Design and optimization of multi-material distribution on 3D parts

Abstract

Objects with varying materials offer remarkable flexibility for satisfying complex, application-specific requirements. This thesis focuses on understanding the mechanical behavior of such objects, aiming to design material distributions using a set of limited base materials that enable objects to achieve targeted positions under specified external forces. Despite numerous developments in physics-based modeling, material optimization as an inverse problem remains challenging.

Firstly, few frameworks are available that allow users to specify forces and displacements simply while ensuring the final solution is less dependent on initial conditions. Such instability often leads to inconsistent solutions. Secondly, traditional methods may fail to meet user-specified deformation requirements or produce scattering distributions when using a limited set of base materials for material optimization. A more compact material distribution is preferred, as the interfaces between different materials can introduce weaknesses during fabrication. Thirdly, designing material distributions using a set of given base materials is time-consuming. Such optimization problems can be considered discrete combinatorial optimization problems, which are difficult to solve with numerous variables. Moreover, the optimized results are highly sensitive to mesh resolution, making consistency difficult to achieve across different resolutions.

To address these challenges, this thesis introduces a comprehensive framework that incorporates geometric deformations into FEM optimization, reducing dependence on initial material assignments. To meet deformation accuracy requirements while promoting compact distributions, an L0-formulation is proposed to avoid explicit dithering of discrete materials, thus improving optimization performance and compactness. To enhance optimization efficiency using a set of base materials, a novel differentiable interpolation method is proposed through relaxation, significantly reducing optimization time while maintaining accurate deformation. Additionally, an improved material reduction method has been developed to mitigate the issue of resolution-dependent optimization results, ensuring more stable and consistent solutions across different mesh resolutions.

The research in this thesis has broad applications, such as designing customized shoes and chairs for personalized comfort, controlling tweezers for precise force application, and optimizing the deformation behavior of bridges under external forces. Moreover, this research provides insights into how the proposed methods can be further integrated with microstructure design to enhance control over object deformation using a single base material.