Modeling three-dimensional-printed trabecular metal structures with a homogenization approach: Application to hemipelvis reconstruction

The application of three-dimensional printing technologies to metal materials allows us to design innovative, low-weight, patient-specific implants for orthopedic prosthesis. This is particularly true when the reconstruction of extensive metastatic bone defect is planned. Modeling complex three-dimensional-printed highly repetitive trabecular-like structures based on finite elements is computationally demanding, while homogenization algorithms offer the advantage of reduced simulation cost and time, allowing an effective evaluation of new personalized design suitable for clinical needs. This article describes and discusses the implementation of a reliable method for the multiscale modeling of trabecular structures by means of asymptotic expansion homogenization. Following the material characterization of the Ti6Al4V alloy obtained by electron beam melting technology, the asymptotic expansion homogenization was applied to two alternative low-density cell-unit designs. Model predictions demonstrated satisfactory agreement with compressive experimental tests and cantilever bending tests performed on both designs (differences lower than 5.5%). The method was extended to a real patient-specific hemipelvis reconstruction, exploiting the capability of the asymptotic expansion homogenization approach in quantitatively describing the effect of cell-unit designs and three-dimensional-printing stack direction (i.e. cell-unit orientation) both on the overall mechanical response of the implant and on the stress distribution. The hemipelvis implant filled with the higher density cell unit demonstrated to be 14% stiffer than using the lower density one, while changing the cell-unit orientation affected the stiffness up to 10%. The maximum stress values reached at the anchors were affected in a minor extent by the investigated design parameters.