Customizing and optimizing lattice materials poses a challenge to designers. This study proposed a data-driven generative method to customize and optimize lattice material. The method utilizes subdivision modeling to parametrically describe lattice morphologies and skeletons. Next, the homogenization method is employed to analyze elastic moduli for collecting a dataset. Then, a two-tiered machine learning (ML) framework is proposed to predict the elastic modulus for a forward design. The first-tier model employs polynomial regression to estimate relative density, which serves as an additional input feature for the second-tier model. The prediction accuracy of the second-tier model is improved through the additional inputs. The forward and reverse design strategies offer a flexible and accurate means of tailoring lattice properties to meet specific performance requirements. Two case studies demonstrate the practical value of the framework: customizing a lattice material to achieve a desired elastic modulus and optimizing the mechanical performance of lattice materials under relative density constraints. The results show that the prediction accuracy of the elastic modulus using the two-tiered ML model achieved an error of less than 10% compared to finite element analysis, demonstrating the reliability of the proposed approach. Furthermore, the optimization design achieved up to a 25% improvement in mechanical performance compared to conventional lattice configurations under the same relative density constraints. These findings underscore the advantages of combining generative design, machine learning, and genetic algorithms to navigate complex design spaces and achieve enhanced material performance.

In response to the increasing demand for high-performance capacitors, with a simultaneous emphasis on minimizing their physical size, a common practice involves etching deep vias and coating them with functional layers to enhance operational efficiency. However, these deep vias often cause warpages during the processing stage. This study focuses on the numerical modeling of wafer warpage that occurs during the deposition of three thin layers onto these vias. A multi-step mechanical and thermal homogenization approach is proposed to estimate the warpage of the silicon wafer. The efficiency and accuracy of this numerical homogenization strategy are validated by comparing detailed and homogenized models. The multi-step homogenization method yields more accurate results compared to the conventional direct homogenization method. Theoretical analysis is also conducted to predict the shape of the wafer warpage, and this study further explores the impact of via depth and substrate thickness.