Bio-inspired selective nodal decoupling for ultra-compliant interwoven lattices

Architected materials, particularly lattices, offer extraordinary mechanical properties due to their efficient use of material. Stretch-dominated lattices excel in high stiffness at low volume fractions, while bending-dominated lattices prioritize compliance and energy absorption. This research focuses on bending-dominated lattices, aiming to significantly enhance their compliance. The design inspiration comes from the Venus flower basket, a deep-sea sponge with a remarkably compliant lattice structure despite its brittle silica composition. While previous bio-inspired designs often focused on the overall topology of natural structures, this study delves into finer details, specifically the selective nodal decoupling observed in the Venus flower basket. This decoupling, where struts are not fully connected at nodes, is hypothesized to contribute to the sponge's exceptional compliance. The primary research question is whether this selective nodal decoupling principle can be generalized to improve the compliance of existing lattice designs, leading to a significant advancement in the field of architected materials.

Cellular materials like honeycombs, foams, and lattices have expanded the range of high-performance materials. Advances in computational design and additive manufacturing have enabled the creation of architected materials with unprecedented properties. Bio-inspired designs often focus on abstracting the unit cell topology from nature. However, closer examination reveals secondary features with functional benefits, as seen in honeybee nests where wall coping and corner radius impact flexural rigidity and stress minimization. While much research explores the stiffness-to-weight ratio of lattices, the compliance aspect remains less investigated. The Venus flower basket has garnered interest for its remarkable mechanical properties, with studies exploring various hierarchical levels of design. However, the impact of selective nodal decoupling on compliance has not been adequately addressed. Previous work on 3D woven materials and interpenetrating lattices demonstrates some benefits in compliance but lacks the simplicity and generalizability of the proposed approach. This study differentiates itself by introducing a simple and universally applicable method to generate woven 3D structures by selectively decoupling nodes, leading to unprecedented compliance levels.

The research employed a bio-inspired approach, abstracting the selective nodal decoupling observed in the Venus flower basket. This principle was then applied to several common lattice topologies: Body-Centered Cubic (BCC), Diamond, Fluorite, and a hybrid BCC-FCC lattice. The BCC lattice, being bending-dominated, served as the initial baseline. Interwoven lattices were generated by splitting the BCC unit cell into planes, decoupling struts at the centroidal node, and merging the pairs of struts to create an interwoven unit cell. Polyamide-12 (PA12) specimens were fabricated using Selective Laser Sintering (SLS) with varying strut diameters (1.2, 1.5, and 1.8 mm) and a constant unit cell size (15 mm). Quasi-static compression tests were performed on three replicates for each strut diameter and lattice type. The experimental results were validated using finite element simulations employing a nonlinear, shear-deformable 3D beam model with an elasto-viscoplastic material model for PA12. The simulations accurately captured the experimental behavior, including instabilities, contact, and inelastic material behavior. To assess the generality of the approach, the same process was repeated for the Diamond, Fluorite, and hybrid BCC-FCC lattices. Finally, larger 10x10x10 unit cell lattices were created and tested to minimize edge effects for comparison with literature data on the Ashby plot.

Compression tests revealed a remarkable increase in compliance for interwoven lattices compared to their traditional counterparts. For instance, the interwoven BCC (i-BCC) lattice demonstrated a 21.5-fold reduction in effective stiffness compared to the traditional BCC lattice. Simulations confirmed the experimental observations, revealing a more homogeneous force distribution in the i-BCC lattice, leading to smoother plateau regions in the load-displacement curves and a reduction in the localization of buckling. The study's key finding is the significant increase in compliance observed across various lattice types. For all four lattice shapes tested, the compliance increased between 4 and 21 times. The power-law relationship between normalized effective modulus (E*/Es) and relative density (ρ*/ρs) was analyzed (E*/Es = (ρ*/ρs)^m), showing a substantial increase in the exponent 'm' for interwoven lattices, often doubling its value. This signifies a greater increase in compliance for a given relative density compared to traditional lattices. Maxwell's criterion was also used to explain the increase in compliance, suggesting that the interweaving increased the number of available mechanisms for deformation. Finally, the comparison with literature data via an Ashby plot revealed that the interwoven lattices from this study demonstrated superior compliance compared to most other reported 3D woven cellular materials.

The findings confirm the hypothesis that selective nodal decoupling significantly enhances the compliance of bending-dominated lattices. The increase in compliance is not limited to the BCC lattice; it extends to other lattice topologies, highlighting the generalizability of this design strategy. This approach offers a simple and effective method to achieve high compliance without drastically increasing manufacturing complexity. The observed homogeneity in force distribution and reduction in buckling localization contributes to the improved compliance and smoother load-displacement curves. The results have significant implications for designing compliant architected materials, particularly for applications requiring high compliance at large relative densities, such as piezoelectric sensors, energy absorbers, and vibration dampers. Future research could explore the optimization of interweaving distance and localized nodal decoupling for further compliance enhancement.

This research successfully demonstrated a novel bio-inspired design strategy for ultra-compliant interwoven lattices. The selective nodal decoupling method, inspired by the Venus flower basket, provides a simple and effective way to significantly increase the compliance of existing lattice structures. The general applicability across different lattice types has been shown. Future research should focus on further optimizing the design by modulating the interweaving distance and selectively decoupling nodes in specific regions to maximize compliance. Also, a study incorporating the cylindrical geometry of the Venus flower basket could yield further insights into its remarkable compliance.

The study focused on a specific material (PA12) manufactured using SLS. The results may vary with different materials and manufacturing processes. The current research is limited to quasi-static compression tests; dynamic loading behavior should be further investigated. While the study suggests the potential correlation between nodal decoupling and the resilience of young Venus flower baskets, further research is needed to definitively establish this connection.