An Elastohydrodynamic Lubrication Framework for Hip Prostheses based on Isogeometric Analysis

Abstract

The hip prosthesis modeling involves complex fluid-structure interaction between lubricant flow and solid deformation, which is a typical elastohydrodynamic lubrication regime. This study introduces a novel numerical framework for addressing such challenges through Non-Uniform Rational B-Splines (NURBS)-based isogeometric analysis (IGA). A new form of the Reynolds equation, derived in the parametric space of curved surfaces rather than spherical coordinates, is introduced to streamline discretization within the IGA framework and integration with solid mechanics. Additionally, the momentum balance equation is utilized for calculating solid deformations, providing a more accurate description than the conventional Boussinesq approximation. Furthermore, a developed mass-conserving cavitation formulation is incorporated to depict the formation and volumetric distribution of cavitation bubbles in hip prostheses. These equations are discretized utilizing NURBS basis functions and solved simultaneously via the Newton-Raphson method, enabling efficient strong coupling and rapid convergence. This IGA-based framework also facilitates future integration of nonlinear solid deformation and frictional contact.