Diffusive kinks turn kirigami into machines

Kinks, boundaries between distinct material configurations, are crucial in mechanical metamaterials for functionalities like logic, shape-changing, and locomotion. Existing kink propagation mechanisms rely on inertia or external loads, limiting applications in overdamped systems. This research investigates the emergence of propagating kinks in purely dissipative kirigami, inspired by the sequential folding of *Mimosa Pudica*. The authors hypothesize that by combining the shape-morphing capabilities of kirigami with the dynamic response of viscoelastic polymers, they can engineer a synthetic analog of this diffusive kink. The study's importance lies in extending the understanding and application of kinks beyond inertia- or load-driven mechanisms, opening avenues for novel soft robotics and material design in various fields including poroelasticity, colloidal assemblies, and microfluidics.

The paper reviews existing work on kinks in materials science, spanning various scales from ferroelectrics and shape-memory alloys to flexible metamaterials. It highlights the use of beams, kirigami, hinged mechanisms, and inflatable structures in creating metamaterials with controlled kink motion for tasks like logic and locomotion. However, the reliance on inertia or external loading for kink propagation is noted as a limitation. The authors contrast this with the naturally occurring diffusive kink observed in *Mimosa Pudica*, where sequential folding is attributed to a reaction-diffusion process. This biological example serves as inspiration for the development of synthetic analogs exhibiting similar diffusive kink behavior.

The researchers employ a multi-texture viscoelastic kirigami design, utilizing two 3D-printable photopolymers (Agilus and TangoPlus) with different viscoelastic properties. These materials are strategically patterned within the kirigami unit cells to control buckling modes in response to loading rates. At low rates, the kirigami buckles symmetrically; at high rates, anti-symmetrically. This tunable buckling is explored through experimental stress-strain curves and high-speed imaging. Viscoelastic snap-back, a gradual transition from the high-speed anti-symmetric to the low-speed symmetric mode, is observed and quantified using 3D tracking techniques. A viscoelastic von Mises truss model is developed to capture this snapping behavior, with a dimensionless equation of motion derived to quantify the influence of material properties, geometry, and imperfections. This model is extended to a one-dimensional strip of unit cells, resulting in a reaction-diffusion equation describing the propagation of diffusive kinks. Finite element method (FEM) simulations using Abaqus are employed to model the kirigami's nonlinear behavior, including the effects of geometric imperfections inherent in 3D printing. Experimental validation is performed by creating and testing kirigami strips, observing and quantifying the propagation of diffusive kinks through high-speed imaging and strain measurements. The experimental setup includes a custom-made test bench for controlled stretching speeds.

The key findings include the experimental observation and theoretical modeling of diffusive kinks in viscoelastic kirigami. The authors demonstrate that the buckling mode of the kirigami is tunable by controlling the loading rate. The viscoelastic snap-back phenomenon is identified and modeled, showing a transition from a metastable high-speed mode to a stable low-speed mode. A reaction-diffusion equation is derived from a viscoelastic von Mises truss model, predicting the emergence of diffusive kinks. FEM simulations confirm the propagation of these kinks, influenced by geometric imperfections. Experimental results show the successful creation and observation of diffusive kinks in kirigami strips, traveling at a constant velocity. The velocity of the kink is shown to be related to the energy difference between the up-state and down-state. The authors also demonstrate that the diffusive kink can be externally triggered by applying a load, mimicking the *Mimosa Pudica* response. Finally, the functionalities of the diffusive kinks are showcased through applications such as sensing, dynamic 2D shape morphing (from a “plus” to a “minus” sign), object transport, and manipulation using integrated arm-links, grippers, and paddles, illustrating the potential of these kinks to perform basic mechanical tasks.

The findings address the research question by demonstrating the feasibility of creating and harnessing diffusive kinks in synthetic materials. The significance lies in the development of a new mechanism for creating propagating kinks, independent of inertia or external continuous loading. This opens up new possibilities for designing materials with dynamic, adaptive functionalities. The ability to mimic the slow, sequential motion of biological systems, such as *Mimosa Pudica*, adds a valuable concept to soft robotics, offering potential for energy-efficient and bio-inspired designs. The applications demonstrated – sensing, shape morphing, and object manipulation – showcase the versatility of this approach, suggesting broader applicability in various fields.

This research successfully demonstrates the creation and utilization of diffusive kinks in viscoelastic kirigami. The ability to control and harness these kinks for basic mechanical tasks opens new avenues in soft robotics and adaptive materials. Future research could explore the use of materials with even greater viscoelastic contrast to enhance the robustness and functionality of diffusive kink-based machines. Investigating more complex kirigami designs and exploring applications in other fields like microfluidics and bio-inspired systems are promising future research directions.

The current study focuses on relatively simple kirigami designs and limited functionalities. The forces generated by the kirigami are bounded by the material properties used. While geometric imperfections are leveraged, their precise control and reproducibility could be improved. Further investigations into the effects of various geometric parameters and material properties could lead to a more comprehensive understanding and optimization of diffusive kink propagation.