CAREER: Designing Vector Field Flows for Computational Knitting and Curved Layer 3D Printing

Computational fabrication via technologies such as 3D printing and computational knitting are key methods that form a significant part of modern advanced manufacturing, allowing for production of state-of-the-art composites, ceramics, medical grafts, and architectural formworks in complex geometries. Furthermore, recent advances have allowed for curved layer fabrication, producing objects and materials that have superior strength and quality characteristics due to control over build direction. Underlying many of these technologies is the fundamental problem of constructing a surface or volume from a single continuous curve, representing a toolpath or fiber path. To maximize utilization of these technologies, the research team will produce mathematical design frameworks for solving this problem under various fabrication modalities. The frameworks will be tailored to achieve domain-specific performance goals and accommodate domain-specific user design constraints. All resulting tools will be released as open-source implementations for use and further development by industry and academic researchers. Parts of the research will also be incorporated into coursework on geometry processing and graphics, and into graduate- and undergraduate-level research projects, via theses and summer research programs. The research effort will be divided into three thrusts. First, the team will build upon prior work understanding the global topology of vector field flows on surfaces and construct an appropriate discretization and optimization framework that achieves the necessary path continuity and spacing constraints crucial to the fabrication modalities at hand. Second, the work will more closely explore application of the general optimization framework to the specific use case of computational knitting, where the space-filling curve follows the path of stitches that are produced by the machine. In this setting, the team will explore optimal geometric shaping, and incorporation of user design constraints as communicated by industry partners, who are using these methods to produce garments and curved surface composites. Thirdly, the team will look to extend the topological understanding and optimization frameworks to the challenging volumetric setting. This will target the nascent fabrication methodology of curved-layer 3D printing. The global topologies for volumetric fields are much more complex, and not yet fully understood from the theoretical perspective. Incorporation of structural and manufacturing constraints into layer design will also be considered, in collaboration with engineering colleagues. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2543971 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT,01002930DB NSF RESEARCH & RELATED ACTIVIT,01003031DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Edward Chien | Institution: Trustees of Boston University, BOSTON, MA | Award Amount: $400,823 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2543971 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2543971.html