Multi-fidelity sequential optimisation method for metamaterials with negative Poisson's ratio

Negative Poisson's ratio (NPR) metamaterials exhibit outstanding advantages in load-bearing, energy absorption, and buffering, with broad prospects for applications in aerospace, shipbuilding, and related fields. However, the highly nonlinear performance-parameter relationship of NPR metamaterials makes the optimisation design targeting special mechanical properties challenging and time-consuming. This paper proposes a multi-fidelity constrained sequential optimisation method based on the lower-confidence-bound criterion (MF-CLCB) for NPR metamaterials. It simultaneously considers the optimal prediction of Poisson's ratio and the precision of the stress and modulus constraint boundaries during optimisation. It adaptively updates the metamaterial parameters and the simulation fidelity based on their contribution to NPR improvement, effectively balancing the accuracy and time cost. Specifically, the optimisation was conducted for an NPR metamaterial with an eccentrically symmetric chiral structure. The structure was parametrically modelled and two fidelity analysis models of the metamaterial were established through finite element simulations and experimentally validated. The MF-CLCB method was then applied to the optimisation of this NPR metamaterial, yielding a design that satisfies required constraints and achieves a promising NPR. The optimised design was prepared for fabrication and experimentally verified for its superiority, demonstrating a 13.28% improvement in the target Poisson's ratio compared to the initial design.