Eberhardt A W, Keer L M, Lewis J L, Vithoontien V
Department of Orthopaedic Surgery, University of Minnesota, Minneapolis 55455.
J Biomech Eng. 1990 Nov;112(4):407-13. doi: 10.1115/1.2891204.
The stress distribution in the region of contact between a layered elastic sphere and a layered elastic cavity is determined using an analytical model to stimulate contact of articulating joints. The purpose is to use the solution to analyze the effects of cartilage thickness and stiffness, bone stiffness and joint curvature on the resulting stress field, and investigate the possibility of cracking of the material due to tensile and shear stresses. Vertical cracking of cartilage as well as horizontal splitting at the cartilage-calcified cartilage interface has been observed in osteoarthritic joints. The current results indicate that for a given system (material properties mu and nu constant), the stress distribution is a function of the ratio of contact radius to layer thickness (a/h), and while tensile stresses are seen to occur only when a/h is small, tensile strain is observed for all a/h values. Significant shear stresses are observed at the cartilage-bone interface. Softening of cartilage results in an increase in a/h, and a decrease in maximum normal stress. Cartilage thinning increases a/h and the maximum contact stress, while thickening has the opposite effect. A reduction in the indenting radius reduces a/h and increases the maximum normal stress. Bone softening is seen to have negligible effect on the resulting contact parameters and stress distribution.
使用一个分析模型来模拟关节的接触，从而确定分层弹性球体与分层弹性腔之间接触区域的应力分布。目的是利用该解决方案来分析软骨厚度和刚度、骨刚度以及关节曲率对所得应力场的影响，并研究由于拉伸应力和剪切应力导致材料开裂的可能性。在骨关节炎关节中已观察到软骨的垂直开裂以及软骨 - 钙化软骨界面处的水平分裂。当前结果表明，对于给定系统（材料属性μ和ν恒定），应力分布是接触半径与层厚度之比（a/h）的函数，并且虽然仅当a/h较小时才会出现拉伸应力，但对于所有a/h值都观察到了拉伸应变。在软骨 - 骨界面处观察到显著的剪切应力。软骨软化会导致a/h增加，最大法向应力减小。软骨变薄会增加a/h和最大接触应力，而增厚则有相反的效果。压痕半径减小会降低a/h并增加最大法向应力。骨软化对所得接触参数和应力分布的影响可忽略不计。
