Knee prostheses modelling: deformation of the low rigidity component

BRENDA WEISS; SEBASTIÁN UBAL; JOSÉ DI PAOLO

San Jaun

Congreso; SABI 2022 : XXIII Congreso Argentino de Bioingenieria. XII Jornada de Ingeniería Clínica; 2022

Facultad de Ingeniería, Universidad Nacional de San Juan

The synovial fluid is usually assumed to be Newtonian despite its viscoelastic behavior. In this paper a model based on the Reynolds equation and the Phan-Thien and Tanner rheological law (PTT) is presented. The model, of the ellipsoid-on-plane type, contemplates the curvature of the articular surfaces and assumes the tibial component, typically made of ultra-high molecular weight polyethylene (UHMWPE), deforms elastically according to either the column model (EoPEc) or the resolution of the 3D linear elasticity equations (EoPE). Using a numerical procedure based on the Finite Element Method, the non-Newtonian lubrication flow governing equations were simultaneously solved to find the component of the total stress tensor for the PTT model, in the direction perpendicular to the flow, and the lubricating film thickness. From these results the friction forces and friction coefficients on the articular surfaces were calculated. Simulations corresponding to the squeeze film lubrication mode were carried out, varying the relaxation constant λ of the fluid. Small differences in friction coefficients are observed when comparing the EoPE and EoPEc models. However, the EoPEc model leads to overestimates of the lubricant film thickness, regardless of the value of λ considered, so the quantitative predictions derived from the EoPE model are more conservative, especially when the height of the lubrication channel is considered.