Shape optimization of a cementless hip stem for a minimum of interface stress and displacement.

The primary stem stability is an essential factor for success of cementless hip stems. A correct choice of the stem geometry can improve the stem stability and, consequently, increase the life time of a hip implant. In this work, it is proposed a computational model for shape optimization of cementless hip stems. The optimization problem is formulated by the minimization of relative displacement and stress on bone/stem interface using a multi-criteria objective function. Also multiple loads are considered to incorporate several daily life activities. Design variables are parameters that characterize the geometry of selected cross sections, which are subject to geometric constraints to ensure a clinically admissible shape. The stem/bone set is considered a structure in equilibrium with contact conditions on interface. The contact formulation allows us to analyze different lengths of porous coating. The optimization problem is solved numerically by a steepest descent method. The interface stress and relative displacement are obtained solving the contact problem by the finite element method. Numerical examples are presented for a two-dimensional model of a hip stem, however, the formulation is general and can be applied to the three-dimensional case. The model gives indications about the relation between shape, porous coating and prosthesis stability.