Advanced manufacturing processes provide a tremendous opportunity to fabricate materials with precisely defined architectures. To fully leverage these capabilities, however, materials architectures must be optimally designed according to the target application, base material used, and specifics of the fabrication process. Computational topology optimization offers a systematic, mathematically driven framework for navigating this new design challenge. The design problem is posed and solved formally as an optimization problem with unit cell and upscaling mechanics embedded within this formulation. This article briefly reviews the key requirements to apply topology optimization to materials architecture design and discusses several fundamental findings related to optimization of elastic, thermal, and fluidic properties in periodic materials. Emerging areas related to topology optimization for manufacturability and manufacturing variations, nonlinear mechanics, and multiscale design are also discussed.
The rapid advance of additive manufacturing technologies has provided new opportunities for creating complex structural shapes. In order to fully exploit these opportunities, however, engineers must re-think the design process and leverage these new capabilities while respecting manufacturing constraints inherent in various processes. Topology optimization, as a free-from design tool, is a potentially powerful approach to addressing this design challenge provided the manufacturing process is properly accounted for. This work examines geometric constraints related to feature size and the layer-by-layer nature of the manufacturing process. A simple modification to the Heaviside Projection Method, an approach for naturally achieving geometric constraints in topology optimization, is proposed and demonstrated to have clear, understandable impact on three-dimensional optimized beam designs.
Proximal femur anatomy and bone mineral density vary widely among individuals, precluding the use of one predefined finite element (FE) model to determine the stress field for all proximal femurs. This variability poses a challenge in current prosthetic hip design approach. Given the numerous options for generating computed tomography (CT)‐based FE models, selecting the best methods for defining the mechanical behavior of the proximal femur is difficult. In this study, a combination of computational and experimental approaches was used to explore the susceptibility of the predicted stress field of the proximal femur to different combinations of density–elasticity relationships, element type, element size, and calibration error. Our results suggest that FE models with first‐order voxelized elements generated by the Keyak and Falkinstein density–elasticity relationship or quadratic tetrahedral elements generated by the Morgan density–elasticity relationship lead to accurate estimations of the mechanical behavior of human femurs. Other combinations of element size, element type, and mathematical relationships produce less accurate results, especially in the cortical bone of the femoral neck and calcar region. The voxelized model was more susceptible to variation of element size and density–elasticity relationships than FE models with quadratic tetrahedral elements. Regardless of element type, the stress fields predicted by the Keyak and Falkinstein and the Morgan relationships were the most robust to calibration error when deriving material density from CT‐generated Hounsfield data. These results provide insight into the implementation of a robust platform for designing patient‐specific implants capable of maintaining or modifying the stress in bones.
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