A computational study on dynamic behavior of articular cartilage under cyclic compressive loading and magnetic field

The dynamic behavior of articular cartilage (a soft porous biological tissue) with strain-dependent nonlinear permeability under cyclic compressive loading and magnetic field is investigated computationally. The compressive force is applied on top surface of the cylindrical plug of the tissue by means of a porous filter. The study of mechanical and deformational behavior of soft porous tissues such as articular cartilage under dynamic compressive loading and magnetic field is useful in understanding the underlying mechano-biological process that may lead to the development of a treatment and recovery protocol in a diseased state. In the present study, a linear biphasic mixture theory of porous media has been employed to derive the governing equations in terms of solid displacement and interstitial fluid pressure in the tissue. Exact solutions for the solid displacement, fluid pressure, and relative fluid velocity are provided for the constant permeability case which have also been used to validate the numerical method. On the other hand, the full nonlinear problem has been solved numerically using the method of lines and the outcomes are presented graphically to assess the effects of various emerging parameters. The results indicate that there is an increase in the solid dilatation due to application of magnetic field and this effect is more prominent at relatively high loading frequencies. In general, a repeated compressive force has generated an oscillating positive-negative hydrostatic pressure within the tissue, however, a strong magnetic field at comparatively high loading frequency enforces the tissue to have only the positive (supra-ambient) pressure. The outcomes have also revealed that the pattern of the dynamic behavior of the tissue is strongly dependent on the loading frequency. A considerable phase shift in the dilatation and fluid pressure has been noticed due to the loading frequency as well as magnetic effects. It has also been found that the permeability parameter has a minimal impact on the solid deformation and fluid pressure in all scenarios with a very small phase shift.