An acetabular cup with larger abduction angles is able to affect the normal function of the cup seriously that may cause early failure of the total hip replacement (THR). Complexity of the finite element (FE) simulation in the wear analysis of the THR is usually concerned with the contact status, the computational effort, and the possible divergence of results, which become more difficult on THRs with larger cup abduction angles. In the study, we propose a FE approach with contact transformation that offers less computational effort. Related procedures, such as Lagrangian Multiplier, partitioned matrix inversion, detection of contact forces, continuity of contact surface, nodal area estimation, etc. are explained in this report. Through the transformed methodology, the computer round-off error is tremendously reduced and the embedded repetitive procedure can be processed precisely and quickly. Here, wear behaviors of THR with various abduction angles are investigated. The most commonly used combination, i.e., metal-on-polyethylene, is adopted in the current study where a cobalt-chromium femoral head is paired with an Ultra High Molecular Weight Polyethylene (UHMWPE) cup. In all illustrations, wear coefficients are estimated by self-averaging strategy with available experimental datum reported elsewhere. The results reveal that the THR with larger abduction angles may produce deeper depth of wear but the volume of wear presents an opposite tendency; these results are comparable with clinical and experimental reports. The current approach can be widely applied easily to fields such as the study of the wear behaviors on ante-version, impingement, and time-dependent behaviors of prostheses etc. 
The study of wear behaviors on abducted hip joint prostheses by an alternate finite element approach