Metamaterials from the Deep: Optimized Mechano-Fluidic Materials Inspired by Deep-Sea Sponges

Metamaterials from the Deep: Optimized Mechano-Fluidic Materials Inspired by Deep-Sea Sponges | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Metamaterials from the Deep: Optimized Mechano-Fluidic Materials Inspired by Deep-Sea Sponges Costas Grigoropoulos, Timon Meier, Sergey Litvinov, Runxuan Li, and 9 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7756357/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Multifunctional materials that balance mechanical resilience and fluid dynamic efficiency are increasingly critical in engineering applications, yet the synergistic optimization of these properties remains a challenge due to inherent trade-offs, computational and experimental expense, and the complexity of high-dimensional design spaces. Inspired by the hierarchical skeleton of the deep-sea sponge Euplectella aspergillum , which shows distinct mechanical and fluidic characteristics, this study presents a framework that integrates high-fidelity Finite Element Analysis for mechanics, Volume of Fluid methods for flow simulations, and multi-objective Bayesian optimization. Using high-performance computing, our approach efficiently explores complex design spaces to identify Pareto-optimal solutions. Optimized lattices showed an average 140% improvement in critical buckling force across a range of volume fractions relative to baseline designs, along with significant reductions in drag, lift, and vortex shedding, achieved with porosities as low as 5%. Fabricated using stereolithography and validated through mechanical compression tests and stereo particle image velocimetry, experimental results align with computational simulations. By achieving simultaneous optimization of mechanical and fluidic performance, this research establishes a methodology for designing lightweight, high-performance materials with applications in aerospace, civil engineering, and energy systems. Physical sciences/Engineering/Mechanical engineering Physical sciences/Materials science/Structural materials/Mechanical properties Physical sciences/Engineering Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Nature, through millions of years of evolutionary processes, has developed a wide range of structures and materials that show efficiency, adaptability, and multifunctionality. This natural optimization, driven by survival and reproduction, has led to biological designs that often surpass both intuitive and engineered solutions. As our understanding of these systems deepens, so does our ability to draw inspiration from them, fueling the field of biomimetic engineering 1 , 2 . From the self-cleaning properties of lotus leaves 3 to the impact resistance of mollusk shells 4 , the adhesive capabilities of gecko feet 5 , and the color-changing abilities of chameleon skin 6 , nature offers a vast repository of design principles. Load-bearing biological structures are especially compelling for their ability to achieve mechanical strength with minimal material. Examples for lightweight yet strong structures include the trabecular bone, with its optimized lattice structure 7 , and the honeycomb architecture 8 found in beehives. Marine organisms, which face unique challenges in their aquatic environments, offer additional inspiration. The deep-sea glass sponge, Euplectella aspergillum 9 , 10 , commonly known as Venus’ flower basket, is a notable example of structural efficiency and multifunctionality 11 – 14 . This organism has evolved a skeletal system that combines lightweight design with high mechanical strength 15 – 19 and distinctive fluid dynamic interactions 20 – 25 . Over millions of years, shaped the sponge's structure has evolved to withstand the extreme conditions of its deep-sea habitat, such as high pressures, limited light, cold temperatures, and persistent exposure to fluid flows. The skeletal structure of Euplectella aspergillum consists of a lattice-like arrangement of silica spicules, forming a cylindrical structure with a hierarchical organization spanning multiple length scales 11 . Previous studies have highlighted both mechanical and fluidic aspects of this architecture. Weaver et al. 12 demonstrated the structural integrity of its six-level hierarchical design, ranging from nanometers to centimeters, emphasizing its efficiency in material use and mechanical stability. Fernandes et al. 15 highlighted that the sponge's checkerboard-like square lattice with double-diagonal reinforcement achieves optimal buckling resistance for a given volume fraction, outperforming conventional lattice designs in mechanical behavior. Vangelatos et al. 18 used Finite Element Analysis (FEA) to analyze nonlinear buckling and developed an optimized sponge-inspired metamaterial that carried higher loads with less volume using topology optimization. On the fluid side, Chen et al. 19 found that the ridge helical system spiraling the cylindrical sponge lattice improves radial stiffness and fluid permeability. Falcucci et al. 20,23 carried out high-performance computing (HPC) flow simulations on a complete skeletal model of Euplectella aspergillum , showing that the sponge skeleton reduces hydrodynamic stress and drag forces. Fernandes et al. 21 demonstrated that the sponge's ridge system suppresses von Kármán vortex shedding 26 , 27 . This suppression prevents resonance vibrations, reduces lift force oscillations across flow regimes, and improves mechanical performance. Together, these characteristics make Euplectella a compelling model for engineered structures where both mechanical resilience and fluid control are important, such as offshore platforms, aerospace components, and biomedical scaffolds. Despite extensive research into the mechanical and fluid dynamic characteristics of Euplectella aspergillum , a critical gap remains in addressing how these attributes interact and can be simultaneously optimized with the structural properties in engineered systems. Previous studies have predominantly focused on either mechanical or fluid dynamic aspects, without emphasizing the synergies and trade-offs that define multifunctional designs. Addressing these challenges requires an integrated framework capable of balancing competing objectives, which is increasingly important given the demand for lightweight structures and efficient fluid management in engineering applications. Recent advances in computational modeling, simulation techniques, multi-objective optimization, and HPC now offer the tools to address this complexity, enabling the development of designs that integrate and optimally balance both mechanical and fluidic performance. This work presents an automated framework that combines high-fidelity computational fluid dynamics (CFD) and FEA simulations within a multi-objective Bayesian optimization (MOBO) 28 , 29 scheme. While traditional optimization algorithms, like NSGA-II 30 and MOEA/D 31 have been widely used for multi-objective optimization, they struggle to handle the computational expense of high-fidelity simulations. In contrast, MOBO is effective for optimizing costly black-box functions with a limited number of evaluations 32 , 33 and can be parallelized on HPC resources. Using these capabilities, our framework efficiently explores complex design spaces to identify Pareto-optimal solutions inspired by the Euplectella skeleton, balancing mechanical resilience and hydrodynamic performance. The study combines computational modeling, 3D fabrication using high precision stereolithography (SLA), and experimental validation through mechanical compression tests and stereo particle image velocimetry (SPIV) flow measurements. By integrating computational simulations, multi-objective optimization, and experimental methods, we establish a methodology for translating bioinspired principles into multifunctional designs. This research not only advances the understanding of Euplectella’s structural principles but more importantly demonstrates their relevance in engineering, where lightweight, resilient, and efficient multifunctional designs are critical. Results Design Framework We translate biological insights into engineered multifunctional designs, developing a computational framework inspired by the hierarchical lattice structure of Euplectella aspergillum . As illustrated in Fig. 1 , the sponge skeleton features a checkerboard-like grid of longitudinal and circumferential beams, diagonal reinforcements, and helical ridges curling over the tubular structure. Together these features contribute to lightweight construction, improved buckling resistance, and passive vortex suppression. Building on the structural insights from Euplectella aspergillum , we developed a parameterized design space that captures the sponge’s key architectural features in an idealized cylindrical lattice model. The abstraction incorporates the square lattice of longitudinal and circumferential beams, reinforced by double diagonals and external helical ridges, and serves as the foundation for computational modeling and optimization. The cylindrical lattice is defined with constant length L and diameter D . The multiple spicule fibers within the sponge are represented as beams with rectangular cross sections, described by the design parameters width W and height H . Additional design parameters include the number of vertical beams N V ​, the number of circumferential beams N C ​, the radius of the semi-ellipsoidal cross section for the helical ridges R H ​, the number of loops in the helical ridges N L ​, and the counts for clockwise (CW) and counterclockwise (CCW) helical ridges N CW , N CCW ​. Each parameter was chosen to enable precise control over the structural elements, with boundaries set by the sponge’s skeletal features sies and stability constraints for the computational simulations. An overview of all design parameters and their ranges are shown in Table 1 . Table 1 Overview of geometric design parameters for optimization Parameter Description Parameter range L Length of cylindrical lattice 100 mm D Diameter of cylindrical lattice 22 mm W Width of cross section 0.15–0.65 mm H Height of cross section 0.15–0.65 mm N v Number of vertical beams 20–50 N c Number of circumferential beams 30–74 R H Radius of semi-ellipsoid of helical ridges 0.6–1.6 mm N L Number of loops for helical ridges 1–6 N CW Number of clockwise helical ridges 1–3 N CCW Number of counterclockwise helical ridges 1–3 Geometries were generated using custom Python scripts, as detailed in Supplementary Information (SI), and evaluated with high-fidelity FEA and CFD simulations to capture mechanical and fluidic performance. FEA simulations, implemented through the ANSYS® Python environment (PyAnsys), were used to study how variations in geometry affect the mechanical behavior of the lattice. In parallel, CFD simulations were performed in Basilisk using a Volume of Fluid (VOF) scheme with an embedded boundary approach and adaptive mesh refinement (AMR) to resolve fluid forces and vortex shedding. During the MOBO stage, coarser AMR settings were applied to efficiently explore the design space, while for the final Pareto-optimal designs, the CFD involved grids at a resolution that enabled Direct Numerical Simulations (DNS). We selected a \(\:Re=UD/\nu\:=2100\) for optimization as it corresponds to typical deep-sea flow conditions 20 . Building on our previous work with inverse design framework 34 , 35 , we applied MOBO to explore the design space and identify optimal trade-offs between mechanical and fluid dynamic properties. The optimization was conducted using the Thompson Sampling Efficient Multi-Objective Optimization (TS-EMO) algorithm, developed by Bradford et al. 29 . Objective and cost functions are defined in the Materials and Methods section. To manage the computational expense of FEA and VOF-based CFD, we conducted large scale parallel simulations. Our multi-stage workflow is summarized in Fig. 2 . It starts with parameterization of the sponge-inspired lattice, including helical ridges and diagonal reinforcements (Fig. 2 A). MOBO then evaluates candidate designs through iterative FEA and CFD simulations to capture both mechanical and fluidic performance (Fig. 2 B). The resulting Pareto-optimal geometries illustrate different trade-offs between strength and flow efficiency, with potential applications in wind-resistant structures, biomedical