Anisotropic Nonlinear Friction at Biomaterial Interfaces: Theory and Application

The interface friction exists in natural and artificial joints as well as many engineering systems in which different bodies articulate. It often plays an important role in mechanics of the system. In the cementless arthroplasty, the friction between the prosthesis (including stems and screws) and the host bone is exploited to increase the stability of the operation. Our previous experimental studies have shown that the interface between bone and various porous coated surfaces exhibit a nonlinear friction that remains nearly the same in different directions; a nonlinear isotropic friction [1,2]. More recent bidirectional friction tests between cancellous bone or polyurethane cubes and a metallic porous coated plate have demonstrated that the interface load-displacement curve is highly nonlinear with significant coupling between two perpendicular directions [3]. Model studies incorporating measured nonlinear response have demonstrated the importance of proper simulation of nonlinear response as compared with Coulomb friction and of the coupling between orthogonal directions [3–5]. In this study, we aim to extend the earlier model studies to incorporate nonlinear direction-dependent anisotropic friction between two surfaces. Our objectives are set to: (a) develop constitutive equations to present interfaces with nonlinear anisotropic friction properties; and (b) implement and apply in a finite element study of a cube resting on a block subjected to normal and shear loads.