Wayne J S, Woo S L, Kwan M K
Orthopaedic Bioengineering Laboratory, San Diego Veterans Affairs Medical Center, CA.
J Biomech Eng. 1991 Nov;113(4):397-403. doi: 10.1115/1.2895418.
The finite element method using the principle of virtual work was applied to the biphasic theory to establish a numerical routine for analyses of articular cartilage behavior. The matrix equations that resulted contained displacements of the solid matrix (mu) and true fluid pressure (p) as the unknown variables at the element nodes. Both small and large strain conditions were considered. The algorithms and computer code for the analysis of two-dimensional plane strain, plane stress, and axially symmetric cases were developed. The u-p finite element numerical procedure demonstrated excellent agreement with available closed-form and numerical solutions for the configurations of confined compression and unconfined compression under small strains, and for confined compression under large strains. The model was also used to examine the behavior of a repaired articular surface. The differences in material properties between the repair tissue and normal cartilage resulted in significant deformation gradients across the repair interface as well as increased fluid efflux from the tissue.
利用虚功原理的有限元方法被应用于双相理论，以建立一个用于分析关节软骨行为的数值程序。由此产生的矩阵方程包含固体基质的位移（μ）和真实流体压力（p）作为单元节点处的未知变量。同时考虑了小应变和大应变条件。开发了用于二维平面应变、平面应力和轴对称情况分析的算法和计算机代码。u-p有限元数值程序在小应变下的受限压缩和无受限压缩构型以及大应变下的受限压缩构型方面，与可用的封闭形式和数值解显示出极好的一致性。该模型还用于研究修复后的关节表面的行为。修复组织和正常软骨之间材料特性的差异导致修复界面处出现显著的变形梯度，以及组织中流体流出增加。
