Li L P, Buschmann M D, Shirazi-Adl A
Institute of Biomedical Engineering, Departments of Chemical Engineering and Mechanical Engineering, Ecole Polytechnique of Montreal, PO Box 6079, Station Centre-ville, Que., H3C 3A7, Montreal, Canada.
J Biomech. 2000 Dec;33(12):1533-41. doi: 10.1016/s0021-9290(00)00153-6.
The depth dependence of material properties of articular cartilage, known as the zonal differences, is incorporated into a nonlinear fibril-reinforced poroelastic model developed previously in order to explore the significance of material heterogeneity in the mechanical behavior of cartilage. The material variations proposed are based on extensive observations. The collagen fibrils are modeled as a distinct constituent which reinforces the other two constituents representing proteoglycans and water. The Young's modulus and Poisson's ratio of the drained nonfibrillar matrix are so determined that the aggregate compressive modulus for confined geometry fits the experimental data. Three nonlinear factors are considered, i.e. the effect of finite deformation, the dependence of permeability on dilatation and the fibril stiffening with its tensile strain. Solutions are extracted using a finite element procedure to simulate unconfined compression tests. The features of the model are then demonstrated with an emphasis on the results obtainable only with a nonhomogeneous model, showing reasonable agreement with experiments. The model suggests mechanical behaviors significantly different from those revealed by homogeneous models: not only the depth variations of the strains which are expected by qualitative analyses, but also, for instance, the relaxation-time dependence of the axial strain which is normally not expected in a relaxation test. Therefore, such a nonhomogeneous model is necessary for better understanding of the mechanical behavior of cartilage.
关节软骨材料特性的深度依赖性，即分层差异，被纳入先前开发的非线性纤维增强多孔弹性模型中，以探究材料非均匀性在软骨力学行为中的重要性。所提出的材料变化基于广泛的观察结果。胶原纤维被建模为一种独特的成分，它增强了代表蛋白聚糖和水的其他两种成分。通过确定排水非纤维基质的杨氏模量和泊松比，使得受限几何形状下的总压缩模量符合实验数据。考虑了三个非线性因素，即有限变形的影响、渗透率对膨胀的依赖性以及纤维随拉伸应变的硬化。使用有限元程序提取解以模拟无侧限压缩试验。然后展示该模型的特征，重点关注只有非均匀模型才能获得的结果，结果显示与实验合理吻合。该模型表明力学行为与均匀模型所揭示的行为有显著差异：不仅有定性分析所预期的应变深度变化，例如，还有轴向应变的弛豫时间依赖性，这在弛豫试验中通常是无法预期的。因此，这样的非均匀模型对于更好地理解软骨的力学行为是必要的。
