Controlling the snap-through behavior of kirigami arches

TL;DR

The paper addresses snap-through stability in clamped-clamped kirigami arches under midspan vertical load $P$ and varying support spacing $B$. It introduces a simple two-parameter symmetric cut pattern and analyzes stability via numerical continuation and experiments across different $B$ values. The study reveals that cut patterns can either trigger different bifurcation modes (limit-point or symmetry-point) or suppress stability loss altogether, achieving monotonic monostability for certain configurations. The results provide actionable design rules for tunable stability in kirigami-inspired deployable structures and energy-absorbing devices, with future work aimed at optimizing geometry for targeted stability characteristics.

Abstract

This work examines the snap-through behavior of clamped-clamped kirigami arches made from initially flat, thin, cut sheets under increasing vertical concentrated load acting at midspan. A two-parameter, symmetric pattern is introduced to conduct a numerical parameter analysis across three different support distances. When the support distance is one-quarter of the total length of the sheet, the structure loses stability at a symmetry point bifurcation over a wide range of parameters. Additionally, there exists a small range of parameters where limit point bifurcation occurs. In this case, the cuts can induce symmetry in the stability loss. For larger support distances (half or three-quarters of the total length), limit point bifurcation occurs only for small cuts, and there is a range of cut parameters that leads to monotonic monostability, indicating that no stability loss occurs. These findings are supported by experimental data. Overall, our research demonstrates that carefully designed cut patterns can either control the mode of stability loss in kirigami arches or suppress it entirely.

Figures (10)

• Figure 1: a) Illustration of the cut pattern and its parameters $a$ and $b$. Dark grey regions are considered to be stress-free, and they are neglected in the calculation of the effective moment of inertia of the sheet. b) Mechanical model of the structure. The dashed thick line is the inverted shape after snap-through. c) Three-dimensional visualization of the structure in the initial state ($P=0$) and after snap-through ($P>P_{crit}$).
• Figure 2: Schematic load-height diagram visualizing a limit point bifurcation. Red and black denote the unstable and stable points, respectively.
• Figure 3: Critical value of the load in terms of the pattern parameters $a$ and $b$. a) For $B=0.25L$, all the patterns lead to stability loss. b) In case $B=0.5L$, there is no stability loss in the white region. c) In case $B=0.75L$, there is no stability loss in the white region.
• Figure 4: Shaded illustration of equilibrium surfaces for different $a$ parameters (rows) and $B$ support distances (columns). Grey and red colors correspond to stable and unstable states, respectively.
• Figure 5: $P-H$ diagrams for different support distances (rows). The length of the cut, $a=0.5$, was kept constant, and only the width, $b$, changed (columns). Black and red correspond to stable and unstable configurations, respectively.