Shape optimization of randomly oriented short fibers for bone cement reinforcements

Fibers can be used to improve the mechanical properties of bone cement for the long-term stability of hip prosthesis. However, debonding of the fibers from the matrix due to the poor fiber/matrix interface is a major failure mechanism for such fiber-reinforced bone cements. Optimization of the shape of the fibers can improve load transfer between the fibers and the matrix, thereby providing improved overall mechanical performance. This paper presents a procedure for structural shape optimization of short reinforcement fibers using finite element analyses. The effects of fiber orientation and interfacial bond were investigated to obtain the optimal fiber shape for bone cement reinforced with randomly oriented fibers. The composite is regarded as an array of unit cells containing a tilting fiber embedded in the matrix. This method provides proper boundary conditions for the center unit cell. The design objective based on the center unit cell is then optimized to maximize the stiffness of the reinforced bone cement. As opposed to aligned fiber composites, where the optimum shape is an enlarged-end fiber, the general optimal fiber shape for randomly oriented fibers is a variable diameter fiber (VDF). Due to the mechanical interlock between the fibers and the matrix, the VDF can both bridge matrix cracks effectively and improve the stiffness of the composite when fibers are randomly oriented.