Corner-Sharing Tetrahedra for Modeling Micro-structure.

Area of Science:

• Computational geometry
• Materials science
• Computer-aided design

Background:

• Micro-structure design is crucial for material properties.
• Existing methods can be complex and lack integrated structural guarantees.
• Representing micro-structures within complex geometries poses challenges.

Purpose of the Study:

• Introduce Corner-Sharing Tetrahedra (CoSTs) as a new micro-structure representation.
• Demonstrate CoSTs' capability for designing regular and irregular micro-structures at multiple scales.
• Enable efficient local operations for design, analysis, and property adjustment.

Main Methods:

• Developed a minimalist, constraint-graph representation using CoSTs.
• Utilized local graph manipulation for accessing and modifying the micro-structure space.
• Integrated geometric and material details locally and on-demand.

Main Results:

• CoSTs provide built-in structural guarantees like connectivity and minimal rigidity.
• The CoSTs space is fully accessible via local operations.
• Efficient local operations facilitate analysis and adjustment of static physical properties.

Conclusions:

• CoSTs offer a powerful and flexible framework for micro-structure design.
• The method supports multi-scale design within curved objects.
• CoSTs are suitable for applications requiring detailed geometric and material properties, such as additive manufacturing.