Triphasic finite element model for swelling porous media
Triphasic finite element model for swelling porous media
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DOI：
10.1002/fld.1650200821
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发表时间：
1995-04
影响因子：
1.8
通讯作者：
H. Snijders;Jmrj Jacques Huyghe;J. J. Janssen-J.
中科院分区：
文献类型：
--
作者：
H. Snijders;Jmrj Jacques Huyghe;J. J. Janssen-J.
描述椎间盘组织和其它膨胀多孔介质的机械行为的方程是三个耦合的偏微分方程，其中出现几何和物理非线性。边界条件与变形有关。为了求解任意几何形状和任意边界条件的方程，我们使用有限元（FE）方法。利用加权残数法将微分方程改写成积分形式。积分的域通过一组形状函数（即有限元）来定义。通过应用高斯定理和关于参考状态（全拉格朗日）的重写，得到非线性方程。这些都是通过解决的牛顿-拉夫逊技术。为了得到一个有限的方程组，加权残差方程离散。选择形状函数作为加权函数（Galerkin方法）。这种离散化导致非对称刚度矩阵。给出了在商业FE包DIANA（DIANA Analysis B.V，德尔夫特，荷兰）中实现的元素的一般描述。无侧限压缩的示意性椎间盘与不同的蛋白多糖浓度的数值结果。
SUMMARY The equations describing the mechanical behaviour of intervertebral disc tissue and other swelling porous media are three coupled partial differential equations in which geometric and physical non-linearities occur. The boundary conditions are deformation-dependent. To solve the equations for an arbitrary geometry and arbitrary boundary conditions, we use the finite element (FE) method. The differential equations are rewritten in an integral form by means of the weighted residual method. The domain of the integral is defined via a set of shape functions (i.e. finite elements). By applying the Gauss theorem and rewriting with respect to the reference state (total Lagrange), non-linear equations are obtained. These are solved by means of the Newton-Raphson technique. In order to get a finite set of equations, the weighted residual equations are discretized. The shape functions are chosen as weighting functions (Galerkin method). This discretization results in a non-symmetric stiffness matrix. A general description is given for the elements implemented into the commercial FE package DIANA (DIANA Analysis B.V, Delft, Netherlands). The numerical results of unconfined compression of a schematic intervertebral disc with varying proteoglycan concentration are given.