一种用于关节软骨连续谱双相多孔粘弹性模型的数值方法。

A numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage.

作者信息

Haider Mansoor A, Schugart Richard C

机构信息

Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695-8205, USA.

出版信息

J Biomech. 2006;39(1):177-83. doi: 10.1016/j.jbiomech.2004.10.037. Epub 2005 Jan 19.

DOI:10.1016/j.jbiomech.2004.10.037

PMID:16271602

Abstract

A method for numerical solution of the continuous spectrum linear biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. The method is based on an alternate formulation of the continuous spectrum stress-strain law that is implemented using Gaussian quadrature integration combined with quadratic interpolation of the strain history. For N time steps, the cost of the method is O(N). The method is applied to a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. For a range of relaxation times that are representative of articular cartilage, accuracy of the method is demonstrated by direct comparison to a theoretical Laplace transform solution.

摘要

提出了一种用于数值求解关节软骨连续谱线性双相多孔粘弹性（BPVE）模型的方法。该方法基于连续谱应力 - 应变定律的一种交替公式，该公式通过高斯求积积分结合应变历史的二次插值来实现。对于N个时间步长，该方法的计算成本为O(N)。该方法应用于一维受限压缩BPVE应力松弛问题的有限差分解。对于一系列代表关节软骨的松弛时间，通过与理论拉普拉斯变换解直接比较，证明了该方法的准确性。