implants, and fluid management devices. Selected designs were fabricated and tested through compression experiments and SPIV measurements (Fig. 2 C). These experiments provided validation of the computational results. Details of the simulation, optimization, fabrication, and testing procedures are provided in the Materials and Methods section. Pareto Front Analysis The optimization produced a design space mapping the trade-offs between mechanical strength and fluidic efficiency (Fig. 3 A). Pareto-optimal designs are shown in red. Convergence was monitored using the hypervolume metric (Fig. 3 B), which leveled off in later batches, indicating that further iterations would likely add little benefit and providing a natural stopping point. The Pareto front makes clear that gains in one objective come at the expense of the other. Simulations of selected designs (Fig. 3 C) highlight these trade-offs: Design I for example is optimized for reduced vortex shedding and drag, while design A emphasizes mechanical strength. These examples highlight the balance between fluid stability and structural strength, influenced by features such as helical ridge density, lattice configuration, and beam cross-section. Analysis of clusters and outliers along the Pareto front further highlighted trends. For example, modifying helical ridge pitch can reduce vortex shedding with only modest reductions in mechanical strength. The Pareto front thus provides a practical tool for selecting designs based on application priorities. Four representative points were chosen for experimental validation, spanning designs from fluidically efficient to mechanically robust. Full parameter configurations of Pareto-optimal designs are given in the SI, Table S1 . Fabrication and experimental validation of selected designs Designs A, D, H, and I were selected from the Pareto front to represent a spectrum of performance attributes, covering mechanically robust, fluid-efficient, and balanced designs. The selected designs were fabricated using an Anycubic Photon D2 DLP printer with a resolution of 51 µm, enabling features and pore sizes as small as 150 µm, comparable to those of the deep-sea sponge. The printed geometries were validated with optical microscopy to confirm dimensional accuracy. Mechanical performance was assessed by measuring critical buckling load and deformation under compression. Results showed high repeatability across four samples, confirming the reliability of the fabrication process. Force–displacement curves from the experiments closely matched predictions from nonlinear buckling analyses (Fig. 4 ). Agreement was consistent across key metrics, including Young’s modulus (effective stiffness) and buckling behavior, with deviations between experimental and simulated stiffness values below 5%. Experimentally observed buckling locations, shown in supplementary videos and SI, Figure S3, also matched simulated behavior, confirming the accuracy of the computational model. Validation of fluidic performance was carried out using CFD cylinder baseline and SPIV, providing time-resolved velocity fields around the fabricated structures under quasi-steady flow at Reynolds number ~ 2100. Results (Fig. 5 ) show that all optimized designs, regardless of porosity, substantially reduce hydrodynamic loading compared to the solid cylinder benchmark. The cylinder also served as a reference to validate the CFD simulations as detailed in SI, Figure S6. For the reference solid cylinder, the drag coefficient remained close to 1.0, consistent with literature. The optimized designs reduced drag to 0.8–0.85 (Fig. 5 A). Lift fluctuations were also suppressed (Fig. 5 B): Design A, the most rigid structure, reduced the RMS lift coefficient by 39%, while the most porous, Design I, achieved an 84% reduction. Power spectral density of the lift signal (Fig. 5 C) confirmed the attenuation of vortex shedding, with all optimized designs showing reduced spectral peaks near 0.9 Hz, matching the expected Strouhal number of ~ 0.21. Wake dynamics are illustrated by vorticity plots of the solid cylinder (Fig. 5 D) and optimized Design I (Fig. 5 E). The cylinder generates strong alternating vortices close to the body, whereas Design I shifts vortex formation downstream and lowers overall vorticity. These trends were supported by SPIV measurements recorded within the wake region, from the cylinder up to approximately three diameters downstream, as indicated by the dashed box in Fig. 5 E. A representative SPIV snapshot is shown in Fig. 5 F, with velocity magnitude shown by background color and overlaid streamlines and vectors illustrating flow direction and structure. To compare CFD and SPIV data, velocity fields were extracted from simulations over the same spatial domain. Side-by-side snapshots and time-resolved videos (SI, Figures S11-13) show agreement in velocity magnitude and flow structure. Some differences were observed between SPIV and CFD results as detailed in SI: vortex shedding appeared more pronounced and initiated closer to the structure in the SPIV data, likely due to fabrication-induced surface roughness or boundary effects in the water tunnel. Nonetheless, both experimental and numerical data confirm the similar wake topology and reduction in unsteady flow. Quantitative comparisons presented in SI, Figure S14 support these findings. Dominant shedding frequencies from CFD and SPIV matched within approximately 20%. Average transverse (lift direction) velocities in the wake were on average 0.011 m/s higher in SPIV, consistent with the more visible shedding. Importantly, both datasets showed that optimized designs reduced transverse velocities by a factor of three to five and lowered vortex intensity compared to the solid cylinder baseline, confirming the effectiveness of the optimization in stabilizing wake dynamics and reducing hydrodynamic forces. Discussion This study establishes a robust design framework for multi-objective optimization of multifunctional structures that balance fluidic and mechanical performance. Inspired by the hierarchical skeleton of Euplectella aspergillum , we couple fluid dynamics and structural mechanics, through high-fidelity simulations and experiments. Using automated FEA and CFD simulations with MOBO on HPC resources, our framework identified Pareto-optimal designs that balance competing objectives. Each design represents a trade-off between mechanical strength and fluidic efficiency, echoing the dual functionality of the Euplectella , where structural integrity and flow permeability are simultaneously maintained under extreme conditions. Compared to the initial Latin Hypercube samples, optimized structures improved critical buckling force by an average of 140% while maintaining or reducing material use. Nonlinear FEA predictions agreed with experimental compression tests across buckling loads, force-displacement responses, and failure locations (SI, Figure S3), confirming the accuracy of the computational simulations. SPIV measurements confirmed the CFD predictions of drag reduction and vortex suppression. The observed wake stabilization is consistent with prior findings that increasing porosity attenuates turbulence kinetic energy (TKE), elongates shear layers, and suppresses vortex shedding 36 – 39 . In our case, the time-averaged TKE in the cylinder wake was about 50% higher and peaked roughly one diameter closer to the body than in the optimized designs, while CFD predicted an even more pronounced downstream shift than observed in SPIV as shown in SI, Figure S13. Our results further show that porosities as low as 5% are sufficient to suppress vortex shedding, a significant reduction compared to the effective porosity of natural Euplectella structures. This highlights how targeted geometric refinement through optimization can exceed biological benchmarks for specific functional metrics. While natural sponges may retain higher porosities due to multifunctional biological roles 40 – 42 , our designs isolate specific performance attributes. Prior work on perforated cylinders reported similar wake suppression at porosities around 8% 38 , with similar wake suppression mechanisms 36 , 39 . Although those studies were typically conducted at higher Reynolds numbers, our results show that optimization can achieve comparable benefits at lower porosities. To reduce computational cost, fluidic and mechanical simulations were decoupled during optimization. Harmonic FEA of four Pareto-optimal designs (A, D, H, I) showed that the first structural resonance occurred above 20 Hz (Fig. 6 ), far above the vortex shedding frequencies of 0.85–1.1 Hz (Strouhal ≈ 0.21) confirmed by CFD and SPIV. This clear spectral separation indicates minimal energy transfer between flow and structure, thereby justifying the decoupled approach, which reduced computational expense while preserving the essential physics of each domain. Although valid under these conditions, future work should explore fully coupled fluid–structure interaction (FSI) models to capture transient dynamics, resonance interactions, and fatigue effects, especially at higher Reynolds numbers or under cyclical loading. While global vortex shedding occurs at frequencies well below structural resonance, localized shedding from smaller-scale features may occur at higher frequencies, potentially overlapping with structural modes. Modal analysis and dynamic testing could study these interactions and guide designs for long term durability. Beyond the specific performance improvements, this framework demonstrates how multifunctional designs can be applied across engineering domains. In underwater settings, such as offshore platforms and pipelines, drag reduction and structural resilience are both critical. In biomedical applications, flow-permissive stents and filtration devices benefit from combining strength with low fluid resistance 43 . In aerospace and civil engineering, high strength-to-weight ratios are essential for components in bridges and aircraft. Other potential uses include energy-absorbing structures for transportation and sports 44 , high-throughput water purification and flow catalysts 25 , 45 , and multifunctional metamaterial solutions for sensing, energy harvesting, and communication 46 , 47 . Recent advances in cellular fluidics and bubble-resolved transport within architected lattices further highlight opportunities for programmable multiphase flow control in such systems 48 , 49 . Our framework opens several paths for future work. Scalable fabrication could bring these designs into industrial applications 50 . Machine learning surrogates or reduced-order models may cut computational costs and speed up exploration of large design spaces. Further validation across different Reynolds number regimes, or the development of adaptive structures with tunable porosity and stiffness, would broaden applications in robotics, infrastructure, and flow control. The same approach can also be applied to other biological systems with multifunctional geometries, especially when combined with generative design and AI-based optimization. Conclusion We developed a bioinspired framework that integrates FEA, CFD, MOBO, and experiments to optimize multifunctional lattice structures. Inspired by Euplectella aspergillum , the framework produced Pareto-optimal designs that balance mechanical strength and fluidic efficiency. Optimized lattices achieved up to 140% higher buckling loads than baseline structures while also reducing drag, lift fluctuations, and vortex shedding. This work shows how computational optimization can incorporate and refine biological design principles to create targeted, high-performance solutions that surpass conventional engineering structures. The framework provides a pathway for lightweight, resilient, and fluid-efficient materials with applications in offshore, biomedical, aerospace, and civil engineering. Future efforts focused on scalability, adaptability, and dynamic performance can extend the reach of these multifunctional designs. Materials and Methods This section details the methodologies, parameters, and materials used throughout the study. It includes the multi-objective optimization framework, computational simulations, fabrication techniques, and experimental techniques applied. Multi-Objective Optimization Framework Two cost functions were defined to capture the competing objectives of structural strength and fluidic performance. The mechanical cost function F mech , Eq. 1: $$\:{F}_{mech}=\:-\:\raisebox{1ex}{${F}_{Buckling}$}\!