Mechanical Modeling of Fractal Interlocking

Topological interlocking is an effective joining approach in both natural and engineering systems. Especially, hierarchical/fractal interlocking are found in many biological systems and can significantly enhance the system mechanical properties. Inspired by the hierarchical/ fractal topology in nature, mechanical models for Koch fractal interlocking were developed as an example system to better understand the mechanics of fractal interlocking. In this investigation, Koch fractal interlocking with different number of iterations N were designed. Theoretical contact mechanics model was used to analytically capture the mechanical behavior of the fractal interlocking. Then finite element (FE) simulations were performed to study the deformation mechanism of fractal interlocking under finite deformation. It was found that by increasing the number of iterations, the contact area increases and the interlocking stiffness and strength also significantly increase. The friction coefficient of contact plays an important role in determining the mechanical properties of fractal interlocking.