Chao E Y S, Volokh K Y, Yoshida H, Shiba N, Ide T
Orthopaedic Biomechanics Laboratory, Johns Hopkins University, Baltimore, Maryland 21205-2196, USA.
Mol Cell Biomech. 2010 Sep;7(3):175-92.
This paper is written to honor Professor Y. C. Fung, the applied mechanician who has made seminal contributions in biomechanics. His work has generated great spin-off utility in the field of musculoskeletal biomechanics. Following the concept of the Rigid Body-Spring Model theory by T. Kawai (1978) for non-linear analysis of beam, plate, and shell structures and the soil-gravel mixture foundation, we have derived a generalized Discrete Element Analysis (DEA) method to determine human articular joint contact pressure, constraining ligament tension and bone-implant interface stresses. The basic formulation of DEA to solve linear problems is reviewed. The derivation of non-linear springs for the cartilage in normal diarthrodial joint contact problem was briefly summarized. Numerical implementation of the DEA method for both linear and non-linear springs is presented. This method was able to generate comparable results to the classic contact stress problem (the Hertzian solution) and the use of Finite Element Modeling (FEM) technique on selected models. Selected applications in human knee and hip joints are demonstrated. In addition, the femoral joint prosthesis stem/bone interface stresses in a non-cemented fixation were analyzed using a 2D plane-strain approach. The DEA method has the advantages of ease in creating the model and reducing computational time for joints of irregular geometry. However, for the analysis of joint tissue stresses, the FEA technique remains the method of choice.
本文旨在致敬冯元桢教授，这位应用力学家在生物力学领域做出了开创性贡献。他的工作在肌肉骨骼生物力学领域产生了巨大的衍生效用。遵循河合俊夫（1978年）提出的刚体-弹簧模型理论概念，用于梁、板和壳结构以及土石混合地基的非线性分析，我们推导出一种广义离散元分析（DEA）方法，以确定人体关节接触压力、约束韧带张力和骨-植入物界面应力。回顾了用于求解线性问题的DEA基本公式。简要总结了正常动关节接触问题中软骨非线性弹簧的推导过程。介绍了DEA方法在线性和非线性弹簧方面的数值实现。该方法能够产生与经典接触应力问题（赫兹解）以及在选定模型上使用有限元建模（FEM）技术相当的结果。展示了在人体膝关节和髋关节中的选定应用。此外，使用二维平面应变方法分析了非骨水泥固定中股骨关节假体柄/骨界面应力。DEA方法具有易于创建模型和减少不规则几何形状关节计算时间的优点。然而，对于关节组织应力分析，有限元分析（FEA）技术仍然是首选方法。
