ANISOTROPHY AND NONLINEARITY OF CARTILAGE MECHANICS

关节软骨是腹泻关节的承托材料。它的主要机械功能是以最小的摩擦和磨损在关节表面传递大载荷；在正常情况下，软骨可以维持这种功能七到八十年。从工程角度来看，软骨的力学性能被认为是显著的，是任何传统工程承载材料无法比拟的。然而，尽管对软骨进行了几十年复杂的生物力学研究，但由于其显著的多功能性和复杂性，对软骨力学的准确理解仍然难以捉摸。研究表明，关节软骨的力学反应可能会随着持续时间和加载或变形速率的变化而变化，即软骨表现出粘弹性。此外，研究表明，当测试平行和垂直于劈裂线方向的组织时，软骨的拉伸刚度是不同的，即它表现出各向异性。研究还发现，软骨在压缩状态下的刚度可能比在拉伸状态下小一到两个数量级，即表现出拉压非线性。各种研究也证实，这些测量的性质可能从软骨的浅层到深层变化，即组织表现出深度依赖的不均匀性。迄今为止，还没有单一的关节软骨本构模型能够描述其在文献中描述的各种测试条件下的力学响应。该提议的假设是：(1)软骨是正交异性的，需要比迄今为止测量的更多的材料常数来描述其力学响应；(2)软骨的拉压非线性要求这些常数中的一些（但不是全部）具有不同的拉压值；(3)结合软骨正交异性和拉压非线性的理论框架，采用混合理论，可以为所有测试配置提供理论和实验之间的一致性；当在分析中加入组织不均匀性时，这种一致性得到改善。因此，本课题的具体目的是沿着表征材料对称面的三个相互垂直的方向，对人体髌骨软骨样品进行拉伸、压缩、剪切和渗透测试，如通过实验确定一套完整的软骨弹性和渗透常数；为了确定这些常数是否确实描述了一种正交各向异性材料；通过实验评估软骨的深度依赖性不均匀性；并将瞬态和平衡实验响应与新提出的具有深度依赖非均匀性的双相，辛向正交各向异性，顺向线性弹性模型的相应预测进行比较。为了实现这些目标，建议使用最新的技术来测量组织力学性能。

Articular cartilage is the bearing material of diarthrodial joints. Its primary mechanical function is to transmit large loads across the articular surfaces of joints with minimal friction and wear; under normal conditions, cartilage can maintain this function for seven to eight decades. From an engineering perspective, the mechanical behavior of cartilage is considered to be remarkable, unmatched by any traditional engineering bearing material. However, despite several decades of sophisticated biomechanical studies of cartilage, an accurate understanding of cartilage mechanics remains elusive due to its remarkable versatility and complexity. Studies have demonstrated that the mechanical response of articular cartilage may vary as a function of duration and rate of loading or deformation, i.e., cartilage exhibits viscoelasticity. Furthermore, it has been shown that the tensile stiffness of cartilage differs when testing the tissue parallel and perpendicular to the split line directions, i.e., it exhibits anisotropy. It has also been established that the stiffness of cartilage in compression may be one to two orders of magnitude smaller than in tension, i.e., it exhibits tension-compression nonlinearity. Various studies have also confirmed that these measured properties may vary from the superficial to the deep zone of cartilage, i.e., the tissue exhibits depth-dependent inhomogeneity. To date, no single constitutive model of articular cartilage has been able to describe its mechanical response under the various testing conditions described in the literature. The hypotheses of this proposal are that (1) cartilage is orthotropic, requiring more material constants than have been measured to date to describe its mechanical response; (2) the tension-compression nonlinearity of cartilage requires that some, but not all of these constants have different values in tension and compression; and (3) that a theoretical framework encompassing cartilage orthotropy and tension-compression nonlinearity, using mixture theory, can provide agreement between theory and experiment for all testing configurations; this agreement improves when incorporating tissue inhomogeneity in the analysis. Therefore, the specific aims of this proposal are to test human patellar cartilage samples in tension, compression, shear and permeation, along the three mutually perpendicular directions which are hypothesized to characterize the planes of material symmetry, such as to determine experimentally a complete set of elastic and permeability constants of cartilage; to determine whether these constants indeed describe an orthotropic material; to experimentally assess the depth-dependent inhomogeneity of cartilage; and to compare transient and equilibrium experimental responses to corresponding predictions from a newly proposed biphasic, octantwise orthotropic, conewise linear elasticity model with depth-dependent inhomogenous properties. To achieve these aims, it is proposed to use the most current techniques for measurement of tissue mechanical properties.