Analysis of some Contact Problems in Human Joints after Arthroplasty

A general anisotropic model of unilateral contact with adhesion and friction is proposed. The model is applied to the numerical analysis of contact between pelvis and acetabulum after arthroplasty. Clinical evidence confirms the role of not only friction but also of adhesion at the bone-implant interface. We have elaborated a general model of unilateral contact with friction and adhesion applicable to the study of such an interface. Numerical implementation has been performed using the finite element method preceded by a regularization of unilateral conditions. Numerical solutions pertain to the development of zone of adhesion loss. For a discussion of phenomena occurring at the bone-implant interface see [

1

,

2

] The performed numerical analysis pertains to the case of isotropy of bone adhesion but the general anisotropic model presented here can also be used. Also, our approach applies to any joint after arthroplasty and fixation with or without bone cement. Also, one may envisage applications to dental biomechanics. According to clinical data failure of the hip prosthesis is mainly caused by loosening of the acetabulum and not the stem. Surprisingly, in the relevant biomechanical literature not the acetabulum but stem loosening is most often analyzed. Hence the importance of study like the one performed in this paper. Our next goal is to take into account the influence of wear debris, on prostheses loosening. To this end the model proposed by Shillor et al. [

3

] will be generalized.