Surrogate-assisted inverse design of irregular elliptical perforated metamaterials with target nonlinear stiffness

The inverse design of irregular elliptical perforated metamaterials with prescribed nonlinear stiffness is challenging due to nonlinear and non-unique geometry-response mappings induced by pore geometry, buckling, and contact. This study develops a surrogate-assisted framework combining automated finite element method (FEM) simulations, a deep neural network (DNN) surrogate, and an evolutionary algorithm (EA). A periodic unit cell with four independent elliptical holes is parameterized by 12 geometric variables, and a 30 000-sample dataset is constructed using stratified Latin hypercube sampling with geometric feasibility filtering. The stress–strain curves are interpolated, standardized, and compressed into an 8-dimensional principal component analysis representation for DNN training. The responses are classified into linear, decreasing, increasing, and S-type stiffness modes, revealing the effects of ligament rotation, microbeam buckling, pore-wall contact, and densification. Partial dependence analysis shows that semi-axis parameters mainly control stiffness magnitude, whereas pore orientations affect nonlinear characteristics. For inverse design, the trained DNN is coupled with database-seeded EA search to generate ranked candidate pools, followed by nonlinear FEM verification. Validation on 19 targets confirms that diverse nonlinear stiffness responses can be reproduced within the sampled response envelope.