Modeling of biomedical interfaces with nonlinear friction properties

Proper isotropic and anisotropic friction constitutive equations are developed based on previous friction measurements at cancellous bone-porous coated implant interfaces exhibiting nonlinear load-displacement curves. The simulated friction response is dependent on relative tangential displacements in both orthogonal directions. The interface constitutive matrix contains cross-stiffness terms identical in isotropic friction but different in anisotropic friction. These terms are due mainly to nonlinearity in response and vanish in unidirectional friction along a principal direction and in cases with Coulomb or linear friction. The interface ultimate resistance is evaluated by an elliptic criterion which becomes circular in isotropic cases. These constitutive relations are implemented in a finite element program which is employed to analyze a bone cube sliding on top of a porous-surfaced metallic plate, an experimental model used in our earlier measurements. The results for both isotropic and anisotropic frictions demonstrate the coupling between two orthogonal directions. The direction of resultant displacement under a variable load coincides with that of the load only when the friction is isotropic with coupling terms considered. In anisotropic friction, the resultant displacement occurs in a direction different from that of loading. Our previous bi-directional measurements corroborate well the findings of this study.