Date of Award

Fall 2017

Project Type


Program or Major

Mechanical Engineering

Degree Name

Master of Science

First Advisor

Yaning Li

Second Advisor

Igor Tsukrov

Third Advisor

Christine Ortiz


Topological interlocking is an effective joining approach in both natural and engineering systems. Especially, hierarchical/fractal interlocking were 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 and without adhesive layers were designed for different number of iterations N. Theoretical contact mechanics model was used to capture the deformation mechanisms of the fractal interlocking with no adhesive layers under relatively small deformation. Then finite element (FE) simulations were performed to study the mechanical behavior of fractal interlocking under finite deformation. The designs were also fabricated via a multi-material 3D printer (Objet Connex 260) and mechanical experiments were performed to further explore the mechanical performance of the new designs.

It was found that the load-bearing capacity of Kotch fractal interlocking can be effectively increased via fractal design. In general, when the fractal complexity (it is specifically represented as number of hierarchy N in the present Koch fractal design) increases, the stiffness of the fractal interlocking will increase significantly. Also, when N increases, the stress are more uniformly distributed along the fractal boundary of the top and bottom pieces of the fractal interlocking, which efficiently reduce local stress concentration, and therefore the overall strength of the interlocking also increases.

However, the mechanical responses of fractal interlocks are also sensitive to imperfections, such as the gap between the interlocked pieces and the rounded tips. When fractal complexity increases, the mechanical properties will become more and more sensitive to the imperfection and eventually, the negative influences from imperfection can even become dominant. Therefore, considering the imperfection, there is an optimal level of fractal complexity to reach the maximum mechanical performance. This result is in consistent with fractal interlocks in different biological systems.

Except topology, the influences of friction, material properties and damage evolution, and the adhesive layer on the mechanical performance of Koch fractal interlocking were also evaluated via non-linear FE simulations and mechanical experiments on 3D printed Koch interlocking specimens. It was found that the adhesive layer can significantly improve the load transmission of the fractal interlocking and therefore can effectively amplify the interlocking efficiency.