Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

Committee Chair/Advisor

Suyi LI

Committee Member

Atul Kelkar

Committee Member

Ardalan Vahidi

Committee Member

Oliver Myers


The emergence of mechanical metamaterials — which derive their properties primarily from the underlying architecture rather than the constituent material — has unleashed a new era of material design and functionalities. To fully materialize the promising potentials of metamaterials, it is crucial to develop versatile, scalable, and easy-to-fabricate methods that can both generate and tailor the underlying periodic architecture. To this end, we propose the use of kirigami — a popular recreational art of cutting and manipulating paper — as a platform to create periodicity and super-stretchability. Kirigami has become a design and fabrication framework for constructing metamaterials, robotic tools, and mechanical devices of vastly different sizes. In this dissertation, our target is to study the mechanical behavior --- mostly in the field of dynamics and kinematics--- of kirigami metamaterials and establish a framework for future studies. For the first time, our study focuses on wave propagation in a buckled kirigami sheet with uniformly distributed parallel cuts.
When we apply an in-plane stretching force that exceeds a critical threshold, this kirigami sheet buckles and generates an out-of-plane periodic deformation pattern that can change the propagation direction of passing waves. That is, waves entering the buckled Kirigami unit cells through its longitudinal direction can turn to the out-of-plane direction. As a result, the stretched kirigami sheet shows wave propagation bandgaps in specific frequency ranges. We have two approaches toward manipulating the bandgap, 1) Tuning the bandgap by controlling the stretching displacement to change the distribution of cross-section of area and distribution of moment of inertia inside of the periodic unit cell of kirigami metamaterial and 2) programming stretched kirigami material by intentionally sequencing its constitutive mechanical bits. Such sequencing exploits the multi-stable nature of the stretched-buckled kirigami, which allows each mechanical bit to settle into two stable equilibria with different shapes (aka. “0” and “1” states). Therefore, by designing the sequence of 0 and 1 bits, one can fundamentally change the underlying periodicity of the kirigami and thus program the phononic bandgap frequencies. To this end, our study develops an algorithm to identify the unique periodicities using “n-strings” consisting of n mechanical bits.

Author ORCID Identifier




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