\left/\:\!\raisebox{-1ex}{${V}_{sponge}$}\right.\:\left(1\right)$$ was designed to maximize the lattice’s buckling resistance while minimizing material usage, where F Buckling is the standardized critical buckling force obtained from FEA and V Sponge is the lattice volume. The fluid dynamic cost function F fluid , Eq. 2: $$\:{F}_{fluid}=\:\alpha\:*\stackrel{-}{{F}_{D}}+\beta\:*\stackrel{-}{{F}_{L}}+\gamma\:*{\sigma\:}_{{F}_{L}}\:\:\:\:\:\:\:\:\:\left(2\right)$$ combined average drag forces ( \(\:\stackrel{-}{{F}_{D}})\) , average lift \(\:\left(\stackrel{-}{{F}_{L}}\right)\) forces, and \(\:{\sigma\:}_{{F}_{L}}\) the over time calculated standard deviation of the lift force, a measure for lift force oscillations and vortex shedding. Weighting factors were chosen as \(\:\alpha\:=\beta\:=0.2\) and \(\:\gamma\:=\) 0.6, to emphasize suppression of unsteady lift. The overall optimization problem was therefore formulated as a bi-objective optimization, minimizing F mech and F fluid ​ simultaneously. The optimization process was initialized with 50 Latin Hypercube samples 51 . We then applied the Thompson Sampling Efficient Multi-Objective (TSEMO) algorithm 29 to generate Pareto-optimal solutions, iterating through 22 batches of 20 samples each. TSEMO uses gaussian processes as surrogates and Thompson sampling in conjunction with the hypervolume quality indicator and NSGA-II to choose a new evaluation point at each iteration. The algorithm outperforms NSGA-II and MOEA/D in approximating a Pareto front, has the capacity to handle noisy functions and offers the ability for batch evaluations. The AutoOED 52 platform was used as a graphical interface to monitor optimization progress and adjust parameters. Details of the optimization algorithms and setup can be found in 29,52 . Given the high computational cost of high-fidelity FEA and especially VoF-based CFD simulations, all runs were carried out on the FASRC Cannon cluster at Harvard University. Each job was executed on a Sapphire Rapids node with 112 processes. Structures were evaluated in batches of 20, which allowed efficient parallelization. While batch optimization may require more evaluations to converge, running designs simultaneously minimized overhead and enabled much greater throughput within the same timeframe. In total, the CFD simulations required approximately 10,000 node-hours. Automation was achieved through parameterized Python scripts that generated geometries of the sponge-inspired lattices. These were passed directly to CFD and FEA solvers, with data management and transfers handled via the Globus platform 53 . Once convergence criteria were met, selected designs from the Pareto front were fabricated and validated experimentally through compression tests and SPIV. Finite Element Analysis (FEA) for Mechanical Properties Finite Element Analysis was used to predict the mechanical response of each design, focusing on critical buckling load, stiffness, and failure points. Models were created in ANSYS® Mechanical™ 2024 R1 using the Parametric Design Language (APDL) and automated through PyMAPDL, which enabled direct scripting of lattice geometries and simulation runs. Different lattice configurations were generated by varying geometric parameters in the code. Lattices were modeled with Timoshenko beam elements (BEAM188) and assigned linear elastic material properties based on tests of solid, cured Anycubic DLP Craftsman resin. Compression tests on bulk samples gave a Young’s modulus of 1.1 GPa and Poisson’s ratio of 0.49. For each design, the cylindrical lattice was assumed to be fully constrained at its base ( u x = u y = u z = 0). Two types of simulations were performed: a linear static analysis (Analysis type: STATIC) to determine the stiffness of the lattice, and a linear buckling analysis (Analysis type: BUCKLE) to obtain the critical buckling force. In the simulation process, a uniform compressive pressure parallel to the z -axis was applied to all nodes on the top surface. In addition to the linear analyses, nonlinear buckling simulations were performed for pareto optimal designs to achieve higher accuracy and to better capture real-world failure behavior. These included geometric imperfections, large deformations (NLGEOM), and post-buckling behavior. Initial imperfections were introduced by scaling the first buckling mode from the linear analysis, simulating manufacturing irregularities. Nonlinear analyses provided improved predictions of load-bearing capacity and stress distribution. Predicted failure locations closely matched experimental observations. This confirmed the validity of the computational model and offered deeper insight into the failure mechanisms and robustness of the sponge-inspired designs. Additional harmonic simulations were conducted for final designs with boundary conditions applied to replicate the SPIV setup as further detailed in SI. Computational Fluid Dynamics (CFD) Simulations CFD simulations were used to analyze the fluidic behavior of the designs, focusing on vortex shedding, drag, and flow stability. Parametric geometries were converted to STL files via custom Python scripts provided in SI and imported into the CFD solver for meshing and analysis. Simulations were performed with the open-source code Basilisk 54 , which solves the full Navier–Stokes equations using the Volume of Fluid (VOF) method. The approach follows Popinet et al. 55 and combines adaptive mesh refinement (AMR) with a penalty method for boundary conditions. AMR dynamically refined the mesh in regions with steep gradients, such as fluid–solid interfaces, high-vorticity shear layers, and wake structures, while coarsening it in quiescent zones to optimize computational cost without sacrificing accuracy. The penalty method introduced localized forcing to impose no-slip boundary conditions on complex geometries, such as helical ridges and lattice structures, without requiring explicit geometric meshing. The top and front boundaries were treated as periodic during the optimization (perpendicular to the axis of the sponge). For the refined simulations of the selected, optimized geometries, no-slip wall conditions were applied to the top boundary, which was positioned adjacent to the ends of the sponge, as detailed in SI, Figures S4-5. At the inlet (left boundary), a constant flat velocity profile was imposed, with zero normal gradients for pressure and face pressure. At the outlet (right boundary), the normal velocity gradient was zero, while the pressure and face pressure were fixed to zero, ensuring smooth outflow and a reference pressure level. The domain size was L = 12.5D , where D is the diameter of the structure, and the mesh cell size was adaptively refined, ranging from \(\:L/{2}^{8}\) to \(\:L/{2}^{11}\:\) during the optimization and from \(\:L/{2}^{10}\) to \(\:L/{2}^{13}\) for the refined simulations. The finest mesh resolution \(\:L/{2}^{13}\approx\:0.0015D\) was approximately five times smaller than the smallest structural features and pore sizes, ensuring accurate geometric representation and flow resolution. Coarser cells were retained in low-gradient areas to reduce cost. Viscosity was set to match the Reynolds number based on the inlet velocity, and the radius of the sponge. The simulations were performed from the initial flat velocity in the domain up to 200 dimensionless time units. A method and implementation from Wald et al. 56 was used for iso-surface extraction in post-processing. Visualization was performed using ParaView 57 . The complete code, along with documentation and execution scripts, is available at https://github.com/cselab/sponge . Fabrication Selected designs from the Pareto front were fabricated with an Anycubic Photon D2 DLP printer (ANYCUBIC Technology Co., Ltd), which provides 51 µm resolution suitable for reproducing complex geometries. Printing was performed with Anycubic DLP Craftsman Resin, whose material properties (E = 1.1 GPa, ν = 0.49) were determined from Instron compression tests and used in simulations. Fabrication parameters included an exposure time of 2.2 s, a layer thickness of 50 µm, and post-processing with cleaning and UV curing for 5 minutes to complete polymerization. Geometric accuracy was verified by optical microscopy, with all structures within ± 50 µm of the STL models, consistent with the printer resolution. Minor adjustments were applied where necessary to match the intended design dimensions. Mechanical Testing Mechanical tests were performed to validate the FEA predictions. Compression experiments were carried out on an Instron 5944 universal testing machine (Instron Corporation, Norwood, MA) using a 2 kN load cell (Instron 2580-2KN). Uniaxial compressive forces were applied at a strain rate of 0.1 s⁻¹ until failure, indicated by buckling. Tests were recorded at 60 fps to capture the location and progression of failure. Load and displacement were sampled every 0.02 s to track stress–strain behavior and buckling loads with high precision. For each design, four samples were tested to confirm repeatability. Stereo Particle Image Velocimetry (SPIV) SPIV was used to evaluate the fluidic performance of the fabricated designs, focusing on vortex shedding, flow stability, and drag reduction. Experiments were conducted in a vertical recirculating flow loop (SI, Figure S9). The bulk flow rate was monitored using a Coriolis flowmeter, and rate was steady within 1%. The sponge samples were mounted 4.5 inches downstream of a 5th order polynomial contraction and flow conditioner to ensure a nominal top-hat inlet flow profile. 3D velocity fields on a plane 5 mm from the sample’s centerline were obtained using Stereo PIV (SPIV) 58 . To achieve this, the water was seeded with Potters 110P8 hollow glass microspheres 5–25 µm in diameter. A dual-cavity Nd:YAG laser was used to illuminate a nominally 60 mm × 60 mm cross-section of the wake at a 4.76 mm offset from the channel centerline. Two FlowMaster Imager ProX PIV cameras (1600 × 1200 pixels) with Scheimpflug adapters were positioned to capture the wake from the rear of the cylinder to a region 2–3 diameters downstream. SPIV image pairs with nominally 3 ms interframe delay were recorded at a sampling frequency of 14 Hz, with 40 seconds of data collected for each test case. Velocity fields were reconstructed in DaVis 7.2 using a multi-pass cross-correlation algorithm, with a final interrogation window size of 32 × 32 pixels and 50% overlap. Detailed experimental results for varying sponge geometries are provided in the SI, Figures S10-14. Declarations Acknowledgments The computations in this paper were run on the FASRC Cannon cluster supported by the FAS Division of Science Research Computing Group at Harvard University. Support to this work by the US National Science Foundation under grant 2134534 and 2124826 is gratefully acknowledged. Author contributions: Conceptualization: TM, SL, ZV, MEY Methodology and formal analysis: TM, SL Investigation: TM, SL, RL Fabrication and experiments: TM, AK, DH, SAM, SM Visualization: TM, RL, BWB, SL, MEY Funding acquisition: CG Project administration: TM, SL, CG, PK Supervision: CG, PK Writing – original draft: TM, SL, RL, BWB Writing – review & editing: TM, SL, AK, ZV, MEY, SAM, XZ, PK, CPG Competing interests: Authors declare that they have no competing interests. Data and materials availability: Supplementary material related to this article can be found online at the corresponding doi. The datasets and codes developed in the current study will be freely open sourced at the time of publication. The complete code, along with documentation and execution scripts, will be available at github.com/cselab/sponge. Supplementary files and videos can be found on https://drive.google.com/drive/folders/14u4YHg5V-BYuSPgW9Widze304STfY7ne?usp=drive_link. 