Physics-guided inverse design of energy-absorbing graded auxetic metamaterials via layer-wise decomposition and deep learning

Thickness-graded auxetic lattice metamaterials offer tunable energy absorption and superior crashworthiness, but their highly nonlinear deformation mechanics involving large strains, self-contact, and densification make large-scale design exploration computationally prohibitive. This work introduces a layer-wise decomposition framework that reconstructs the global mechanical response of functionally graded auxetic structures from quasi-independent single-layer contributions, reducing the required nonlinear finite element analyses from over 10,000 full-structure simulations to only 11 single-layer runs. The framework is validated against experimental compression tests on additively manufactured thermoplastic polyurethane (TPU) specimens, with errors below 3%. The resulting dataset underpins forward and inverse deep neural network (DNN) models for energy absorption prediction and optimal thickness-distribution identification. A physics-guided neural network (PGNN) is further developed by embedding a regression-derived thickness-energy relationship as a hard constraint in the loss function. PGNN achieves reliable extrapolation beyond the training domain with errors below 2.5%, and reaches stable convergence with only 10 training samples compared with 2145 required by the conventional DNN. The proposed framework establishes a computationally efficient and physically consistent approach for the inverse design of thickness-graded auxetic metamaterials, demonstrated here for the investigated enhanced re-entrant architecture and with potential for extension to other graded lattice configurations.