A joint prosthesis device comprises a head configured to fit within a cup. The cup includes a concave cup surface defined by at least one radius of curvature RC. The head includes a convex head surface defined by at least one radius of curvature RH. The convex head surface is configured to engage the concave cup surface. The convex head surface provides an articulation zone where the head surface engages the cup surface. RC differs from RH in the articulation zone by a first amount. The convex head surface also provide a peripheral zone outside of the articulation zone. RC differs from RH in the peripheral zone by a second amount that is greater than the first amount. The peripheral zone generally extends over an area subtended by a minimum angle having a vertex at a center of the head.