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Supplementary Files Video1OptimizationProgress.mp4 Video 1: Optimization Progress Video2DesignACompression.mp4 Video 2: Design A Compression Experiments Video3DesignDCompression.mp4 Video 3: Design D Compression Experiments Video4DesignHCompression.mp4 Video 4: Design H Compression Experiments Video5DesignICompression.mp4 Video 5: Design I Compression Experiments Video6VorticityComparsionZ.mp4 Video 6: Vorticity Comparsion Z-Slice Video7VorticityComparisonY.mp4 Video 7: Vorticity Comparison Y-Slice Video8DesignACFDSPIV.mp4 Video 8: Design A CFD and SPIV Comparison Video9DesignDCFDSPIV.mp4 Video 9: Design D CFD and SPIV Comparison Video10DesignHCFDSPIV.mp4 Video 10: Design H CFD and SPIV Comparison Video11DesignICFDSPIV.mp4 Video 11: Design I CFD and SPIV Comparison OptimizationResults.xlsx Excel File Listing Design Parameters and Cost Funtions for All Data Points During Optimization CodeSTLGeneration.zip Code to Generate STL Files FEACode.zip Code to Perform FEA Simulations SupplementaryInformation.docx Supplementary Information Document Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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1","display":"","copyAsset":false,"role":"figure","size":578228,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStructure of \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eEuplectella aspergillum\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e and Bioinspired Applications: \u003c/strong\u003e(A) Photograph of the deep-sea sponge \u003cem\u003eEuplectella aspergillum\u003c/em\u003e, showing its hierarchical, checkerboard-like lattice structure. (B) Insets highlight key geometrical features. (C) These features contribute to lightweight construction, buckling resistance, and passive vortex suppression. Features are translated into engineered lattices and optimized through simulations. (D) FEA evaluates mechanical stability and buckling resistance. (E) CFD simulations (VOF and embedded boundary) capture flow behavior and vortex reduction. (F) Examples of multifunctional applications, including wind-resistant buildings and vascular stents.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/43fe2e71ead5c80c875d39ff.png"},{"id":93797200,"identity":"90a15f36-3d45-44ba-9899-2941c5c088b2","added_by":"auto","created_at":"2025-10-17 15:55:49","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":238147,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eBioinspired Design and Optimization Framework: \u003c/strong\u003e(A) The \u003cem\u003eEuplectella aspergillum\u003c/em\u003e-inspired architected material, where key design parameters, including lattice geometry, helical ridge structures, and diagonal reinforcements, are derived from the natural form of the sponge. These parameters serve as the foundation for creating bioinspired architected materials with enhanced mechanical and fluidic properties. (B) Flowchart illustrating the MOBO process. It starts with an initial LHS set of 50 design points, followed by batch generation for optimization. Batches of size 20 are parallelized on HPC resources, where high-fidelity FEA and CFD simulations are used to iteratively evaluate the multi-objective cost functions, optimizing both mechanical and fluidic performance. (C) Experimental characterization of selected Pareto-optimal designs, where compression tests assess the mechanical properties and SPIV is used to measure fluid dynamics.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/8d5f1bc66a0425bed34e526c.png"},{"id":93797203,"identity":"0c9d5ba8-41d2-46c5-9faf-bad060e2fa6e","added_by":"auto","created_at":"2025-10-17 15:55:49","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":304264,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePareto Front of Optimization: \u003c/strong\u003e(A) Normalized cost function space (see Materials and Methods, Eqs. 1 and 2), showing the trade-off between fluidic efficiency and mechanical robustness. Red points indicate non-dominated solutions (A–L), with A most optimized for mechanical strength and L for fluidic efficiency. (B) Hypervolume progression during MOBO optimization. Improvements level off in later batches, suggesting that further iterations would yield minimal gains, providing a natural stopping criteria for the optimization. (C) Simulations of selected designs (A, D, H, I) with FEA displacement contours and CFD 3D vorticity fields. These designs represent different trade-offs on the Pareto front and were chosen for experimental validation.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/e0dc82788b171553205b5957.png"},{"id":93797201,"identity":"823d3f21-8d1e-4246-9e1e-15ad010c2b2f","added_by":"auto","created_at":"2025-10-17 15:55:49","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":268749,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCompression tests on optimized designs\u003c/strong\u003e: Comparison of experimental and simulated force–displacement curves for Pareto-optimal designs A, D, H, and I. Each plot (A–D) shows results for one design, including experimental and FEA curves along with corresponding displacement and stress field plots. Simulated and experimental results agree closely, capturing effective stiffness and buckling locations.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/77e26706d61808d320116229.png"},{"id":93797777,"identity":"6d9a9079-4e1b-43c6-8263-7f5f7975af7a","added_by":"auto","created_at":"2025-10-17 16:03:49","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":372265,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eHydrodynamic performance of optimized designs compared to a solid cylinder. \u003c/strong\u003e(A) Drag coefficients from CFD simulations. The solid cylinder shows a baseline drag of ~1.0, while optimized designs achieve 0.8–0.85. (B) Lift coefficient over time under quasi-steady flow conditions. Optimized designs reduce both amplitude and variability of unsteady lift. (C) Power spectral density of the lift force signal, showing a dominant shedding frequency around 0.9 Hz (Strouhal number ≈ 0.21), consistent with literature and validating simulation accuracy. Peak magnitudes are reduced in all optimized designs. (D) Vorticity field around the solid cylinder, showing the onset of periodic vortex shedding in the near wake. (E) Vorticity field of Design I, with reduced vortex intensity and downstream-shifted shedding. The dashed box marks the SPIV measurement region. (F) SPIV snapshot of the wake region for Design I. Background color shows velocity magnitude, vectors and streamlines indicate flow direction.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/05ae0403e9caf5d0e7ada81d.png"},{"id":93797209,"identity":"2a600aef-64ba-46f6-9175-95e8b9c4d5bd","added_by":"auto","created_at":"2025-10-17 15:55:50","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":115546,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eHarmonic response of Pareto-optimal designs A, D, H, and I under radial excitation. \u003c/strong\u003eDisplacement amplitude versus frequency (0–100 Hz). The first resonance occurs above 20 Hz for all designs, well above vortex shedding frequencies (dashed blue line), supporting decoupled fluid–structure simulations.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/d1197f6dc0eda41bcc4e2a32.png"},{"id":93798836,"identity":"36c655a4-9a91-4632-ab48-6bed5b447783","added_by":"auto","created_at":"2025-10-17 16:19:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2732030,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/bca06521-5826-43bc-8d86-b1d3ff8f0aeb.pdf"},{"id":93798552,"identity":"775e5b67-0408-439d-8b12-a9ae2db8ada5","added_by":"auto","created_at":"2025-10-17 16:11:49","extension":"mp4","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":14658595,"visible":true,"origin":"","legend":"\u003cp\u003eVideo 1: Optimization Progress\u003c/p\u003e","description":"","filename":"Video1OptimizationProgress.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/1bbe758696ed2e93dccb2e48.mp4"},{"id":93797221,"identity":"3ea2285c-faa3-4d80-89c4-383fa3c730c1","added_by":"auto","created_at":"2025-10-17 15:55:50","extension":"mp4","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":48264534,"visible":true,"origin":"","legend":"\u003cp\u003eVideo 2: Design A Compression Experiments\u003c/p\u003e","description":"","filename":"Video2DesignACompression.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/e51c220e3884a24f88653624.mp4"},{"id":93797219,"identity":"5ad7da4e-e6dc-48ef-ba02-f92724db7f27","added_by":"auto","created_at":"2025-10-17 15:55:50","extension":"mp4","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":32727798,"visible":true,"origin":"","legend":"Video 3: Design D Compression Experiments","description":"","filename":"Video3DesignDCompression.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/e3eb172dfb83021ec5b57b87.mp4"},{"id":93797222,"identity":"64724e37-aa5b-443c-9234-28f91b3a9739","added_by":"auto","created_at":"2025-10-17 15:55:50","extension":"mp4","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":29448743,"visible":true,"origin":"","legend":"Video 4: Design H Compression Experiments","description":"","filename":"Video4DesignHCompression.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/35e25705f629f7f9acc80d35.mp4"},{"id":93797214,"identity":"c6a9f07b-ff41-43e8-ab71-503ba5bfa15b","added_by":"auto","created_at":"2025-10-17 15:55:50","extension":"mp4","order_by":5,"title":"","display":"","copyAsset":false,"role":"supplement","size":25962977,"visible":true,"origin":"","legend":"\u003cp\u003eVideo 5: Design I Compression Experiments\u003c/p\u003e","description":"","filename":"Video5DesignICompression.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/8da41c5fb6430abbdf46fa35.mp4"},{"id":93797788,"identity":"efaa71fe-67ce-4522-9738-7f6e94f78831","added_by":"auto","created_at":"2025-10-17 16:03:50","extension":"mp4","order_by":6,"title":"","display":"","copyAsset":false,"role":"supplement","size":17124267,"visible":true,"origin":"","legend":"Video 6: Vorticity Comparsion Z-Slice","description":"","filename":"Video6VorticityComparsionZ.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/d56b4416083f6bb4b80fe6d0.mp4"},{"id":93797218,"identity":"3824aaac-49f7-4796-9399-1cce3ceb98b8","added_by":"auto","created_at":"2025-10-17 15:55:50","extension":"mp4","order_by":7,"title":"","display":"","copyAsset":false,"role":"supplement","size":19217145,"visible":true,"origin":"","legend":"Video 7: Vorticity Comparison Y-Slice","description":"","filename":"Video7VorticityComparisonY.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/5b05b8ad29650fdb0d39dd73.mp4"},{"id":93797215,"identity":"1cc02eed-2387-44ea-b8a7-45ce0ffa695f","added_by":"auto","created_at":"2025-10-17 15:55:50","extension":"mp4","order_by":8,"title":"","display":"","copyAsset":false,"role":"supplement","size":7434704,"visible":true,"origin":"","legend":"Video 8: Design A CFD and SPIV Comparison","description":"","filename":"Video8DesignACFDSPIV.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/f97b263989808b150e733511.mp4"},{"id":93797231,"identity":"f7227672-157b-4e46-828f-b12ebd05b25b","added_by":"auto","created_at":"2025-10-17 15:55:50","extension":"mp4","order_by":9,"title":"","display":"","copyAsset":false,"role":"supplement","size":7246575,"visible":true,"origin":"","legend":"Video 9: Design D CFD and SPIV Comparison","description":"","filename":"Video9DesignDCFDSPIV.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/32119a92c03bf51c39a4b588.mp4"},{"id":93797787,"identity":"b9a62731-521f-4479-8a1c-c7f4f573069f","added_by":"auto","created_at":"2025-10-17 16:03:50","extension":"mp4","order_by":10,"title":"","display":"","copyAsset":false,"role":"supplement","size":6929154,"visible":true,"origin":"","legend":"Video 10: Design H CFD and SPIV Comparison","description":"","filename":"Video10DesignHCFDSPIV.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/1a6acb0c4e0a65ce6a1b543e.mp4"},{"id":93797236,"identity":"894aa66e-ba51-4522-8e89-016981c39205","added_by":"auto","created_at":"2025-10-17 15:55:50","extension":"mp4","order_by":11,"title":"","display":"","copyAsset":false,"role":"supplement","size":7572330,"visible":true,"origin":"","legend":"Video 11: Design I CFD and SPIV Comparison","description":"","filename":"Video11DesignICFDSPIV.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/0795feb3395a620efa2dc36d.mp4"},{"id":93797781,"identity":"78198391-1505-4920-9deb-78d090979540","added_by":"auto","created_at":"2025-10-17 16:03:50","extension":"xlsx","order_by":12,"title":"","display":"","copyAsset":false,"role":"supplement","size":129325,"visible":true,"origin":"","legend":"Excel File Listing Design Parameters and Cost Funtions for All Data Points During Optimization","description":"","filename":"OptimizationResults.