Garcia J J, Altiero N J, Haut R C
Department of Materials Science and Mechanics, College of Engineering and Orthopaedic, Michigan State University, East Lansing 48824, USA.
J Biomech Eng. 2000 Feb;122(1):1-8. doi: 10.1115/1.429622.
Articular cartilage is known to behave nonlinearly for large deformations. Mechanical properties derived from small strain experiments yield excessively large deformations in finite element models used in the study of severe blunt impact to joints. In this manuscript, a method is presented to determine the nonlinear elastic properties of biphasic cartilage based on a transversely isotropic hypo-elastic model. The elastic properties were estimated by fitting two force-displacement curves (in rapid loading and at equilibrium) obtained from large deformation indentation relaxation tests on cartilage using a nonporous spherical indentor. The solid skeleton of the cartilage was modeled as a transversely isotropic hypo-elastic material and a commercial finite element program was employed to solve the problem of a layer indented by a rigid sphere. Components of the hypo-elasticity tensor were made dependent on deformation according to the variations defined by a transversely isotropic hyperelastic formulation given earlier by others. Material incompressibility was assumed during the initial stage of rapid loading. The analysis was utilized for the determination of in situ properties of rabbit retropatellar cartilage at large deformations. The model was able to fit the material response to rapid loading and equilibrium indentation test data to approximately 50 percent strain. This material model suggested even higher percentage of stress supported by the fluid phase of cartilage than given earlier by small deformation theories of biphasic cartilage.
已知关节软骨在大变形情况下表现出非线性行为。从小应变实验得出的力学性能，在用于研究关节严重钝性撞击的有限元模型中会产生过大的变形。在本论文中，提出了一种基于横观各向同性次弹性模型来确定双相软骨非线性弹性性能的方法。通过拟合使用无孔球形压头对软骨进行大变形压痕松弛试验获得的两条力-位移曲线（快速加载时和平衡时）来估计弹性性能。软骨的固体骨架被建模为横观各向同性次弹性材料，并使用商业有限元程序来解决刚性球体压痕一层软骨的问题。根据其他人之前给出的横观各向同性超弹性公式所定义的变化，使次弹性张量的分量依赖于变形。在快速加载的初始阶段假定材料不可压缩。该分析用于确定兔髌后软骨在大变形时的原位性能。该模型能够将材料对快速加载和平衡压痕试验数据的响应拟合到大约50%的应变。该材料模型表明，软骨液相所承受的应力百分比甚至比双相软骨小变形理论之前给出的还要高。
