Compressive stress relaxation behavior of articular cartilage and its effects on fluid pressure and solid displacement due to non-Newtonian flow

In this study, we investigate the effects of the power-law index and permeability parameter on the deformation of soft tissue (articular cartilage) which is bathed in the non-Newtonian fluid under stress-relaxation in compression. Ramp displacement is imposed on the surface of hydrated soft tissue. Deformation of the tissue and the fluid pressure is examined for the fast and slow rate of compression. We have employed a linear biphasic mixture theory to develop a mathematical model for compressive stress-relaxation behavior of articular cartilage for non-Newtonian flow. Numerical results indicate that shear-thinning fluids induce less solid deformation and exhibit more fluid pressure as compared to shear-thickening fluids for fast and slow rate of compression. The results also show that linear permeability induces more deformation as compared to strain-dependent nonlinear permeability due to viscoelastic nature of articular cartilage.