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/4ad6b8e0e4dc68ac5293b7b9.xlsx"},{"id":93797230,"identity":"2eb5c740-aedc-488e-83e0-74b70a74c8d5","added_by":"auto","created_at":"2025-10-17 15:55:50","extension":"zip","order_by":13,"title":"","display":"","copyAsset":false,"role":"supplement","size":13637,"visible":true,"origin":"","legend":"Code to Generate STL Files","description":"","filename":"CodeSTLGeneration.zip","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/3b2df229d9026e59c0755eeb.zip"},{"id":93797782,"identity":"29d47fb8-12ea-43bd-a8c9-0dba953abb48","added_by":"auto","created_at":"2025-10-17 16:03:50","extension":"zip","order_by":14,"title":"","display":"","copyAsset":false,"role":"supplement","size":8621,"visible":true,"origin":"","legend":"Code to Perform FEA Simulations","description":"","filename":"FEACode.zip","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/3a98611c49253835cd3cd2eb.zip"},{"id":93797239,"identity":"c0b62355-d269-4389-b426-59faaa6b1919","added_by":"auto","created_at":"2025-10-17 15:55:51","extension":"docx","order_by":15,"title":"","display":"","copyAsset":false,"role":"supplement","size":58604641,"visible":true,"origin":"","legend":"Supplementary Information Document","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-7756357/v1/752ff209506284b70c1514ba.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Metamaterials from the Deep: Optimized Mechano-Fluidic Materials Inspired by Deep-Sea Sponges","fulltext":[{"header":"Introduction","content":"\u003cp\u003eNature, through millions of years of evolutionary processes, has developed a wide range of structures and materials that show efficiency, adaptability, and multifunctionality. This natural optimization, driven by survival and reproduction, has led to biological designs that often surpass both intuitive and engineered solutions. As our understanding of these systems deepens, so does our ability to draw inspiration from them, fueling the field of biomimetic engineering \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. From the self-cleaning properties of lotus leaves \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e to the impact resistance of mollusk shells \u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e, the adhesive capabilities of gecko feet \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e, and the color-changing abilities of chameleon skin \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e, nature offers a vast repository of design principles.\u003c/p\u003e\u003cp\u003eLoad-bearing biological structures are especially compelling for their ability to achieve mechanical strength with minimal material. Examples for lightweight yet strong structures include the trabecular bone, with its optimized lattice structure \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e, and the honeycomb architecture \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e found in beehives. Marine organisms, which face unique challenges in their aquatic environments, offer additional inspiration. The deep-sea glass sponge, \u003cem\u003eEuplectella aspergillum\u003c/em\u003e \u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e, commonly known as Venus\u0026rsquo; flower basket, is a notable example of structural efficiency and multifunctionality \u003csup\u003e\u003cspan additionalcitationids=\"CR12 CR13\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. This organism has evolved a skeletal system that combines lightweight design with high mechanical strength \u003csup\u003e\u003cspan additionalcitationids=\"CR16 CR17 CR18\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e and distinctive fluid dynamic interactions \u003csup\u003e\u003cspan additionalcitationids=\"CR21 CR22 CR23 CR24\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. Over millions of years, shaped the sponge's structure has evolved to withstand the extreme conditions of its deep-sea habitat, such as high pressures, limited light, cold temperatures, and persistent exposure to fluid flows. The skeletal structure of \u003cem\u003eEuplectella aspergillum\u003c/em\u003e consists of a lattice-like arrangement of silica spicules, forming a cylindrical structure with a hierarchical organization spanning multiple length scales \u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003ePrevious studies have highlighted both mechanical and fluidic aspects of this architecture. Weaver et al. \u003csup\u003e12\u003c/sup\u003e demonstrated the structural integrity of its six-level hierarchical design, ranging from nanometers to centimeters, emphasizing its efficiency in material use and mechanical stability. Fernandes et al. \u003csup\u003e15\u003c/sup\u003e highlighted that the sponge's checkerboard-like square lattice with double-diagonal reinforcement achieves optimal buckling resistance for a given volume fraction, outperforming conventional lattice designs in mechanical behavior. Vangelatos et al. \u003csup\u003e18\u003c/sup\u003e used Finite Element Analysis (FEA) to analyze nonlinear buckling and developed an optimized sponge-inspired metamaterial that carried higher loads with less volume using topology optimization. On the fluid side, Chen et al. \u003csup\u003e19\u003c/sup\u003e found that the ridge helical system spiraling the cylindrical sponge lattice improves radial stiffness and fluid permeability. Falcucci et al. \u003csup\u003e20,23\u003c/sup\u003e carried out high-performance computing (HPC) flow simulations on a complete skeletal model of \u003cem\u003eEuplectella aspergillum\u003c/em\u003e, showing that the sponge skeleton reduces hydrodynamic stress and drag forces. Fernandes et al. \u003csup\u003e21\u003c/sup\u003e demonstrated that the sponge's ridge system suppresses von K\u0026aacute;rm\u0026aacute;n vortex shedding \u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. This suppression prevents resonance vibrations, reduces lift force oscillations across flow regimes, and improves mechanical performance. Together, these characteristics make \u003cem\u003eEuplectella\u003c/em\u003e a compelling model for engineered structures where both mechanical resilience and fluid control are important, such as offshore platforms, aerospace components, and biomedical scaffolds.\u003c/p\u003e\u003cp\u003eDespite extensive research into the mechanical and fluid dynamic characteristics of \u003cem\u003eEuplectella aspergillum\u003c/em\u003e, a critical gap remains in addressing how these attributes interact and can be simultaneously optimized with the structural properties in engineered systems. Previous studies have predominantly focused on either mechanical or fluid dynamic aspects, without emphasizing the synergies and trade-offs that define multifunctional designs. Addressing these challenges requires an integrated framework capable of balancing competing objectives, which is increasingly important given the demand for lightweight structures and efficient fluid management in engineering applications.\u003c/p\u003e\u003cp\u003eRecent advances in computational modeling, simulation techniques, multi-objective optimization, and HPC now offer the tools to address this complexity, enabling the development of designs that integrate and optimally balance both mechanical and fluidic performance. This work presents an automated framework that combines high-fidelity computational fluid dynamics (CFD) and FEA simulations within a multi-objective Bayesian optimization (MOBO) \u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e scheme. While traditional optimization algorithms, like NSGA-II \u003csup\u003e30\u003c/sup\u003e and MOEA/D \u003csup\u003e31\u003c/sup\u003e have been widely used for multi-objective optimization, they struggle to handle the computational expense of high-fidelity simulations. In contrast, MOBO is effective for optimizing costly black-box functions with a limited number of evaluations \u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e and can be parallelized on HPC resources.\u003c/p\u003e\u003cp\u003eUsing these capabilities, our framework efficiently explores complex design spaces to identify Pareto-optimal solutions inspired by the \u003cem\u003eEuplectella\u003c/em\u003e skeleton, balancing mechanical resilience and hydrodynamic performance. The study combines computational modeling, 3D fabrication using high precision stereolithography (SLA), and experimental validation through mechanical compression tests and stereo particle image velocimetry (SPIV) flow measurements. By integrating computational simulations, multi-objective optimization, and experimental methods, we establish a methodology for translating bioinspired principles into multifunctional designs. This research not only advances the understanding of \u003cem\u003eEuplectella\u0026rsquo;s\u003c/em\u003e structural principles but more importantly demonstrates their relevance in engineering, where lightweight, resilient, and efficient multifunctional designs are critical.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eDesign Framework\u003c/h2\u003e\u003cp\u003eWe translate biological insights into engineered multifunctional designs, developing a computational framework inspired by the hierarchical lattice structure of \u003cem\u003eEuplectella aspergillum\u003c/em\u003e. As illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the sponge skeleton features a checkerboard-like grid of longitudinal and circumferential beams, diagonal reinforcements, and helical ridges curling over the tubular structure. Together these features contribute to lightweight construction, improved buckling resistance, and passive vortex suppression.\u003c/p\u003e\u003cp\u003eBuilding on the structural insights from \u003cem\u003eEuplectella aspergillum\u003c/em\u003e, we developed a parameterized design space that captures the sponge\u0026rsquo;s key architectural features in an idealized cylindrical lattice model. The abstraction incorporates the square lattice of longitudinal and circumferential beams, reinforced by double diagonals and external helical ridges, and serves as the foundation for computational modeling and optimization.\u003c/p\u003e\u003cp\u003eThe cylindrical lattice is defined with constant length \u003cem\u003eL\u003c/em\u003e and diameter \u003cem\u003eD\u003c/em\u003e. The multiple spicule fibers within the sponge are represented as beams with rectangular cross sections, described by the design parameters width \u003cem\u003eW\u003c/em\u003e and height \u003cem\u003eH\u003c/em\u003e. Additional design parameters include the number of vertical beams \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eV\u003c/em\u003e\u003c/sub\u003e​, the number of circumferential beams \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e​, the radius of the semi-ellipsoidal cross section for the helical ridges \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e​, the number of loops in the helical ridges \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e​, and the counts for clockwise (CW) and counterclockwise (CCW) helical ridges \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eCW\u003c/em\u003e,\u003c/sub\u003e \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eCCW\u003c/em\u003e\u003c/sub\u003e​. Each parameter was chosen to enable precise control over the structural elements, with boundaries set by the sponge\u0026rsquo;s skeletal features sies and stability constraints for the computational simulations. An overview of all design parameters and their ranges are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eOverview of geometric design parameters for optimization\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eParameter\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDescription\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eParameter range\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLength of cylindrical lattice\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e100 mm\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDiameter of cylindrical lattice\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e22 mm\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eW\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eWidth of cross section\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.15\u0026ndash;0.65 mm\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eH\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHeight of cross section\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.15\u0026ndash;0.65 