Applying the Hashin–Shtrikman bounds to predict stiffness of multicomponent 3D printed structures: Towards regenerative orthopaedic medicine

Abstract

Customised orthopaedic implants made from polymer materials would have advantages over metallic implants, if the mechanical properties could be matched more closely to bone. Here, the Hashin–Shtrikman bounds for isotropic composites are used to examine the feasibility of using scaffolds made from 3D printed polyether–etherketone (PEEK) that may adequate modulus immediately after printing, but when integrated and mineralised could approach the modulus of bone. The ability to predict the mechanical properties of 3D printed objects is essential for skeletal implants that require both immediate and long-term strength, such as the mandible and the femur. However, there is no method for predicting the change in mechanical properties due to the effect of ossification of bone scaffolds. Our aim was to calculate the upper and lower limits of the elastic moduli of polymer composites using the Hashin–Shtrikman bounds for isotropic composite solids and use them to compare the pre- and post-ossification properties for a range of scaffolds. We describe 3D printed PEEK as a composite of fully dense PEEK and air, water or bone. We confirm, by mechanically testing three designs, that our 3D printed scaffolds lie within the Hashin–Shtrikman bounds for PEEK–air composites. Improvements in strength achieved by integrating the PEEK scaffold with bone are predicted by calculating the Hashin–Shtrikman bounds for a three-phase composite and show the feasability of reaching bone equivalence. These predictions can be implemented for orthopaedic applications, customising the implant such that it can provide the appropriate immediate and long-term mechanical support for a specific implant size.