An implicit numerical method for wear modeling applied to a hip joint prosthesis problem

Some phenomenological wear models exist, but they are most of the time used to post-process numerical simulations. In certain situations however, material loss may be sufficient to change the contact area, contact stresses. In such cases, coupling the wear loss estimation to the mechanical contact modelling becomes essential. It can be done, and is done most of the time, by updating geometry between time-steps, introducing no further non-linearity. The option chosen here is on the contrary a fully coupled model where the wear displacement field is added to the unknowns of the frictional contact problem and requires one more equation. This equation is an adaptation of the Archard’s wear law to a local formulation in the context of dynamic and large displacements applications. This method allows simulation of the entire wear process in only a few loading cycles. We even quite accurately simulate the process in a single cycle. This is made possible via our fully coupled approach and an adaptation of the wear factor. The wear factor is artificially increased in order to decrease the number of cycles. A detailed description of the resolution of discrete equations is presented. The solver is a non linear Gauss Seidel algorithm adapted to wear conditions which derives from the ‘Non Smooth Contact Dynamics’ method. The wear model is validated on a total hip arthroplasty problem. Numerical observations are based on previously published experimental results.