mm\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ev\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNumber of vertical beams\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e20\u0026ndash;50\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNumber of circumferential beams\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e30\u0026ndash;74\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRadius of semi-ellipsoid of helical ridges\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.6\u0026ndash;1.6 mm\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNumber of loops for helical ridges\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u0026ndash;6\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eCW\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNumber of clockwise helical ridges\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u0026ndash;3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eCCW\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNumber of counterclockwise helical ridges\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u0026ndash;3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eGeometries were generated using custom Python scripts, as detailed in Supplementary Information (SI), and evaluated with high-fidelity FEA and CFD simulations to capture mechanical and fluidic performance. FEA simulations, implemented through the ANSYS\u0026reg; Python environment (PyAnsys), were used to study how variations in geometry affect the mechanical behavior of the lattice. In parallel, CFD simulations were performed in Basilisk using a Volume of Fluid (VOF) scheme with an embedded boundary approach and adaptive mesh refinement (AMR) to resolve fluid forces and vortex shedding. During the MOBO stage, coarser AMR settings were applied to efficiently explore the design space, while for the final Pareto-optimal designs, the CFD involved grids at a resolution that enabled Direct Numerical Simulations (DNS). We selected a \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Re=UD/\\nu\\:=2100\\)\u003c/span\u003e\u003c/span\u003e for optimization as it corresponds to typical deep-sea flow conditions \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eBuilding on our previous work with inverse design framework \u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e,\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e, we applied MOBO to explore the design space and identify optimal trade-offs between mechanical and fluid dynamic properties. The optimization was conducted using the Thompson Sampling Efficient Multi-Objective Optimization (TS-EMO) algorithm, developed by Bradford et al. \u003csup\u003e29\u003c/sup\u003e. Objective and cost functions are defined in the Materials and Methods section. To manage the computational expense of FEA and VOF-based CFD, we conducted large scale parallel simulations.\u003c/p\u003e\u003cp\u003eOur multi-stage workflow is summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. It starts with parameterization of the sponge-inspired lattice, including helical ridges and diagonal reinforcements (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA). MOBO then evaluates candidate designs through iterative FEA and CFD simulations to capture both mechanical and fluidic performance (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB). The resulting Pareto-optimal geometries illustrate different trade-offs between strength and flow efficiency, with potential applications in wind-resistant structures, biomedical implants, and fluid management devices. Selected designs were fabricated and tested through compression experiments and SPIV measurements (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eC). These experiments provided validation of the computational results. Details of the simulation, optimization, fabrication, and testing procedures are provided in the Materials and Methods section.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003ePareto Front Analysis\u003c/h3\u003e\n\u003cp\u003eThe optimization produced a design space mapping the trade-offs between mechanical strength and fluidic efficiency (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA). Pareto-optimal designs are shown in red. Convergence was monitored using the hypervolume metric (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB), which leveled off in later batches, indicating that further iterations would likely add little benefit and providing a natural stopping point.\u003c/p\u003e\u003cp\u003eThe Pareto front makes clear that gains in one objective come at the expense of the other. Simulations of selected designs (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eC) highlight these trade-offs: Design I for example is optimized for reduced vortex shedding and drag, while design A emphasizes mechanical strength. These examples highlight the balance between fluid stability and structural strength, influenced by features such as helical ridge density, lattice configuration, and beam cross-section.\u003c/p\u003e\u003cp\u003eAnalysis of clusters and outliers along the Pareto front further highlighted trends. For example, modifying helical ridge pitch can reduce vortex shedding with only modest reductions in mechanical strength. The Pareto front thus provides a practical tool for selecting designs based on application priorities. Four representative points were chosen for experimental validation, spanning designs from fluidically efficient to mechanically robust. Full parameter configurations of Pareto-optimal designs are given in the SI, Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\n\u003ch3\u003eFabrication and experimental validation of selected designs\u003c/h3\u003e\n\u003cp\u003eDesigns A, D, H, and I were selected from the Pareto front to represent a spectrum of performance attributes, covering mechanically robust, fluid-efficient, and balanced designs.\u003c/p\u003e\u003cp\u003eThe selected designs were fabricated using an Anycubic Photon D2 DLP printer with a resolution of 51 \u0026micro;m, enabling features and pore sizes as small as 150 \u0026micro;m, comparable to those of the deep-sea sponge. The printed geometries were validated with optical microscopy to confirm dimensional accuracy. Mechanical performance was assessed by measuring critical buckling load and deformation under compression. Results showed high repeatability across four samples, confirming the reliability of the fabrication process.\u003c/p\u003e\u003cp\u003eForce\u0026ndash;displacement curves from the experiments closely matched predictions from nonlinear buckling analyses (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Agreement was consistent across key metrics, including Young\u0026rsquo;s modulus (effective stiffness) and buckling behavior, with deviations between experimental and simulated stiffness values below 5%. Experimentally observed buckling locations, shown in supplementary videos and SI, Figure S3, also matched simulated behavior, confirming the accuracy of the computational model.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eValidation of fluidic performance was carried out using CFD cylinder baseline and SPIV, providing time-resolved velocity fields around the fabricated structures under quasi-steady flow at Reynolds number\u0026thinsp;~\u0026thinsp;2100. Results (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) show that all optimized designs, regardless of porosity, substantially reduce hydrodynamic loading compared to the solid cylinder benchmark. The cylinder also served as a reference to validate the CFD simulations as detailed in SI, Figure S6.\u003c/p\u003e\u003cp\u003eFor the reference solid cylinder, the drag coefficient remained close to 1.0, consistent with literature. The optimized designs reduced drag to 0.8\u0026ndash;0.85 (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eA). Lift fluctuations were also suppressed (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB): Design A, the most rigid structure, reduced the RMS lift coefficient by 39%, while the most porous, Design I, achieved an 84% reduction. Power spectral density of the lift signal (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eC) confirmed the attenuation of vortex shedding, with all optimized designs showing reduced spectral peaks near 0.9 Hz, matching the expected Strouhal number of ~\u0026thinsp;0.21.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWake dynamics are illustrated by vorticity plots of the solid cylinder (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eD) and optimized Design I (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eE). The cylinder generates strong alternating vortices close to the body, whereas Design I shifts vortex formation downstream and lowers overall vorticity. These trends were supported by SPIV measurements recorded within the wake region, from the cylinder up to approximately three diameters downstream, as indicated by the dashed box in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eE. A representative SPIV snapshot is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eF, with velocity magnitude shown by background color and overlaid streamlines and vectors illustrating flow direction and structure.\u003c/p\u003e\u003cp\u003eTo compare CFD and SPIV data, velocity fields were extracted from simulations over the same spatial domain. Side-by-side snapshots and time-resolved videos (SI, Figures S11-13) show agreement in velocity magnitude and flow structure. Some differences were observed between SPIV and CFD results as detailed in SI: vortex shedding appeared more pronounced and initiated closer to the structure in the SPIV data, likely due to fabrication-induced surface roughness or boundary effects in the water tunnel. Nonetheless, both experimental and numerical data confirm the similar wake topology and reduction in unsteady flow. Quantitative comparisons presented in SI, Figure S14 support these findings. Dominant shedding frequencies from CFD and SPIV matched within approximately 20%. Average transverse (lift direction) velocities in the wake were on average 0.011 m/s higher in SPIV, consistent with the more visible shedding. Importantly, both datasets showed that optimized designs reduced transverse velocities by a factor of three to five and lowered vortex intensity compared to the solid cylinder baseline, confirming the effectiveness of the optimization in stabilizing wake dynamics and reducing hydrodynamic forces.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study establishes a robust design framework for multi-objective optimization of multifunctional structures that balance fluidic and mechanical performance. Inspired by the hierarchical skeleton of \u003cem\u003eEuplectella aspergillum\u003c/em\u003e, we couple fluid dynamics and structural mechanics, through high-fidelity simulations and experiments. Using automated FEA and CFD simulations with MOBO on HPC resources, our framework identified Pareto-optimal designs that balance competing objectives. Each design represents a trade-off between mechanical strength and fluidic efficiency, echoing the dual functionality of the \u003cem\u003eEuplectella\u003c/em\u003e, where structural integrity and flow permeability are simultaneously maintained under extreme conditions.\u003c/p\u003e\u003cp\u003eCompared to the initial Latin Hypercube samples, optimized structures improved critical buckling force by an average of 140% while maintaining or reducing material use. Nonlinear FEA predictions agreed with experimental compression tests across buckling loads, force-displacement responses, and failure locations (SI, Figure S3), confirming the accuracy of the computational simulations.