Compressive stress relaxation behavior of articular cartilage with MHD effects

We have developed a theoretical framework to investigate the deformation of the cartilage's solid phase in response to electrically conducting fluid flow. The purpose is to comprehend compression-induced cartilage stress–relaxation behavior. The biphasic mixture theory forms the model's foundation, which combines the nonlinear strain-dependent permeability found earlier in an experiment. In this investigation, it was assumed that the fluid and solid phases were intrinsically incompressible and nondissipative; however, mathematical modeling also developed for the fluid phase's and solid matrix's viscoelastic behaviors. A set of coupled partial differential equations (PDEs) was developed to characterize the slow rate and fast rate of compression in the presence of Lorentz forces for solid deformation and fluid pressure. The method of lines (MOL) is used to solve the resulting system, and graphs are produced to illustrate the relationship of the magnetic parameter with solid deformation and fluid pressure.