Functionally varied negative-stiffness metamaterial core sandwich structures with three-phase bending deformation

This paper introduces a novel class of negative-stiffness (NS) core sandwich composite structures that exhibit unique mechanical performance, including shape recovery, superelasticity, and energy absorption (EA) in bending and shear mode. The core of these structures consists of a periodic cellular arrangement of double-curved beams that undergo consecutive local snap-buckling transitions between multiple equilibrium states, enabling the structures to change shape reversibly between their initial and deformed configurations. To characterize the force-displacement relationship of the core, a comprehensive analysis was conducted using a combination of 3D printed models and finite-element simulations. The metamaterial core with gradient-thickness negative-stiffness beams were examined under uniform compression, demonstrating that the snap-through behavior of the curved beams was intricately controlled by the beam thickness in each row. The numerical simulations accurately predicted the deformation characteristics of the graded cellular core, supporting the design of a metamaterial core with functionally varied beam thickness for nonuniform transverse loading. This led to spatially controlled NS core material with specific EA of around 50 J kg⁻¹ and an apparent core shear strength of 0.1 MPa, all mainly within the reusable elastic regime. The resulting sandwich structures efficiently mitigated the localized effect from concentrated compressive forces and achieved complete snap-through buckling in all curve beams. Three-point bending response revealed three distinct phases of flexural deformation: the local facial bending phase, the sequential core-snapping superelastic phase, and the global bending phase.