Unveiling dynamic bifurcation of Resch-patterned origami for self-adaptive impact mitigation structure

Abstract

A long-standing challenge in impact mitigation is the development of versatile and omnifarious protective structures capable of encompassing a wide spectrum of scenarios, for example, ranging from low-speed pedestrian impacts to high-speed vehicle collisions. However, most existing impact mitigation strategies rely on fixed geometries or pre-tuned material properties targeting specific impact speed, lacking the ability to adapt in real time. Here, we draw inspiration from origami to design impact mitigation structures that exhibit multi-modal and self-adaptive behavior. We introduce a Resch-patterned origami structure that hosts two distinctive deformation modes: a monostable folding mode and a bistable unfolding mode featuring snap-through. Impact experiments reveal a speed-dependent dynamic bifurcation, wherein the structure autonomously switches between folding and unfolding in response to the applied impact velocity. This dynamic bifurcation, intrinsically distinct from kinematic or static origami bifurcations, enables real-time selection of deformation pathways that enhance energy dissipation across a broad range of impact conditions. We further demonstrate the scalability and practical relevance of this mechanism by fabricating tessellations in a bumper-like configuration and evaluating their performance using a pendulum-based mannequin impact test. Together, these results establish dynamic bifurcation in origami-based structures as an adaptive impact mitigation strategy. This approach enables scalable and programmable protective systems that autonomously select deformation modes in real time, with broad relevance to adaptive robotics, smart protective armor, and aerospace damping technologies.

Figures (4)

• Figure 1: Hexagonal Resch origami and its folding motion. (a) Top and side views of the Resch origami folding. The dimension of the hexagonal Resch pattern is determined solely by the side length of the hexagon $a$. (b) Definition of height $h_{\rm c}$ and folding ratio $\gamma$. (c) Variation of normalized height $h_{\rm c}/a$ as a function of folding ratio $\gamma$. (d) Potential energy landscape and bifurcation diagram under out-of-plane load $P_z$. (e) Force-displacement and (f) Potential energy profile along the folding (blue) and unfolding path (red). Postures during deformation along (g) folding and (h) unfolding path.
• Figure 2: Dynamic bifurcation of Resch origami. (a) Drop tower configuration. The height of the impactor at (b) $v_{\rm impact}=2.0$ m/s, (c) $2.5$ m/s, and (d) $3.0$ m/s. The inset figures of each panel schematically display the folding mode that Resch origami follows. (e) Histogram of folding, unfolding, and snap-through as a function of impact speed. Deformation sequence of the Resch origami in the experiment undergoing (i) contact, (ii) subduction, and (iii) fold/unfold phases when (f) $v_\mathrm{impact}=2.0$ m/s and (g) $3.0$ m/s. (h) Numerically estimated radial force exerted on the outer hexagons during the subduction phase. Sub-panels correspond to the subduction displacement in (top) $v_{\rm impact}=2.0$ and (bottom) $3.0$ m/s cases. (i) Subduction displacement as a function of impact speed. (j) Coefficient of restitution as a function of impact speed. Blue open-square symbol, folding mode; orange open-square symbol, unfolding mode; red open-square symbol, snap-through mode; black cross symbol, EPS.
• Figure 3: Dynamic bifurcation of multi-orbit tessellation. Crease patterns of (a) 3-orbit and (b) 4-orbit tessellations with the definition of partial and full snap of vertices. (c) Impactor with a hemispherical head. Histograms of (d) response type and (e) number of snapped vertices, and (f) map of snapped vertex locations for the (top) 3- and (bottom) 4-orbit tessellations ($D_\mathrm{impactor}=40$ mm). (g-i) The same for the impactor size of (top) $D_\mathrm{impactor}=20$ mm and (bottom) $D_\mathrm{impactor}=80$ mm (3-orbit tessellation). (j) Effect of $N_\mathrm{orbit}$ with $D_\mathrm{impactor}=40$ mm. (k) Effect of $D_\mathrm{impactor}$ with $N_\mathrm{orbit}=3$.
• Figure 4: Large-scale Resch-patterned impact mitigation system. (a) Pendulum-based experimental set-up. (b) Magnified view of components and pendulum angle $\psi$. (c) Laser-cut rectangular Resch origami tessellation (PET). (d) Definition of folding ratio $\gamma_{\mathrm{rect}}$. (e) Snapshot of Resch origami in bifurcating configuration at (top) $\psi_0=15^\circ$ for low impact speed and (bottom) $\psi_0=30^\circ$ for high impact speed. (f) Histogram of folding and snap-through as a function of impact speed. (g) Average number of snapped vertices per trial (standard deviation shown as error bars). (h) Location of snapped vertices. (i) Coefficient of restitution. (j) Peak force measured by the force sensor embedded in the mannequin.