Analytical modelling of the elastomeric layer in soft layer hip replacements.

A mechanical analysis is carried out for a flat deformable layer, firmly anchored to a rigidsubstrate, and frictionlessly compressed by a rigid spherical indenter, with reference to the design ofhip replacements whose cup is covered by an elastomeric layer. An available perturbation solutionof differential character, developed for a layer subject to plane strain conditions, indented by acylinder approximated as parabolic in shape and valid for high contact widths, is here extended tothe axisymmetric problem of a layer compressed by a paraboloidal indenter. In addition to theparaboloidal idealization, an accurate mathematical description of the indenter spherical profile isincorporated into the modelling of this contact problem. Perturbed solutions up to the second orderare developed for both compressible and incompressible layers. Selected numerical examples addressingactual joint geometries are included to assess the validity of the proposed analytical modelling,to explore the accuracy in describing the spherical profile and to compare the contact pressure profilesactivated by paraboloidal and spherical indenters.