A constructive framework for discovery, design, and classification of volumetric Bravais weaves

Area of Science:

• Materials Science
• Mathematics
• Mechanics

Background:

• Planar weaves (2D) are well-studied, but systematic design frameworks for 3D volumetric weaves are lacking.
• Current 3D weave design is often ad hoc, relying on stacking 2D weaves with simple connections.
• Volumetric weaves are crucial for advanced applications like composite materials.

Purpose of the Study:

• To establish a formal framework for representing and designing volumetric weaves in 3D space (R^3).
• To introduce and analyze a new class of weaves called volumetric Bravais weaves.
• To demonstrate the potential for expanding the design space of 3D weaves.

Main Methods:

• Defined volumetric weaves using the isometries of Bravais lattices and their Voronoi cells in R^3.
• Analyzed cubic primitive weaves (cP-weaves) as a specific example within the volumetric Bravais weave framework.
• Showcased systematic generation of cP-weaves using lattice and cube isometries.

Main Results:

• Developed a structured description of the design space for volumetric Bravais weaves.
• Demonstrated that cP-weave structures naturally arise from 3D lattice isometries.
• Found the space of cP-weaves to be significantly larger than conventional 2D weaves.

Conclusions:

• The proposed framework provides a systematic approach to designing volumetric weaves.
• Volumetric Bravais weaves offer a rich design space with potential for novel material properties.
• This work lays the foundation for exploring and utilizing complex 3D woven structures.