Comparative Numerical Analysis of Energy Absorption in Semi-Concave Reentrant, Hexagonal, and Trapezoidal Auxetic Cores

This work introduces a semi-concave reentrant (SCR) auxetic metamaterial, alongside trapezoidal and hexagonal honeycomb architectures, designed through systematic lattice configuration and geometric parametric control, and subsequently extended into sandwich panel structures. Initially, the mechanical behavior of the unit cell was investigated through theoretical derivation using Castigliano’s second theorem, providing foundational insight into deformation mechanisms and energy absorption (EA) potential. Building on this theoretical framework, detailed finite element simulations were performed on larger lattice assemblies to evaluate their compressive response, deformation patterns, and EA characteristics under both in-plane and out-of-plane loading. The transition from conventional hexagonal topology to SCR geometry was achieved by introducing inward-inclined cell edges, effectively producing a semi-concave auxetic configuration. Geometric relationships and relative densities of each lattice type were systematically established. Simulation results indicate that trapezoidal lattices exhibit the highest specific EA and peak force under in-plane compression, outperforming SCR and hexagonal lattices. For out-of-plane compression, trapezoidal and hexagonal lattices absorbed 85.7% and 80.3% of the energy, respectively, whereas SCR exhibited comparatively lower absorption. The trapezoidal configuration demonstrates excellent mechanical stability and energy efficiency, achieving 89% out-of-plane and 70% in-plane efficiency, highlighting its suitability for impact mitigation and crashworthiness applications. These findings confirm that integrating theoretical derivation with large-scale simulations provides a robust framework for evaluating lattice architectures, and support the selection of trapezoidal and SCR lattices for lightweight, energy-absorbing structural designs in automotive, aerospace, and protective equipment applications.