\u003c/p\u003e\u003cp\u003eSPIV measurements confirmed the CFD predictions of drag reduction and vortex suppression. The observed wake stabilization is consistent with prior findings that increasing porosity attenuates turbulence kinetic energy (TKE), elongates shear layers, and suppresses vortex shedding \u003csup\u003e\u003cspan additionalcitationids=\"CR37 CR38\" citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. In our case, the time-averaged TKE in the cylinder wake was about 50% higher and peaked roughly one diameter closer to the body than in the optimized designs, while CFD predicted an even more pronounced downstream shift than observed in SPIV as shown in SI, Figure S13. Our results further show that porosities as low as 5% are sufficient to suppress vortex shedding, a significant reduction compared to the effective porosity of natural \u003cem\u003eEuplectella\u003c/em\u003e structures. This highlights how targeted geometric refinement through optimization can exceed biological benchmarks for specific functional metrics. While natural sponges may retain higher porosities due to multifunctional biological roles \u003csup\u003e\u003cspan additionalcitationids=\"CR41\" citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e, our designs isolate specific performance attributes. Prior work on perforated cylinders reported similar wake suppression at porosities around 8% \u003csup\u003e38\u003c/sup\u003e, with similar wake suppression mechanisms \u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. Although those studies were typically conducted at higher Reynolds numbers, our results show that optimization can achieve comparable benefits at lower porosities.\u003c/p\u003e\u003cp\u003eTo reduce computational cost, fluidic and mechanical simulations were decoupled during optimization. Harmonic FEA of four Pareto-optimal designs (A, D, H, I) showed that the first structural resonance occurred above 20 Hz (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e), far above the vortex shedding frequencies of 0.85\u0026ndash;1.1 Hz (Strouhal\u0026thinsp;\u0026asymp;\u0026thinsp;0.21) confirmed by CFD and SPIV. This clear spectral separation indicates minimal energy transfer between flow and structure, thereby justifying the decoupled approach, which reduced computational expense while preserving the essential physics of each domain.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAlthough valid under these conditions, future work should explore fully coupled fluid\u0026ndash;structure interaction (FSI) models to capture transient dynamics, resonance interactions, and fatigue effects, especially at higher Reynolds numbers or under cyclical loading. While global vortex shedding occurs at frequencies well below structural resonance, localized shedding from smaller-scale features may occur at higher frequencies, potentially overlapping with structural modes. Modal analysis and dynamic testing could study these interactions and guide designs for long term durability.\u003c/p\u003e\u003cp\u003eBeyond the specific performance improvements, this framework demonstrates how multifunctional designs can be applied across engineering domains. In underwater settings, such as offshore platforms and pipelines, drag reduction and structural resilience are both critical. In biomedical applications, flow-permissive stents and filtration devices benefit from combining strength with low fluid resistance \u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. In aerospace and civil engineering, high strength-to-weight ratios are essential for components in bridges and aircraft. Other potential uses include energy-absorbing structures for transportation and sports \u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e, high-throughput water purification and flow catalysts \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e,\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e, and multifunctional metamaterial solutions for sensing, energy harvesting, and communication \u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e,\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. Recent advances in cellular fluidics and bubble-resolved transport within architected lattices further highlight opportunities for programmable multiphase flow control in such systems \u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e,\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eOur framework opens several paths for future work. Scalable fabrication could bring these designs into industrial applications \u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. Machine learning surrogates or reduced-order models may cut computational costs and speed up exploration of large design spaces. Further validation across different Reynolds number regimes, or the development of adaptive structures with tunable porosity and stiffness, would broaden applications in robotics, infrastructure, and flow control. The same approach can also be applied to other biological systems with multifunctional geometries, especially when combined with generative design and AI-based optimization.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eWe developed a bioinspired framework that integrates FEA, CFD, MOBO, and experiments to optimize multifunctional lattice structures. Inspired by \u003cem\u003eEuplectella aspergillum\u003c/em\u003e, the framework produced Pareto-optimal designs that balance mechanical strength and fluidic efficiency. Optimized lattices achieved up to 140% higher buckling loads than baseline structures while also reducing drag, lift fluctuations, and vortex shedding.\u003c/p\u003e\u003cp\u003eThis work shows how computational optimization can incorporate and refine biological design principles to create targeted, high-performance solutions that surpass conventional engineering structures. The framework provides a pathway for lightweight, resilient, and fluid-efficient materials with applications in offshore, biomedical, aerospace, and civil engineering. Future efforts focused on scalability, adaptability, and dynamic performance can extend the reach of these multifunctional designs.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cp\u003eThis section details the methodologies, parameters, and materials used throughout the study. It includes the multi-objective optimization framework, computational simulations, fabrication techniques, and experimental techniques applied.\u003c/p\u003e\n\u003ch3\u003eMulti-Objective Optimization Framework\u003c/h3\u003e\n\u003cp\u003eTwo cost functions were defined to capture the competing objectives of structural strength and fluidic performance. The mechanical cost function \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emech\u003c/em\u003e\u003c/sub\u003e, Eq.\u0026nbsp;1:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{F}_{mech}=\\:-\\:\\raisebox{1ex}{${F}_{Buckling}$}\\!\\left/\\:\\!\\raisebox{-1ex}{${V}_{sponge}$}\\right.\\:\\left(1\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewas designed to maximize the lattice\u0026rsquo;s buckling resistance while minimizing material usage, where \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eBuckling\u003c/em\u003e\u003c/sub\u003e is the standardized critical buckling force obtained from FEA and \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003eSponge\u003c/em\u003e\u003c/sub\u003e is the lattice volume. The fluid dynamic cost function \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003efluid\u003c/em\u003e\u003c/sub\u003e, Eq.\u0026nbsp;2:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{F}_{fluid}=\\:\\alpha\\:*\\stackrel{-}{{F}_{D}}+\\beta\\:*\\stackrel{-}{{F}_{L}}+\\gamma\\:*{\\sigma\\:}_{{F}_{L}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(2\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ecombined average drag forces (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{-}{{F}_{D}})\\)\u003c/span\u003e\u003c/span\u003e, average lift \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left(\\stackrel{-}{{F}_{L}}\\right)\\)\u003c/span\u003e\u003c/span\u003e forces, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{{F}_{L}}\\)\u003c/span\u003e\u003c/span\u003e the over time calculated standard deviation of the lift force, a measure for lift force oscillations and vortex shedding. Weighting factors were chosen as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:=\\beta\\:=0.2\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\gamma\\:=\\)\u003c/span\u003e\u003c/span\u003e 0.6, to emphasize suppression of unsteady lift. The overall optimization problem was therefore formulated as a bi-objective optimization, minimizing \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emech\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003efluid\u003c/em\u003e\u003c/sub\u003e​ simultaneously.\u003c/p\u003e\u003cp\u003eThe optimization process was initialized with 50 Latin Hypercube samples \u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e. We then applied the Thompson Sampling Efficient Multi-Objective (TSEMO) algorithm \u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e to generate Pareto-optimal solutions, iterating through 22 batches of 20 samples each. TSEMO uses gaussian processes as surrogates and Thompson sampling in conjunction with the hypervolume quality indicator and NSGA-II to choose a new evaluation point at each iteration. The algorithm outperforms NSGA-II and MOEA/D in approximating a Pareto front, has the capacity to handle noisy functions and offers the ability for batch evaluations. The AutoOED \u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e platform was used as a graphical interface to monitor optimization progress and adjust parameters. Details of the optimization algorithms and setup can be found in \u003csup\u003e29,52\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eGiven the high computational cost of high-fidelity FEA and especially VoF-based CFD simulations, all runs were carried out on the FASRC Cannon cluster at Harvard University. Each job was executed on a Sapphire Rapids node with 112 processes. Structures were evaluated in batches of 20, which allowed efficient parallelization. While batch optimization may require more evaluations to converge, running designs simultaneously minimized overhead and enabled much greater throughput within the same timeframe. In total, the CFD simulations required approximately 10,000 node-hours.\u003c/p\u003e\u003cp\u003eAutomation was achieved through parameterized Python scripts that generated geometries of the sponge-inspired lattices. These were passed directly to CFD and FEA solvers, with data management and transfers handled via the Globus platform \u003csup\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e. Once convergence criteria were met, selected designs from the Pareto front were fabricated and validated experimentally through compression tests and SPIV.\u003c/p\u003e\n\u003ch3\u003eFinite Element Analysis (FEA) for Mechanical Properties\u003c/h3\u003e\n\u003cp\u003eFinite Element Analysis was used to predict the mechanical response of each design, focusing on critical buckling load, stiffness, and failure points. Models were created in ANSYS\u0026reg; Mechanical\u0026trade; 2024 R1 using the Parametric Design Language (APDL) and automated through PyMAPDL, which enabled direct scripting of lattice geometries and simulation runs. Different lattice configurations were generated by varying geometric parameters in the code.\u003c/p\u003e\u003cp\u003eLattices were modeled with Timoshenko beam elements (BEAM188) and assigned linear elastic material properties based on tests of solid, cured Anycubic DLP Craftsman resin. Compression tests on bulk samples gave a Young\u0026rsquo;s modulus of 1.1 GPa and Poisson\u0026rsquo;s ratio of 0.49. For each design, the cylindrical lattice was assumed to be fully constrained at its base (\u003cem\u003eu\u003c/em\u003e\u003csub\u003ex\u003c/sub\u003e = \u003cem\u003eu\u003c/em\u003e\u003csub\u003ey\u003c/sub\u003e = \u003cem\u003eu\u003c/em\u003e\u003csub\u003ez\u003c/sub\u003e= 0). Two types of simulations were performed: a linear static analysis (Analysis type: STATIC) to determine the stiffness of the lattice, and a linear buckling analysis (Analysis type: BUCKLE) to obtain the critical buckling force. In the simulation process, a uniform compressive pressure parallel to the z -axis was applied to all nodes on the top surface. In addition to the linear analyses, nonlinear buckling simulations were performed for pareto optimal designs to achieve higher accuracy and to better capture real-world failure behavior. These included geometric imperfections, large deformations (NLGEOM), and post-buckling behavior. Initial imperfections were introduced by scaling the first buckling mode from the linear analysis, simulating manufacturing irregularities. Nonlinear analyses provided improved predictions of load-bearing capacity and stress distribution. Predicted failure locations closely matched experimental observations. This confirmed the validity of the computational model and offered deeper insight into the failure mechanisms and robustness of the sponge-inspired designs. Additional harmonic simulations were conducted for final designs with boundary conditions applied to replicate the SPIV setup as further detailed in SI.