Improvement of the mechanical properties of bone cement by shape optimization of short fibers

Poor interfacial properties between reinforcement fibers and a polymethylmethacrylate (PMMA) matrix may result in debonding between them, which is an important failure mechanism for fiber-reinforced bone cement. Optimization of the shape of the fibers can improve load transfer between the fibers and the PMMA matrix, thereby providing maximum overall strength performance. This article presents a procedure for structural shape optimization of short reinforcement fibers using finite-element analyses. The composite is modeled by a representative volume element composed of a single short fiber embedded in the PMMA matrix. In contrast to most previous work on this subject, contact elements are employed between the fiber and the matrix to represent a low-strength interface. Most previous models assume a perfect bond. Residual stress, due to matrix cure shrinkage and/or thermal stresses, is also included in the model. The design objective is to improve the mechanical properties of the composite. The effects of two different loading conditions and objective functions, stiffness-based and fracture toughness-based, are examined. The general trend in design optimization is to produce a threaded end short (TES) fiber. Owing to the mechanical interlock between the fibers and the PMMA matrix, the TES fiber can bridge matrix cracks effectively and improve the stiffness of the composite.