Advancing programmable metamaterials through machine learning-driven buckling strength optimization.

• Buckling strength of metamaterial is designed by deep learning and improved compared with benchmark models, validated by 3D printing and compression testing. • The optimization proceeds to transition in dominant buckling mode from in-plane to out-of-plane deformation, converging the eigenvalue of 2nd mode to 1st mode. • The mechanism of superior buckling strength shows that thickness of horizontal beam does not significantly affect buckling strength and post-buckling behavior. Metamaterials are specially engineered materials distinguished by their unique properties not typically seen in naturally occurring materials. However, the challenge lies in achieving lightweight yet mechanically rigid architectures, as these properties are sometimes conflicting. For example, buckling strength is a critical property that needs to be enhanced since buckling can cause catastrophic failure of the lightweight metamaterials. In this study, we introduce a generative machine learning based approach to determine the superior geometries of metamaterials to maximize their buckling strength without compromising their elastic modulus. Our results, driven by machine learning based design, remarkably enhanced buckling strength (over 90 %) compared to conventional metamaterial designs. The simulation results are validated by a series of experimental testing and the mechanism of the high buckling strength is elucidated by correlating stress field with the metamaterial geometry. Our results provide insights into the interplay between shape and buckling strength, unveiling promising avenues for designing efficient metamaterials in future applications. [ABSTRACT FROM AUTHOR]