Nonlinear performance analysis and rapid prediction of out-of-plane deformation in graded honeycombs

Honeycomb structures, known for their excellent properties, are widely used in various advanced applications, including adaptive mirrors and soft wearable devices, due to their out-of-plane deformation capabilities. However, predicting the out-of-plane deformation of graded honeycombs remains challenging. A novel approach for rapidly predicting the out-of-plane deformation of graded honeycombs, considering their isotropic and nonlinear behavior, is presented in this study. Discrete material property spaces for seven honeycomb types were derived using a stiffness-updating nonlinear homogenization method and validated through digital image correlation (DIC) experiments. Prediction of nonlinear equivalent properties within two seconds was achieved by utilizing a hyperparameter optimization neural network (HONN). Graded honeycomb connection criteria (GHCC) were established to ensure performance stability. A rapid and accurate prediction method was enabled by the developed deformation-to-color mapping, which effectively bypasses costly numerical computations. Out-of-plane deformation is accurately forecasted by this approach, which also facilitates the transformation of flat surfaces into various shapes with distinct Gaussian curvatures, thereby opening new possibilities for large-scale deformable structures.