Using a poroelastodynamic model to investigate the dynamic behaviour of articular cartilage

Background and objective: 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. Methods: 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. Results: 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. Conclusion: 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.