Accelerated Search and Design of Stretchable Graphene Kirigami Using Machine Learning

Making kirigami-inspired cuts into a sheet has been shown to be an effective way of designing stretchable materials with metamorphic properties where the 2D shape can transform into complex 3D shapes. However, finding the optimal solutions is not straightforward as the number of possible cutting patterns grows exponentially with system size. Here, we report on how machine learning (ML) can be used to approximate the target properties, such as yield stress and yield strain, as a function of cutting pattern. Our approach enables the rapid discovery of kirigami designs that yield extreme stretchability as verified by molecular dynamics (MD) simulations. We find that convolutional neural networks, commonly used for classification in vision tasks, can be applied for regression to achieve an accuracy close to the precision of the MD simulations. This approach can then be used to search for optimal designs that maximize elastic stretchability with only 1000 training samples in a large design space of $\sim 4\times {10}^6$ candidate designs. This example demonstrates the power and potential of ML in finding optimal kirigami designs at a fraction of iterations that would be required of a purely MD or experiment-based approach, where no prior knowledge of the governing physics is known or available.

Figure 1

Schematic diagrams of a graphene sheet and rectangular graphene unit cells. Each of the grid (colored red) consists of $10\times 16$ rectangular graphene unit cells (colored green).

Figure 2

(a) Stress-strain plot of three representative kirigamis. Inset shows the “typical” kirigami cuts. (b) Yield stress as a function of yield strain for different configurations. Data are colored based on their cut density.

Figure 3

(a) Schematic of the neural network search algorithm. Average yield strains of the top 100 performers as a function of generations for kirigami with allowed cuts of (b) $3\times 5$ and (c) $5\times 5$. (d) Visualization of the top five performers of kirigami with $5\times 5$ allowed cuts in each generation. After the ninth generation, the top three performers remain constant. (e) A comparison between the top performing configurations found by the ML and the typical kirigami configurations with centering cuts. Note that the kirigami visualizations are not scaled to the real physical dimensions for clarity.