Nonlinear Buckling Analysis and Energy Absorption Characteristics of a Bi-layer Cascaded Shell Metamaterial with Semi-rigid Boundaries

To address the conflict between high load-bearing capacity and smooth energy absorption in protective structures, this study proposes a novel bi-layer cascaded metamaterial consisting of a rigid Polylactic Acid (PLA) substrate and hard Thermoplastic Polyurethane (TPU) truncated conical shells. A full-scale three-dimensional numerical model was established to investigate its nonlinear response mechanism under axial compression. The simulation results reveal a distinct sequential buckling mechanism, which effectively mitigates the theoretical elastic peak load while maintaining a high plateau-to-peak force ratio. To accurately predict the mechanical response, a physically-based modified analytical model based on curved beam theory is developed. Considering the non-ideal constraints in engineering applications, a boundary rotational stiffness correction factor (η ≈ 0.51) is derived based on structural stability theory to account for the semi-rigid boundary effect caused by the synergistic deformation of the substrate. Furthermore, a delayed linear support term, activated at the onset of structural densification (approximately half of the shell height), is introduced to characterize the post-collapse stiffness dominated by substrate bending. The modified analytical predictions show good agreement with numerical results, validating the proposed mechanical framework. The structure exhibits a specific energy absorption (SEA) of approximately 25 J/g, demonstrating significant potential for impact protection applications requiring both force-limiting capabilities and high energy dissipation.