A Unified Stiffness Evolution Model and Its Application to 3D-Printed Regular and Re-Entrant Honeycombs

Abstract

The evolution of the elastic modulus in cellular materials involves both post-yield stiffness degradation and densification-induced recovery, yet a unified theoretical framework to describe this non-monotonic behavior remains lacking. This study investigates the stiffness evolution and deformation mechanisms of regular hexagonal (HC) and re-entrant (NHC) honeycombs under quasi-static uniaxial compression. Specimens with varied wall thicknesses were fabricated using fused deposition modeling, and incremental loading–unloading tests were performed along two orthogonal in-plane directions. A stiffness evolution model was developed to describe the complete non-monotonic variation of the global modulus, incorporating a linear elastic pre-yield response within a modified rigid–plastic hardening framework. The model captures both stiffness degradation induced by localized collapse and subsequent recovery driven by structural compaction, outperforming conventional approaches that neglect modulus rebound. Pronounced anisotropy in modulus evolution is observed, governed by direction-dependent collapse mechanisms. Bending-dominated deformation in the 1-direction leads to progressive compaction and earlier stiffness recovery as wall thickness increases. In contrast, fracture-dominated crushing in the 2-direction delays the modulus rebound in thicker specimens due to enhanced structural strength and toughness. These results reveal that wall thickness not only scales the stiffness magnitude but also modulates its evolution path: thicker walls accelerate compaction in bending-dominated modes while delaying it in fracture-dominated modes. The proposed framework provides a robust theoretical foundation for the optimized design of honeycombs and offers predictive insights into the interplay between geometry, thickness, and performance evolution in architected materials.