Porous structures such as trabecular bone are widely seen in nature. These structures are lightweight and exhibit strong mechanical properties. In this paper, we present a method to generate bone-like porous structures as lightweight infill for additive manufacturing. Our method builds upon and extends voxel-wise topology optimization. In particular, for the purpose of generating sparse yet stable structures distributed in the interior of a given shape, we propose upper bounds on the localized material volume in the proximity of each voxel in the design domain. We then aggregate the local per-voxel constraints by their p -norm into an equivalent global constraint, in order to facilitate an efficient optimization process. Implemented on a high-resolution topology optimization framework, our results demonstrate mechanically optimized, detailed porous structures which mimic those found in nature. We further show variants of the optimized structures subject to different design specifications, and we analyze the optimality and robustness of the obtained structures.
Abstract Computer models of random heterogeneous materials are becoming increasingly important in order to support the latest advances in material science, biomedical applications and manufacturing. Such models usually take the form of a microstructure whose geometry is reconstructed from a small material sample, an exemplar. A widely used traditional approach to material reconstruction relies on stochastic optimization to approximate the material descriptors of the exemplar, such as volume fraction and two-point correlation functions. This approach is computationally intensive and is limited to certain types of isotropic materials. We show that formulating material reconstruction as a Markov Random Field (MRF) texture synthesis leads to a number of advantages over the traditional optimization-based approaches. These include improved computational efficiency, preservation of many material descriptors, including correlation functions and Minkowski functionals, ability to reconstruct anisotropic materials, and direct use of the gray-scale material images and two-dimensional cross-sections. Quantifying the quality of reconstruction in terms of correlation functions as material descriptors suggests a systematic procedure for selecting a size of neighborhood, a key parameter in the texture synthesis procedure. We support our observations by experiments using implementation with Gaussian pyramid and periodic boundary conditions. Recent years have witnessed significant progress in example-based texture synthesis algorithms. Given an example texture, these methods produce a larger texture that is tailored to the user's needs. In this state-of-the-art report, we aim to achieve three goals: (1) provide a tutorial that is easy to follow for readers who are not already familiar with the subject, (2) make a comprehensive survey and comparisons of different methods, and (3) sketch a vision for future work that can help motivate and guide readers that are interested in texture synthesis research. We cover fundamental algorithms as well as extensions and applications of texture synthesis.