Revision surgeries of total hip arthroplasty are often caused by a deficient structural compatibility of the implant. Two main culprits, among others, are bone-implant interface instability and bone resorption. To address these issues, in this paper we propose a novel type of implant, which, in contrast to current hip replacement implants made of either a fully solid or a foam material, consists of a lattice microstructure with nonhomogeneous distribution of material properties. A methodology based on multiscale mechanics and design optimization is introduced to synthesize a graded cellular implant that can minimize concurrently bone resorption and implant interface failure. The procedure is applied to the design of a 2D left implanted femur with optimized gradients of relative density. To assess the manufacturability of the graded cellular microstructure, a proof-of-concept is fabricated by using rapid prototyping. The results from the analysis are used to compare the optimized cellular implant with a fully dense titanium implant and a homogeneous foam implant with a relative density of 50%. The bone resorption and the maximum value of interface stress of the cellular implant are found to be over 70% and 50% less than the titanium implant while being 53% and 65% less than the foam implant.

A methodology is proposed to design a spatially periodic microarchitectured material for a twodimensional femoral implant under walking gait conditions. The material is composed of a graded lattice with controlled property distribution that minimizes concurrently bone resorption and interface failure. The periodic microstructure of the material is designed for fatigue fracture caused by cyclic loadings on the hip joint as a result of walking. The bulk material of the lattice is Ti6AL4V and its microstructure is assumed free of defects. The Soderberg diagram is used for the fatigue design under multiaxial loadings. Two cell topologies, square and Kagome, are chosen to obtain optimized property gradients for a two-dimensional implant. Asymptotic homogenization (AH) theory is used to address the multiscale mechanics of the implant as well as to capture the stress and strain distribution at both the macro and the microscale. The microstress distribution found with AH is also compared with that obtained from a detailed finite element analysis. For the maximum value of the von Mises stress, we observe a deviation of 18.6 % in unit cells close to the implant boundary, where the AH assumption of spatial periodicity of the fluctuating fields ceases to hold. In the second part of the paper, the metrics of bone resorption and interface shear stress are used to benchmark the graded cellular implant with existing prostheses made of fully dense titanium implant.The results show that the amount of initial postoperative bone loss for square and kagome lattice implants decreases, respectively, by 53.8% and 58%. In addition, the maximum shear interface failure at the distal end is significantly reduced by about 79%.A set of proof-of-concepts of planar implants have been fabricated via Electron Beam Melting (EBM) to demonstrate the manufacturability of Ti6AL4V into graded lattices with alternative cell size. Optical microscopy has been used to measure the morphological parameters of the cellular microstructure, including cell wall thickness and pore size, and compared them with the nominal values. No sign of fracture or incomplete cell walls was observed, an assessment that shows the satisfactory metallurgical bond of cell walls and the structural integrity of the implants.

a b s t r a c tA numerical method based on asymptotic homogenization theory is presented for the design of lattice materials against fatigue failure. The method is applied to study the effect of unit cell shape on the fatigue strength of hexagonal and square lattices. Cell shapes with regular and optimized geometry are examined. A unit cell is considered to possess a regular shape if the geometric primitives defining its inner boundaries are joined with an arc fillet, whose radius is 1% of the cell length. An optimized cell shape, on the other hand, is obtained by minimizing the curvature of its interior borders, which are conceived as continuous in curvature to smooth stress localization.For a given multi-axial cyclic loading, failure surfaces of metallic hexagonal and square lattices are provided along with their modified Goodman diagrams to assess the effect of mean and alternating stresses on the fatigue strength. In good agreement with the experimental data available in literature, the numerical results show that the shape of the unit cell has a major impact on the fatigue performance of the lattice material. For example under fully reversible tension, the fatigue strength of optimized square lattices of 10% relative density is shown to be 54% higher than that of their conventional counterparts with regular cell geometry.

A multiscale design and multiobjective optimization procedure is developed to design a new type of graded cellular hip implant. We assume that the prosthesis design domain is occupied by a unit cell representing the building block of the implant. An optimization strategy seeks the best geometric parameters of the unit cell to minimize bone resorption and interface failure, two conflicting objective functions. Using the asymptotic homogenization method, the microstructure of the implant is replaced by a homogeneous medium with an effective constitutive tensor. This tensor is used to construct the stiffness matrix for the finite element modeling (FEM) solver that calculates the value of each objective function at each iteration. As an example, a 2D finite element model of a left implanted femur is developed. The relative density of the lattice material is the variable of the multiobjective optimization, which is solved through the non-dominated sorting genetic algorithm II (NSGA-II). The set of optimum relative density distributions is determined to minimize concurrently interface stress distribution and bone loss mass. The results show that the amount of bone resorption and the maximum value of interface stress can be reduced by over 70% and 50%, respectively, when compared to current fully dense titanium stem.

This paper presents a method to improve the fatigue strength of 2D periodic cellular materials under a fully-reversed loading condition. For a given cell topology, the shape of the unit cell is synthesized to minimize any stress concentration caused by discontinuities in the cell geometry. We propose to reduce abrupt geometric changes emerging in the periodic microstructure through the synthesis of a cell shape defined by curved boundaries with continuous curvature, i.e. G2-continous curves. The bending moments caused by curved cell elements are reduced by minimizing the curvature of G2-continuous cell elements so as to make them as straight as possible. The asymptotic homogenization technique is used to obtain the homogenized stiffness matrix and the fatigue strength of the synthesized cellular material. The proposed methodology is applied to synthesize a unit cell topology described by smooth boundary curves. Numeric simulations are performed to compare the performance of the synthesized cellular solid with that of common two dimensional lattice materials having hexagonal, circular, square, and Kagome shape of the unit cell. The results show that the methodology enables to obtain a cellular material with improved fatigue strength. Finally, a parametric study is performed to examine the effect of different geometric parameters on the performance of the proposed cellular geometries.