\u003c/p\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003eComputational Fluid Dynamics (CFD) Simulations\u003c/h2\u003e\u003cp\u003eCFD simulations were used to analyze the fluidic behavior of the designs, focusing on vortex shedding, drag, and flow stability. Parametric geometries were converted to STL files via custom Python scripts provided in SI and imported into the CFD solver for meshing and analysis.\u003c/p\u003e\u003cp\u003eSimulations were performed with the open-source code Basilisk \u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e, which solves the full Navier\u0026ndash;Stokes equations using the Volume of Fluid (VOF) method. The approach follows Popinet et al. \u003csup\u003e55\u003c/sup\u003e and combines adaptive mesh refinement (AMR) with a penalty method for boundary conditions. AMR dynamically refined the mesh in regions with steep gradients, such as fluid\u0026ndash;solid interfaces, high-vorticity shear layers, and wake structures, while coarsening it in quiescent zones to optimize computational cost without sacrificing accuracy. The penalty method introduced localized forcing to impose no-slip boundary conditions on complex geometries, such as helical ridges and lattice structures, without requiring explicit geometric meshing.\u003c/p\u003e\u003cp\u003eThe top and front boundaries were treated as periodic during the optimization (perpendicular to the axis of the sponge). For the refined simulations of the selected, optimized geometries, no-slip wall conditions were applied to the top boundary, which was positioned adjacent to the ends of the sponge, as detailed in SI, Figures S4-5. At the inlet (left boundary), a constant flat velocity profile was imposed, with zero normal gradients for pressure and face pressure. At the outlet (right boundary), the normal velocity gradient was zero, while the pressure and face pressure were fixed to zero, ensuring smooth outflow and a reference pressure level.\u003c/p\u003e\u003cp\u003eThe domain size was \u003cem\u003eL\u0026thinsp;=\u0026thinsp;12.5D\u003c/em\u003e, where \u003cem\u003eD\u003c/em\u003e is the diameter of the structure, and the mesh cell size was adaptively refined, ranging from \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:L/{2}^{8}\\)\u003c/span\u003e\u003c/span\u003e to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:L/{2}^{11}\\:\\)\u003c/span\u003e\u003c/span\u003eduring the optimization and from \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:L/{2}^{10}\\)\u003c/span\u003e\u003c/span\u003e to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:L/{2}^{13}\\)\u003c/span\u003e\u003c/span\u003e for the refined simulations. The finest mesh resolution \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:L/{2}^{13}\\approx\\:0.0015D\\)\u003c/span\u003e\u003c/span\u003e was approximately five times smaller than the smallest structural features and pore sizes, ensuring accurate geometric representation and flow resolution. Coarser cells were retained in low-gradient areas to reduce cost.\u003c/p\u003e\u003cp\u003eViscosity was set to match the Reynolds number based on the inlet velocity, and the radius of the sponge. The simulations were performed from the initial flat velocity in the domain up to 200 dimensionless time units. A method and implementation from Wald et al. \u003csup\u003e56\u003c/sup\u003e was used for iso-surface extraction in post-processing. Visualization was performed using ParaView \u003csup\u003e\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e. The complete code, along with documentation and execution scripts, is available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/cselab/sponge\u003c/span\u003e\u003cspan address=\"https://github.com/cselab/sponge\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003eFabrication\u003c/h2\u003e\u003cp\u003eSelected designs from the Pareto front were fabricated with an Anycubic Photon D2 DLP printer (ANYCUBIC Technology Co., Ltd), which provides 51 \u0026micro;m resolution suitable for reproducing complex geometries. Printing was performed with Anycubic DLP Craftsman Resin, whose material properties (E\u0026thinsp;=\u0026thinsp;1.1 GPa, ν\u0026thinsp;=\u0026thinsp;0.49) were determined from Instron compression tests and used in simulations.\u003c/p\u003e\u003cp\u003eFabrication parameters included an exposure time of 2.2 s, a layer thickness of 50 \u0026micro;m, and post-processing with cleaning and UV curing for 5 minutes to complete polymerization. Geometric accuracy was verified by optical microscopy, with all structures within \u0026plusmn;\u0026thinsp;50 \u0026micro;m of the STL models, consistent with the printer resolution. Minor adjustments were applied where necessary to match the intended design dimensions.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003eMechanical Testing\u003c/h2\u003e\u003cp\u003eMechanical tests were performed to validate the FEA predictions. Compression experiments were carried out on an Instron 5944 universal testing machine (Instron Corporation, Norwood, MA) using a 2 kN load cell (Instron 2580-2KN). Uniaxial compressive forces were applied at a strain rate of 0.1 s⁻\u0026sup1; until failure, indicated by buckling.\u003c/p\u003e\u003cp\u003eTests were recorded at 60 fps to capture the location and progression of failure. Load and displacement were sampled every 0.02 s to track stress\u0026ndash;strain behavior and buckling loads with high precision. For each design, four samples were tested to confirm repeatability.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003eStereo Particle Image Velocimetry (SPIV)\u003c/h2\u003e\u003cp\u003eSPIV was used to evaluate the fluidic performance of the fabricated designs, focusing on vortex shedding, flow stability, and drag reduction. Experiments were conducted in a vertical recirculating flow loop (SI, Figure S9). The bulk flow rate was monitored using a Coriolis flowmeter, and rate was steady within 1%. The sponge samples were mounted 4.5 inches downstream of a 5th order polynomial contraction and flow conditioner to ensure a nominal top-hat inlet flow profile.\u003c/p\u003e\u003cp\u003e3D velocity fields on a plane 5 mm from the sample\u0026rsquo;s centerline were obtained using Stereo PIV (SPIV) \u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e. To achieve this, the water was seeded with Potters 110P8 hollow glass microspheres 5\u0026ndash;25 \u0026micro;m in diameter. A dual-cavity Nd:YAG laser was used to illuminate a nominally 60 mm \u0026times; 60 mm cross-section of the wake at a 4.76 mm offset from the channel centerline. Two FlowMaster Imager ProX PIV cameras (1600 \u0026times; 1200 pixels) with Scheimpflug adapters were positioned to capture the wake from the rear of the cylinder to a region 2\u0026ndash;3 diameters downstream.\u003c/p\u003e\u003cp\u003eSPIV image pairs with nominally 3 ms interframe delay were recorded at a sampling frequency of 14 Hz, with 40 seconds of data collected for each test case. Velocity fields were reconstructed in DaVis 7.2 using a multi-pass cross-correlation algorithm, with a final interrogation window size of 32 \u0026times; 32 pixels and 50% overlap. Detailed experimental results for varying sponge geometries are provided in the SI, Figures S10-14.\u003c/p\u003e\u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe computations in this paper were run on the FASRC Cannon cluster supported by the FAS Division of Science Research Computing Group at Harvard University. Support to this work by the US National Science Foundation under grant 2134534 and 2124826 is gratefully acknowledged.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eConceptualization: TM, SL, ZV, MEY \u003cbr\u003eMethodology and formal analysis: TM, SL \u003cbr\u003eInvestigation: TM, SL, RL \u003cbr\u003eFabrication and experiments: TM, AK, DH, SAM, SM \u003cbr\u003eVisualization: TM, RL, BWB, SL, MEY \u003cbr\u003eFunding acquisition: CG \u003cbr\u003eProject administration: TM, SL, CG, PK \u003cbr\u003eSupervision: CG, PK \u003cbr\u003eWriting – original draft: TM, SL, RL, BWB \u003cbr\u003e Writing – review \u0026amp; editing: TM, SL, AK, ZV, MEY, SAM, XZ, PK, CPG\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests:\u003c/strong\u003e Authors declare that they have no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData and materials availability: \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSupplementary material related to this article can be found online at the corresponding doi. The datasets and codes developed in the current study will be freely open sourced at the time of publication. The complete code, along with documentation and execution scripts, will be available at github.com/cselab/sponge. Supplementary files and videos can be found on https://drive.google.com/drive/folders/14u4YHg5V-BYuSPgW9Widze304STfY7ne?usp=drive_link.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eWegst UGK, Bai H, Saiz E, Tomsia AP, Ritchie RO (2015) Bioinspired structural materials. Nat Mater 14:23\u0026ndash;36\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKitano H (2002) Computational systems biology. Nature 420:206\u0026ndash;210\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEnsikat HJ, Ditsche-Kuru P, Neinhuis C, Barthlott W (2011) Superhydrophobicity in perfection: the outstanding properties of the lotus leaf. 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Springer, Cham. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/978-3-319-68852-7\u003c/span\u003e\u003cspan address=\"10.1007/978-3-319-68852-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7756357/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7756357/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMultifunctional materials that balance mechanical resilience and fluid dynamic efficiency are increasingly critical in engineering applications, yet the synergistic optimization of these properties remains a challenge due to inherent trade-offs, computational and experimental expense, and the complexity of high-dimensional design spaces. Inspired by the hierarchical skeleton of the deep-sea sponge \u003cem\u003eEuplectella aspergillum\u003c/em\u003e, which shows distinct mechanical and fluidic characteristics, this study presents a framework that integrates high-fidelity Finite Element Analysis for mechanics, Volume of Fluid methods for flow simulations, and multi-objective Bayesian optimization. Using high-performance computing, our approach efficiently explores complex design spaces to identify Pareto-optimal solutions. Optimized lattices showed an average 140% improvement in critical buckling force across a range of volume fractions relative to baseline designs, along with significant reductions in drag, lift, and vortex shedding, achieved with porosities as low as 5%. Fabricated using stereolithography and validated through mechanical compression tests and stereo particle image velocimetry, experimental results align with computational simulations. By achieving simultaneous optimization of mechanical and fluidic performance, this research establishes a methodology for designing lightweight, high-performance materials with applications in aerospace, civil engineering, and energy systems.\u003c/p\u003e","manuscriptTitle":"Metamaterials from the Deep: Optimized Mechano-Fluidic Materials Inspired by Deep-Sea Sponges","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-17 15:55:44","doi":"10.21203/rs.3.rs-7756357/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"0416d1e0-69b5-455d-8c3f-1ea41939f9c1","owner":[],"postedDate":"October 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":56366346,"name":"Physical sciences/Engineering/Mechanical engineering"},{"id":56366347,"name":"Physical sciences/Materials science/Structural materials/Mechanical properties"},{"id":56366348,"name":"Physical sciences/Engineering"}],"tags":[],"updatedAt":"2026-04-21T16:10:47+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-17 15:55:44","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7756357","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7756357","identity":"rs-7756357","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}