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Vinayak Krishnamurthy, Sai Ganesh Subramanian, Matthew Eng and Ergun Akleman (left to right) at the Association of Computing Machinery (ACM) Student Research Competition | Image: Dr. Vinayak Krishnamurthy
A recently discovered geometric shape found in animal skin cells is providing Texas A&M University researchers with a bio-inspired methodology for designing a wide array of engineered creations.
 
The interdisciplinary project to develop the shapes -- dubbed Delaunay Lofts by the researchers -- holds potential applications in a range of areas including architectural design, additive manufacturing, metamaterial design, heat transfer, air-flow control and education.
 
Dr. Vinayak Krishnamurthy, an assistant professor in the J. Mike Walker '66 Department of Mechanical Engineering, is leading the project alongside Dr. Ergun Akleman, a professor in the Departments of Visualization and Computer Science and Engineering.
 
Delaunay Lofts are inspired by a geometric shape called a scutoid, which enables animal skin cells to be watertight by slotting together to form a unified shape.
 
The recently published research by Krishnamurthy and Akleman explores the theories and algorithms needed to generate the Delaunay Lofts, as well as the geometric and topological principles that allow for the design of a potentially limitless variety of these types of shapes beyond what is known to occur in nature.
 
"By simply assembling several of these new interlocking shapes, several aesthetically pleasing and physically robust artifacts can be computationally designed and physically manufactured for mechanical structures, architectural tilings and educational puzzle purposes," said Krishnamurthy.
 
Akleman said he is particularly excited that the research enables fundamentals on how to better control the geometry of these shapes  --  a breakthrough important to both theoretical and practical implementations.
 
"We now have a theoretically sound and practically simple methodology
to search for desired shapes," Akleman said. "This is really useful since almost all engineering applications involve the identification of desired shapes."
 
Krishnamurthy said the space-filling properties of the Delaunay Lofts open up great potential for sturdy designs that look to nature for inspiration and provide a new tool with applications ranging from structural design to a new kind of bio-inspired building block toys for children.
 
"Most works on interlocking shapes in the past were performed purely by geometric reasoning," Krishnamurthy said. "Ours is the first to systematically apply geometric reasoning to create new classes of engineered products and systems based on biophysical phenomenon. To this end, our algorithm builds on the intuition for why scutoids occur in skin cells and shows that there many other shapes -- not just scutoids -- that can be constructed using our algorithm."
 
The team is continuing its research to explore the mechanical properties of these shapes and further investigate the physical properties of Delaunay Lofts and how structures using them might withstand stress, torsion and fatigue.
 
Their work is already making waves in engineering.
 
Recently, Krishnamurthy’s graduate student was awarded the first place at the Association of Computing Machinery (ACM) Student Research Competition organized by the ACM-SIGGRAPH 2019 conference for his work on Delaunay Lofts. SIGGRAPH is the premier research event in the area of geometric computing, computer graphics, animation, and computational fabrication and was held in Los Angeles July 28-Aug. 1, 2019. This research is now poised to compete in the ACM Student Research Competition grand finals across all ACM conferences in the country.