Homogenization-based topology optimization of auxetic honeycomb sandwich beams

While topology optimization has gained substantial popularity in recent times, its application in the design of functionally graded auxetic sandwich beams is still relatively limited. This study presents a topology optimization framework for the design of functionally graded auxetic honeycomb sandwich beams and systematically investigates their flexural behaviour, energy absorption characteristics, and deformation modes under three-point bending loading. To support the optimization process, expressions for the homogenized in-plane mechanical properties of honeycomb cellular materials with various microstructures maintained within a fixed unit cell confined space were derived analytically and validated experimentally. Topology-optimized, standard auxetic, and Poisson’s ratio-coupled hybrid sandwich beams were numerically modelled and comprehensively compared under identical relative density and boundary conditions. The topology-optimized sandwich beams demonstrate superior performance across all sandwich beams, achieving superior flexural stiffness, load bearing, and energy absorption capabilities while exhibiting a combined local-global deformation mode that engages a substantially greater number of unit cells compared to the predominantly localized deformation observed in standard beams. Von Mises stress analysis confirms broader spatial stress engagement and more efficient material utilization in the topology-optimized beams. Moreover, the hybrid sandwich beams outperform the standard sandwich beams in flexural and energy absorption properties. Unit cell orientation in standard beams and the relative positioning of unit cells in hybrid sandwich beams are identified as significant design parameters influencing flexural properties. These findings demonstrate that integrating an auxetic lattice core with topology optimization constitutes an effective and versatile strategy for designing lightweight sandwich structures with enhanced mechanical performance.