PyKirigami: An interactive Python simulator for kirigami structures

TL;DR

PyKirigami, a lightweight, open-source Python framework for the efficient deployment simulation of kirigami structures, serves as a fast kinematic prototyping tool for kirigami structures, allowing researchers to verify deployment mechanics and self-contacts prior to performing detailed mechanical analysis or physical fabrication.

Abstract

In recent years, the concept of kirigami has been used in creating deployable structures for various scientific and technological applications. While high-fidelity Finite Element Analysis (FEA) is the standard for analyzing stress distributions and material deformation, it is computationally intensive and often ill-suited for the rapid exploration of vast kinematic configuration spaces. In this work, we develop PyKirigami, a lightweight, open-source Python framework for the efficient deployment simulation of kirigami structures. Unlike continuum mechanics solvers, PyKirigami models tessellations as articulated rigid-body networks, allowing for the real-time simulation of global deployment trajectories and volumetric transformations. The tool incorporates collision detection and interactive actuation, enabling users to validate folding paths and identify geometric locking states in both 2D and 3D topologies. This framework serves as a fast kinematic prototyping tool for kirigami structures, allowing researchers to verify deployment mechanics and self-contacts prior to performing detailed mechanical analysis or physical fabrication.

Figures (17)

• Figure 1: An overview of PyKirigami.a, The computational framework of PyKirigami. b, Using PyKirigami, one can easily simulate the deployment process of different kirigami structures in 2D (top) and 3D (bottom).
• Figure 2: Tile construction and connections in PyKirigami.a, An illustration of the vertex coordinates encoded in the input file via --vertices_file. Here, note that different tiles may contain different number of vertices. b, Geometric construction of the 3D kirigami tiles. (Left) The original polygonal tile $\mathcal{T}_i$, with the dotted arrow showing its normal vector. (Right) The 3D tile geometry constructed by extruding $\mathcal{T}_i$ along its normal vector. Here, the thickness of the tile can be prescribed by the user. c, Three different types of inter-tile connections in PyKirigami. (Top) Spherical joint applied to tiles $\mathcal{T}_{i}$ and $\mathcal{T}_{j}$ such that the rotational degree of freedom equals $3$. (Middle) Hinge joint such that the rotational degree of freedom equals $1$. (Bottom) Fixed joint applied to $\mathcal{T}_{i}$ and world frame such that the object is totally fixed. The arrow represents the rotational degree of freedom.
• Figure 3: Examples of 2D and 3D kirigami deployment achieved by PyKirigami.a, The 2D deployment of the square-to-circle kirigami structure achieved by PyKirigami with automated radial expansion, stabilized by environmental forces. b, The 2D deployment of the compact reconfigurable kirigami model produced by PyKirigami. c, The 2D-to-3D deployment of the square-to-spherical-cap kirigami model achieved by PyKirigami, driven by the target-based force algorithm. d, The 3D-to-3D deployment and reconfiguration of the cylinder kirigami model achieved by PyKirigami, showcasing volumetric shape control.
• Figure 4: Quantitative validation of PyKirigami using the rectangular tessellation kirigami structure. The plot shows the maximal and mean vertex error versus the deployment angle $\theta$. Insets show a comparison of the simulated geometry (gray solid) against the theoretical trajectory (red wireframe) at two points. The left inset shows tessellation at the maximum deviation ($\theta\approx 0.04$) with the magnified view highlighting the drift. The right inset displays the fully deployed state, in which the error is negligible.
• Figure 5: Quantitative validation of PyKirigami using the square-to-disk kirigami structure. Here, we plot the global radius $R$ versus the deployment angle $\theta$ for both the simulations obtained by PyKirigami (red dots) and the analytical result by dudte2023additive (blue solid line). The PyKirigami simulation data align closely with the analytical prediction, confirming that the solver captures the correct kinematic mode. The insets show four snapshots from the simulation.