Chou Dean, Li Yun-Di, Mustansar Zartasha, Chung Chen-Yuan
Department of Biomedical Engineering, National Cheng Kung University, Tainan City, Taiwan; Medical Device Innovation Center, National Cheng Kung University, Tainan City, Taiwan.
Department of Mechanical Engineering, National Central University, Taoyuan City, Taiwan.
Comput Methods Programs Biomed. 2023 May;233:107481. doi: 10.1016/j.cmpb.2023.107481. Epub 2023 Mar 12.
There is still a few studies about the poroelastic model that performed dynamic behaviour, especially for the case of the poroelastic cartilage model. Therefore, this study is aimed to use the poroelastodynamic model to simulate the dynamic behaviour of cartilage.
The governing equations of the poroelastodynamic model is firstly established. The validation of the model is initialised by modifying the equations into the static poroelastic model. The modified equations are then discretised using the finite element method. Mandel's problem is used to validate the discretised equations. The numerical solution calculated using FreeFEM++ is validated with the analytical solution for the quasi-static state and compared with the results generated using COMSOL Multiphysics software. Finally, the quasi-static solution is compared with the dynamic solution to discuss the difference in pore pressure and displacement variations of the poroelastic cartilage model.
The dynamic solution showed transient behaviour at the beginning of the excitation. When the compressive force acts on the cartilage, there are obvious fluctuations during the initial stage and then the dynamic numerical solution gradually approaches the quasi-static value over a period of time. The deduced results of the analytical solution were approximately the same as the numerical simulation results.
This study was able to use the poroelastodynamics equation to simulate the dynamic behaviour of the poroelastic cartilage model. The comparison between the result coming from poroelastodynamics equation with that of the validated numerical solution was satisfactorily compared. The approximate similarity between the results of quasi-static and dynamic solutions underscored the importance of performing the dynamic solution for a more realistic simulation. This dynamic solution can be further used for the analysis of vibration or stress waves in future research.
关于多孔弹性模型动力学行为的研究仍然较少，尤其是多孔弹性软骨模型的情况。因此，本研究旨在使用多孔弹性动力学模型来模拟软骨的动力学行为。
首先建立多孔弹性动力学模型的控制方程。通过将方程修改为静态多孔弹性模型来初始化模型验证。然后使用有限元方法对修改后的方程进行离散化。利用曼德尔问题验证离散化方程。使用FreeFEM++计算的数值解与准静态状态的解析解进行验证，并与使用COMSOL Multiphysics软件生成的结果进行比较。最后，将准静态解与动态解进行比较，以讨论多孔弹性软骨模型孔隙压力和位移变化的差异。
动态解在激励开始时呈现瞬态行为。当压缩力作用于软骨时，初始阶段存在明显波动，然后动态数值解在一段时间内逐渐接近准静态值。解析解的推导结果与数值模拟结果大致相同。
本研究能够使用多孔弹性动力学方程来模拟多孔弹性软骨模型的动力学行为。将多孔弹性动力学方程得到的结果与经过验证的数值解进行了令人满意的比较。准静态解和动态解结果的近似相似性强调了进行动态解以实现更真实模拟的重要性。这种动态解可在未来研究中进一步用于振动或应力波的分析。
