This study proposes a new, doubly re-entrant auxetic unit-cell design that is based on the widely used auxetic honeycomb structure. Our objective was to develop a structure that preserves and enhances the advantages of the auxetic honeycomb while eliminating all negative aspects. The doubly re-entrant geometry design aims to enhance the mechanical properties, while eliminating the buckling deformation characteristic of the re-entrant deformation mechanism. The effects of the geometric modification are described and evaluated using two parameters, offset and deg. A series of experiments were conducted on a wide range of parameters based on these two parameters. Specimens were printed via the vat photopolymerization process and were subjected to a compression test. Our aim was to investigate the mechanical properties (energy absorption and compressive force) and the deformation behaviour of these specimens in relation to the relevant parameters. The novel geometry achieved the intended properties, outperforming the original auxetic honeycomb structure. Increasing the offset and deg parameters results in increasing the energy absorption capability (up to 767%) and the maximum compressive force (up to 17 times). The right parameter choice eliminates buckling and results in continuous auxetic behaviour. Finally, the parameter dependency of the deformation behaviour was predicted by analytical approximation as well.

In this study, we created metamaterials consisting of square unit cells—inspired by fractal geometry—and described the parametric equation necessary for their creation. The area and thus the volume (density) and mass of these metamaterials are constant regardless of the number of cells. They were created with two layout types; one consists solely of compressed rod elements (ordered layout), and in the other layout, due to a geometrical offset, certain regions are exposed to bending (offset layout). In addition to creating new metamaterial structures, our aim was to study their energy absorption and failure. Finite element analysis was performed on their expected behavior and deformation when subjected to compression. Specimens were printed from polyamide with additive technology in order to compare and validate the results of the FEM simulations with real compression tests. Based on these results, increasing the number of cells results in a more stable behavior and increased load-bearing capacity. Furthermore, by increasing the number of cells from 4 to 36, the energy absorption capability doubles; however, further increase does not significantly change this capability. As for the effect of layout, the offset structures are 27% softer, on average, but exhibit a more stable deformation behavior.

In this study, a novel unit cell design is proposed, which eliminates the buckling tendency of the auxetic honeycomb. The novel unit cell design is a more balanced, diagonally reinforced doubly re-entrant auxetic honeycomb structure (x-reinforced auxetic honeycomb for short). We investigated and compared this novel unit cell design against a wide parameter range. Compression tests were carried out on specimens 3D-printed with a special, unique, flexible but tough resin mixture. The results showed that the additional, centrally pronounced reinforcements resulted in increased deformation stability; parameter-independent, non-buckling deformation behaviour is achieved; however, the novel structure is no longer auxetic. Mechanical properties, such as compression resistance and energy absorption capability, also increased significantly—An almost four times increase can be observed. In contrast to the deformation behaviour (which became predictable and constant), the mechanical properties can be precisely adjusted for the desired application. This novel structure was also investigated in a highly accurate, validated finite element environment, which showed that critical stress values are formed in well-supported regions, meaning that critical failure is unlikely. Our novel lattice unit cell design elevated the auxetic honeycomb to the realm of modern, high performance and widely applicable lattice structures.

This work solves the problem associated with the lack of analytical models capable of describing the nonlinear vibration behavior of re-entrant hexagonal units when geometric nonlinearity and structural modifications, such as soft filling, are taken into account. The purpose of this study is to develop an analytical framework that enables prediction and control of vibration characteristics, with particular emphasis on achieving low-frequency response and enhanced energy storage and redistribution within the structure. The proposed approach is based on Lagrangian modeling of the unit cell, leading to a nonlinear equation of motion of the Liénard type that admits a first integral. By exploiting the existence of this integral, an approximate analytical expression for the oscillation period is derived using energy-based methods. The analysis is performed for two configurations: an empty unit and a unit filled with a soft material, allowing direct comparison of their dynamic responses. The analytical results are validated through comparison with numerical simulations and available experimental data. A parametric study is conducted to evaluate the influence of the mass ratio and the re-entrant angle on the oscillation period and frequency. Furthermore, the effects of filling mass, stiffness, and degree of filling are systematically investigated, revealing distinct inertia-dominated and stiffness-dominated regimes. The obtained results provide clear design guidelines for tailoring the dynamic response of re-entrant hexagonal units. It is shown that low-frequency vibration and increased capacity for energy storage can be achieved through appropriate selection of geometric parameters and filling properties, with potential applications in vibration control and structural design.