关节软骨两相多孔介质非线性模型的有限元方法

基于混合物理论的两相多孔介质模型可以准确描述关节软骨的力学行为，关节软骨的渗透率与固体相体积应变相关。本文研究这一模型的非线性有限元法。具体采用伽辽金加权残值法得到有限元平衡方程，编制了有限元程序，进而对关节软骨围限压缩蠕变和应力松弛行为进行了数值模拟。与视渗透率为常数的线性模型的计算结果比较表明，在变形较大时，渗透率随固体相体积应变变化这一非线性效应不容忽视。

Finite Element Method of Nonlinear Biphasic Porous Media Model for Articular Cartilage

Biphasic porous medium model based on mixture theory can be used to accurately depict the mechanical behavior of articular cartilage, and the permeability of articular cartilage is related to volume strain of solid phase. In this paper, the finite element method for this nonlinear model is given. The finite element balance equation is obtained with Galerkin weighted residual procedure, and in turn, the creep and stress relaxation behaviors of articular cartilage under confined compression are numerically simulated using the designed finite element program. The numerical results, comparing with those obtained by linear model, show that the nonlinear effect of permeability depending on volume strain of solid phase cannot be ignored as deformation is not too small.