In skeletal joints two layers of adjacent cartilage are often in relative motion. The individual cartilage layers are often modelled as a poroviscoelastic material. To model the relative motion, noting the separation of scales between the pore level and the macroscale, a homogenization based on multiple scale asymptotic analysis has been used in this study to derive a macroscale model for the relative translation of two poroviscoelastic layers separated by a very thin layer of fluid. In particular the fluid layer thickness is essentially zero at the macroscale so that the two poroviscoelastic layers are effectively in contact and their interaction is captured in the derived model via a set of interfacial conditions, including a generalization of the Beavers-Joseph condition at the interface between a viscous fluid and a porous medium. In the simplifying context of a uniform geometry, constant fixed charge density, a Newtonian interstitial fluid and a viscoelastic scaffold, modelled via finite deformation theory, we present preliminary simulations that may be used to highlight predictions for how oscillatory relative movement of cartilage under load influences the peak force the cartilage experiences and the extent of the associated deformations. In addition to highlighting such cartilage mechanics, the systematic derivation of the macroscale models will enable the study of how nanoscale cartilage physics, such as the swelling pressure induced by fixed charges, manifests in cartilage mechanics at much higher lengthscales.

中文翻译：

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模拟关节软骨：两个相邻多孔粘弹性层的相对运动。

在骨骼关节中，相邻的两层软骨通常处于相对运动中。单个软骨层通常被建模为多孔粘弹性材料。为了模拟相对运动，注意孔隙水平和宏观尺度之间的尺度分离，在本研究中使用基于多尺度渐近分析的均质化来推导一个宏观尺度模型，用于两个孔隙粘弹性层的相对平移。薄薄的一层液体。特别是，流体层厚度在宏观尺度上基本上为零，因此两个多孔粘弹性层有效地接触，并且它们的相互作用通过一组界面条件在派生模型中捕获，包括界面处 Beavers-Joseph 条件的推广介于粘性流体和多孔介质之间。在通过有限变形理论建模的均匀几何形状、恒定固定电荷密度、牛顿间质流体和粘弹性支架的简化背景下，我们提出了初步模拟，可用于突出预测软骨在负载下的振荡相对运动如何影响软骨经历的峰值力和相关变形的程度。除了强调这种软骨力学之外，宏观模型的系统推导将有助于研究纳米级软骨物理，例如由固定电荷引起的膨胀压力，如何在更高长度尺度上表现出软骨力学。通过有限变形理论建模，我们提出了初步模拟，可用于突出预测软骨在负载下的振荡相对运动如何影响软骨经历的峰值力和相关变形的程度。除了强调这种软骨力学之外，宏观模型的系统推导将有助于研究纳米级软骨物理，例如由固定电荷引起的膨胀压力，如何在更高长度尺度上表现出软骨力学。通过有限变形理论建模，我们提出了初步模拟，可用于突出预测软骨在负载下的振荡相对运动如何影响软骨经历的峰值力和相关变形的程度。除了强调这种软骨力学之外，宏观模型的系统推导将有助于研究纳米级软骨物理，例如由固定电荷引起的膨胀压力，如何在更高长度尺度上表现出软骨力学。