椎体-椎间盘固液耦合的轴对称表达、建模与分析
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国家自然科学基金资助(10272006,30470439)


Axisymmetric formulation, modeling and analysis of solid-fluid coupling in vertebra and intervertebral disc
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    摘要:

    目的研究集中载荷作用下椎体-椎间盘的固液耦合问题。方法将椎体-椎间盘视为多孔介质材料,包含固体骨架和隙间流体两相,采用Biot固液耦合方程描述两相影响过程。建立固相平衡方程与液相连续性方程的轴对称表达形式,应用加权残值法得到耦合方程轴对称表达的等效积分形式,离散后得到有限元格式,对时间的离散采用隐式向后差分法。应用有限元程序对椎体-椎间盘的轴对称模型进行数值分析。结果在集中力作用下,椎体-椎间盘孔隙压力随着时间的增大而减小,同时位移随着时间的增大而增大,逐渐两者趋于平衡;压力与位移在力作用点处最大,以此为中心向四周递减。结论载荷对孔压和位移有显著影响;计算结果与现有文献结果基本相符。

    Abstract:

    Objective To investigate the solid-fluid coupling problem in vertebra and intervertebral disc under concentrated loading force. Methods The vertebra and intervertebral disc are considered as porous material, consisting of solid skeleton and pore fluid. Biot equations are used to describe the solid-fluid coupling behavior for vertebra and intervertebral disc. The equilibrium equations and continuum equation were built in axisymmetric forms while the integral forms are derived by weights residual methods. The FE procedure is programmed in FROTRAN to simulate the coupling behavior for vertebra and intervertebral disc. Results The pore-pressure decreases while the displacement increases, both gradually tend to be balanced as time goes by, with higher value in the central area of disc compared with the surrounding ones. Conclusion It showed that external loads obviously affect that pore-pressure and displacement with the present numerical results according with the existing data.

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刘宝胜,杨庆生.椎体-椎间盘固液耦合的轴对称表达、建模与分析[J].医用生物力学,2007,22(4):361-366

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