Tuning the layout of elasticity in materials opens new opportunities to add various functionalities into a system, ranging from load-enduring capacity and shape-morphing capability in aeronautics to self-foldability and controlled diffusion rates in drug delivery applications. Recently, the Japanese art of paper cutting technique called kirigami has positioned itself as a simple yet powerful strategy to program unique functionalities into intrinsically inextensible, stiff materials without adjusting chemical compositions, including elastic softening, creation of complex 3D structures, and extreme stretchability. Thus, various applications have been realized by utilizing the kirigami principle. These applications include wearable electronics, sensors, stretchable lithium batteries, solar trackers, and reconfigurable structures. However, coupling the primary geometric deformation modes (i.e., bending and rotation) in kirigami films to control mechanical response as well as electronic properties (e.g., shift in resonant frequency) have been limited. In this thesis, we present a strategy where the inclusion of carefully designed cuts allows for fine tuning of mechanical and electronic properties of materials.

Starting from fundamentals of kirigami mechanics, we show that stiffness tunability and deformability of kirigami structures are signicantly infuenced by the addition of minor cuts adjacent to major cuts. The dimension and position of minor cuts relative to major cuts determines geometric deformation modes between bending of beams and hinge rotations, which results in high tunability of mechanical properties. The experimental results are validated by beam mechanics with different boundary conditions (Chapter 2). The sensors for human activity monitoring and soft robotic systems require considerable extents of deformation. Furthermore, reducing or eliminating wiring components allows for more compliant and less complex systems by excluding semirigid wiring or connection points. We create a kirigami-inspired passive resonant sensor where the deformation normal to the planar surface changes the capacitance, inductance, and resonant frequency. This study demonstrates that the device allows for accurate measurements of large deformations (> 10X sensor thickness) in both air and water media (Chapter 3).