Researchers engineer a new class of microlattice materials with enhanced stiffness-to-density ratios and giant negative Poisson’s ratios, ideal for lightweight applications.
(Nanowerk Spotlight) Material performance is often constrained by a tradeoff between strength and weight. This tension has motivated decades of effort to develop structural materials that are simultaneously strong, light, and energy-absorbent. While conventional engineering materials such as metals and polymers rely on intrinsic composition for their mechanical properties, a distinct approach has gained ground over the past two decades—designing materials whose properties emerge primarily from geometry.
Mechanical metamaterials fall into this category. They are structured systems whose mechanical behavior—stiffness, compressibility, deformation response—is governed more by architecture than by bulk material properties. Among these, auxetic metamaterials are especially notable. They exhibit a counterintuitive behavior called a negative Poisson’s ratio: when stretched in one direction, they expand rather than contract in the perpendicular direction. This rare feature enables exceptional resistance to indentation, improved energy absorption, and the ability to conform to complex curved surfaces.
Traditional auxetic designs often rely on specific repeating units—re-entrant honeycombs, rotating squares, or chiral networks—that can deform through rotation or flexure of sub-units. These structures have found niche use in protective gear, biomedical implants, and stretchable electronics. Yet, many auxetic systems suffer from high material density, limiting their effectiveness in scenarios where low weight is crucial. In particular, 3D rotating cube metamaterials, while capable of achieving very high stiffness, are relatively dense and lack the porosity required for lightweight applications.
Efforts to address this density issue have looked to nature and crystallography for inspiration. Crystalline structures such as body-centered cubic (BCC) and face-centered cubic (FCC) arrangements are known for their efficient use of space and load distribution. These motifs have been proposed as frameworks for hierarchical materials—structures where each element contains smaller substructures designed to tune specific properties.
Building on this idea, researchers from the University of Modena and Reggio Emilia, the University of Zielona Góra, and the Université de Franche-Comté present a detailed study in Advanced Science (“Lightweight 3D Hierarchical Metamaterial Microlattices”). The team introduces three new classes of 3D hierarchical microlattices—based on BCC, FCC, and a custom tetrahedral cubic (TC) structure—that preserve the desirable properties of rotating cube auxetics while reducing material volume by over 90%.
Schematic showing cubic crystal lattice arrangements and their implementation for the design of hierarchical rotating cube metamaterials. The structures on the right show the representative volume elements of the full block and four hierarchical structures proposed in this work. (Image: Reprinted from DOI:10.1002/advs.202410293, CC BY) (click on image to enlarge)
At the core of these designs is the concept of the rotating cube. In a standard rotating cube metamaterial, rigid cubes rotate around their vertices and edges when compressed, causing the entire material to contract laterally as well as longitudinally—a hallmark of auxeticity. The researchers modified this concept by replacing the solid cubes with truss-based frameworks constructed using the BCC, FCC, and TC lattice geometries. These frameworks act as semi-rigid cubes, capable of flexure while retaining the overall cube shape needed for rotational deformation.
To evaluate these systems, the team ran more than 5,900 finite element simulations varying the geometric parameters that control the size and flexibility of the cube units. Key variables included the length of the cubes, the angles of rotation (θ and φ), and the thickness of the connecting trusses (expressed as a ratio r/l). This broad parametric sweep enabled a detailed analysis of how geometry governs the mechanical behavior of the microlattices.
The results show that the BCC, FCC, and TC configurations retain the negative Poisson’s ratio seen in full-block (non-hierarchical) structures, even though they use significantly less material. The bending-dominated simple cubic (SC) design, by contrast, failed to preserve auxeticity and exhibited much lower stiffness. This configuration was subsequently excluded from further analysis due to its poor mechanical performance.
Stiffness, measured through the normalized Young’s modulus (E*), was consistently highest for the FCC arrangement, followed by BCC and then TC. Importantly, the effective stiffness-to-density ratio (E*/Vf) was greater for the hierarchical structures than their full-block counterparts, demonstrating the efficiency of these designs. The authors also examined strain concentration—how stress distributes across the structure during deformation—and found that the hierarchical trusses reduce local strain hotspots, potentially improving fatigue resistance.
To confirm that the numerical predictions held up in real-world conditions, the team fabricated six microlattice samples using two-photon lithography, a high-resolution 3D printing method suitable for microscale structures. Each sample contained a 5×5×5 array of rotating units. Mechanical testing under compression showed clear auxetic behavior, consistent with the simulations. Digital image correlation was used to track deformation in the central unit cells.
Even though some edge effects and fabrication imperfections affected the measurements, the hierarchical lattices still demonstrated negative Poisson’s ratios and sustained deformation without immediate failure. The experimental results confirmed that auxeticity was preserved over compressive strains of up to 10%, a range that exceeds typical thresholds for this class of metamaterials.
a) An idealized rotating cubes representative unit cell deforming under compressive loading and b) 1/8th of the unit cell showing the geometric parameters l, 𝜃 and ϕ used to define the system. c) Images showing the realistic simulated systems with the ligament/interconnection thickness parameter, r, for the five configurations investigated. d) SEM images of the 5×5×5 BCC, FCC and TC lattice structures fabricated using two-photon additive manufacturing. (Image: Reprinted from DOI:10.1002/advs.202410293, CC BY)
One of the study’s most significant findings is the impact of the truss thickness. As the r/l ratio increased—meaning thicker ligaments connecting the truss elements—the structures became stiffer but less auxetic. Thicker connections also concentrated strain in fewer regions, increasing the likelihood of early failure. This trade-off highlights the importance of optimizing geometry not just for strength but also for deformability and energy distribution.
To contextualize their findings, the researchers compared their designs with three established 3D auxetic systems from the literature: a traditional 3D re-entrant honeycomb by Chen et al. (Smart Materials and Structures, 2017), a 3D anti-tetrachiral lattice by Iantaffi et al. (Materials & Design, 2023), and a hierarchical 3D re-entrant system by Yang et al. (Composites Structures, 2019). While these systems display varying degrees of auxetic behavior, the new hierarchical rotating cube microlattices demonstrated significantly higher effective stiffness at similar volume fractions. This places them at a higher stiffness-to-density tier, making them more efficient for weight-sensitive structural applications.
In biomedical engineering, porous implants that mimic the mechanical behavior of bone while reducing stress shielding are a long-standing goal. These new microlattices, with tunable porosity and mechanical response, could be tailored for such roles. In aerospace, where stiffness-to-weight ratio is often the defining design constraint, hierarchical rotating structures may find use in lightweight panels and structural supports. Their modular, scalable architecture also lends itself to manufacturing at different scales, including larger macro-scale components.
The researchers suggest that further refinement of the interconnection geometry between cube units could improve strain tolerance and enable more complex deformation patterns. Incorporating other auxetic mechanisms, such as chiral or re-entrant geometries, within the hierarchical units could yield even lower Poisson’s ratios. There is also scope to investigate how different base materials affect performance under large deformations or cyclic loading.
This work advances a key challenge in materials science: designing structural materials where geometry, rather than mass, drives performance. By merging ideas from crystallography, mechanical engineering, and microfabrication, the study opens a pathway to functional materials that do not compromise strength for lightness—and do so using design principles that can be generalized across scales and applications.
Get our Nanotechnology Spotlight updates to your inbox!
Thank you!
You have successfully joined our subscriber list.
Become a Spotlight guest author! Join our large and growing group of guest contributors. Have you just published a scientific paper or have other exciting developments to share with the nanotechnology community? Here is how to publish on nanowerk.com.
