamic spherical indentation of a viscoelastic layer: Application to non-destructive testing of articular cartilage
摘要：
近年来，动态压痕试验在生物组织（如关节软骨）的力学性能鉴定和生存能力评估方面都取得了很好的效果。我们考虑无摩擦的平端和球形正弦驱动压痕试验，利用位移控制加载协议。关节软骨组织被建模为粘弹性材料与时间无关的泊松比。我们研究的动态压痕刚度的目的是制定标准的关节软骨的质量评价，以便能够区分其退化状态。特别是，评估动态压痕刚度在平端压痕试验的转折点，我们引入了所谓的不完全储能模量。考虑到动态刚度消失（接触力达到最大值）和动态刚度变为无穷大（压头位移达到最大值）的时刻之间的时间差，我们引入了所谓的不完全损失角。在球面正弦驱动压痕试验中可以引入类似的量，但是，为了考虑厚度效应，需要一种特殊的方法。我们采用渐近建模方法分析和解释的动态球形压痕试验的压头的几何参数和材料的粘弹性特性的结果。非破坏性压痕诊断软骨退变的一些影响进行了讨论。
英文摘要：
In recent years, dynamic indentation tests have been shown to be useful both in identification of mechanical properties of biological tissues (such as articular cartilage) and assessing their viability. We consider frictionless flat-ended and spherical sinusoidally-driven indentation tests utilizing displacement-controlled loading protocol. Articular cartilage tissue is modeled as a viscoelastic material with a time-independent Poisson's ratio. We study the dynamic indentation stiffness with the aim of formulating criteria for evaluation the quality of articular cartilage in order to be able to discriminate its degenerative state. In particular, evaluating the dynamic indentation stiffness at the turning point of the flat-ended indentation test, we introduce the so-called incomplete storage modulus. Considering the time difference between the time moments when the dynamic stiffness vanishes (contact force reaches its maximum) and the dynamic stiffness becomes infinite (indenter displacement reaches its maximum), we introduce the so-called incomplete loss angle. Analogous quantities can be introduced in the spherical sinusoidally-driven indentation test, however, to account for the thickness effect, a special approach is required. We apply an asymptotic modeling approach for analyzing and interpreting the results of the dynamic spherical indentation test in terms of the geometrical parameter of the indenter and viscoelastic characteristics of the material. Some implications to non-destructive indentation diagnostics of cartilage degeneration are discussed.
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