Inverse design of adaptive flexible structures using physical-enhanced neural network

Traditional design and analysis of mechanical metamaterials are complex and time-consuming, owing to their nonlinear characteristics. This paper proposes a computationally efficient inverse design framework to predict the nonlinear strain–stress response considering the buckling behaviour under a tensile load. Design and simulation processes of the structures are based on the reduced order model (ROM) of flexible structures, all within a single software environment, MATLAB/Simscape, using the flexible beam blocks. The physical-enhanced neural network (PENN) design is implemented in MATLAB, utilising the results of the ROM model for training and testing. The ROM model takes 4.5 min on average on a 12-core CPU, whereas the trained PENN predicts the stiffness curve in a fraction of a second on a single-core CPU. After training the model, it was utilised to inverse design the metamaterial structure based on a desired stiffness response. Evolutionary optimisation is employed to iteratively feed various structural parameters into the model to find the optimised parameters of a metamaterial structure that can achieve the desired strain–stress response. The proposed metamaterial structure was experimentally validated through three-dimensional (3D) printing using flexible thermoplastic polyurethane (TPU) filament, demonstrating the efficiency and effectiveness of the proposed methodology.