Fig. 1: Schematic diagram of the physics-aware differentiable design of kirigami.
From: Physics-aware differentiable design of magnetically actuated kirigami for shape morphing
a Compact state (left) of a regular quadrilateral kirigami and its deployed state (right) transformed from the regular compact kirigami following a geometrically feasible path. The repeated four-panel unit cell is shaded in blue, where the arrow shows the magnetization orientation of each panel. b Geometrical compatibility requirements for a four-panel cell in edges (equal-length pairs connected by red curved arrows) and angles around the center node (red sectors). c Torque induced by the applied magnetic field (blue curved arrow) and the mechanical forces/torques induced by deformation (red curved arrows) are required to be in equilibrium for a physically feasible deployed state. d The target deployed state (right) is conformally mapped from the deployed kirigami in Fig. 1a to achieve predetermined shapes (red dashed circular contour as an example) under the magnetic field \({{{{{\bf{B}}}}}}\). However, there is no compact state (left) that can follow a geometrically and physically feasible path to this mapped deployed state. e Compact state (left) and deployed state (right) of the kirigami optimized from the conformally mapped design in Fig.1d, satisfying both physical equilibrium and geometrical compatibility. f This physics-aware optimization integrates two models, the differentiable kinematic model (top) and the differentiable energy model (bottom) under a fixed external magnetic field. The enlarged inset shows the equivalent nonlinear springs for kirigami hinges. The optimization process achieves physical equilibrium by ensuring minimal energy of the deployed kirigami indicated by zero gradients.
