Design strategy of curved-beam based metamaterial with unprecedented lateral deformation mode transition

Mechanical metamaterials exhibiting unconventional Poisson's ratios hold significant promise for applications in flexible electronics, impact protection, medical devices, and shape-shifting structures. However, achieving complex Poisson's ratio behaviors—particularly nonlinear and directional-switching responses under large deformations—remains a considerable challenge. This study introduces a class of variable-thickness curved-beam metamaterials (VCBMs) capable of exhibiting intricate nonlinear lateral displacement responses, including direction-reversing behaviors, under large tensile strains. To enable the customizable design of VCBM unit cells with complex Poisson's ratio profiles, an inverse design framework integrating neural networks (NN) and particle swarm optimization (PSO) is proposed. This framework facilitates the precise tailoring of VCBM unit cells with nonlinear, sign-switching force-lateral displacement curves and enables the development of spatially heterogeneous metamaterials with unprecedented lateral deformation transitions. As a case study, the framework is applied to create metamaterials that transition from a flat configuration to a dumbbell shape and subsequently to a vase-like form under uniaxial stretching. Both numerical simulations and experimental validations confirm the effectiveness of this approach, highlighting the unprecedented lateral displacement mode transitions under tensile loading. The proposed methodology lays the foundation for developing advanced reconfigurable metamaterials with versatile applications in mechanical systems, soft robotics, programmable materials, and medical devices.