The structural efficiency of the sea sponge Euplectella aspergillum skeleton: bio-inspiration for 3D printed architectures

In Nature, despite the diversity of materials, patterns and structural designs, the majority of biomineralized systems share a common feature: the incorporation of multiple sets of discrete elements across different length scales. This paper is the first to assess whether the design features observed in the hexactinellid sea sponge Euplectella aspergillum can be transferred and implemented for the development of new structurally efficient engineering architectures manufactured by three-dimensional (3D) additive manufacturing (AM). We present an investigation into the design and survival strategies found in the biological system and evaluate their translation into a scaled engineering analogue assessed experimentally and through finite-element (FE) simulations. Discrete sections of the skeletal lattice were evaluated and tested in an in situ compression fixture using micro-computed tomography (μCT). This methodology permitted the characterization of the hierarchical organization of the siliceous skeleton; a multi-layered arrangement with a fusion between struts to improve the local energy-absorbing capabilities. It was observed that the irregular overlapping architecture of spicule–nodal point sub-structure offers unique improvements in the global strength and stiffness of the structure. The 3D data arising from the μCT of the skeleton were used to create accurate FE models and replication through 3D AM. The printed struts in the engineering analogue were homogeneous, comprising bonded ceramic granular particles (10–100 µm) with an outer epoxy infused shell. In these specimens, the compressive response of the sample was expected to be dynamic and catastrophic, but while the specimens showed a similar initiation and propagation failure pattern to E. aspergillum, the macroscopic deformation behaviour was altered from the expected predominantly brittle behaviour to a more damage tolerant quasi-brittle failure mode. In addition, the FE simulation of the printed construct predicted the same global failure response (initiation location and propagation directionality) as observed in E. aspergillum. The ability to mimic directly the complex material construction and design features in E. aspergillum is currently beyond the latest advances in AM. However, while acknowledging the material-dominated limitations, the results presented here highlight the considerable potential of direct mimicry of biomineralized lattice architectures as future light-weight damage tolerant composite structures.


Introduction
Advanced composite materials offer the designer considerable design freedom and unique functional performance, such as low weight, high specific strength and stiffness, while offering unique damage tolerance and crashworthiness methodologies. Additionally, with developments in fibrous and polymeric materials, as well as new additive manufacturing (AM) processes (rather than subtractive), advanced composites offer the potential for the integration of system-specific multifunctional capabilities, whereby multiple structural and non-structural functions will reside within the backbone of the structure [1,2].
It is the on-going quest for light-weight, multifunctional and high-performance structural materials which is leading academic and industrial researchers to consider and study biological composites [3] as inspiration for future design concepts. Rigid natural systems such as bone, teeth, nacre and silica sponge are different in structure and composition, yet they share common design principles. The latter include hierarchical structure from nano to macro levels, adaptation of form and structure to function, a unique inorganic -organic composition from simple low mechanically performing structural elements, compared to synthetic systems and the presence of numerous interfaces resulting in highly efficient toughening mechanisms [4]. Through this strategy, mineralized biological composites possess high strength, stiffness and fracture resistance, a combination which is not fully achieved with engineering materials [3,5].
The hierarchical organization of the skeleton of hexactinelid sponge E. aspergillum (figure 1), a silica-based structure, is an excellent example of this design strategy for enhancing the performance of an inherently brittle material. The strength of amorphous silica is determined by the existence of surface flaws, and if its size goes beyond a few micrometres, there is a dramatic loss of strength. To overcome this limitation, and to build structures which are larger than a few micrometres, further hierarchical levels are required to 'modify' silica into an adaptive three-dimensional (3D) cylindrical skeletal lattice [6,7]. A full description of the structural hierarchy of E. aspergillum is beyond the scope of this communication, and the reader is referred to the detailed study by Weaver et al. [8]. However, in summary, and as figure 1 indicates, E. aspergillum is formed of two independent interwoven square lattices, constructed by laminated non-planar cruciform spicules formed of consolidated silica nanoparticles. It is the complex interactions across all these structural levels which yield the superior mechanical performance of the skeleton [8,9], and the motivation for this study.
In hexactinellid sponges, the structural loads exerted onto the spicular skeleton arise primarily through the surrounding ocean currents and the need to support the soft tissue. In this study, the mechanical response of the lattice skeleton to a compressive load is investigated, with the assumption that the latter acts as a static support. For this purpose, portions of the lattice of one sponge skeleton were extracted and compression tested in situ using X-ray micro-computed tomography (m-CT). The combination of m-CT and in situ mechanical loading is particularly useful for understanding the relationship between the morphology and mechanical behaviour of the biological system. In addition, the 3D imaging data obtained from m-CT can be used for the creation of highly accurate meshes for finite-element (FE) modelling and AM/3D printing. In our study, the aim was to employ this methodology to determine if the damage mechanisms translate from the biological system to its engineering counterpart, noting the key limitation of using additive layer manufacturing and current 3D printing technology, namely the elimination of internal micro-architecture.

Specimen extraction
Three 3 Â 3 unit cell samples were extracted from the lower portions of three E. aspergillum specimens, using a scalpel. The samples were washed in distilled water and cleaned for 30 s in an ultrasonic cleaner, then dried at room temperature for 24 h (figure 2). Figure 2 illustrates the three different specimens with the caption detailing the surface volume values of the individual samples.

In situ loading and micro-computed tomography of the sponge skeleton
To secure the upright position of the sample and to ensure flat and parallel surfaces for compression testing, the upper and lower ends of the samples were cast in epoxy resin (EPON 828) with diethylenetriamine (DETA) as curing agent using a silicon mould. The in situ tests were conducted in the specimen chamber of a Bruker SkyScan Material Testing Stage (MTS-50 N), with the lower end fixed to the bottom holder and the upper one free (see the electronic supplementary material, figure S1). The testing stage was positioned inside the m-CT scanner (Bruker SkyScan 1172, Belgium) with the sample loaded in compression at 2 mm s 21 , in several incremental steps. All the scans were performed at a resolution of 5 mm per pixel prior to loading and after each loading cycle. The reconstruction of the grey scale images into cross-sectional image slices was performed with NRecon v.1.6.8 (Bruker SkyScan, Belgium) reconstruction software. The image stacks of each scan were segmented, smoothed with a convolution filter and visualized with VGStudio Max 2.1.

3D printing the engineering analogue
In order to create an engineering analogue, the raw data from the biological system were used to generate a stereolithography model (.stl) in VGStudio Max. The .stl file generated from the biological system was too computationally expensive for further processing and, as a result, the polygonal mesh was simplified with the 'Simplification Editor' function in Avizo Standard v.    royalsocietypublishing.org/journal/rsif J. R. Soc. Interface 16: 20180965 triangulated surface was created with a precision and offset of 0.63 and 0.20 in absolute values, respectively. This allowed a mesh expansion without compromising the overall sponge lattice topology. The resampled mesh was imported into GeoMagic Studio13. The wall thickness of the struts was manually increased using the 'Offset Polygons' function preserving the features of the sponge lattice. The final preparations for 3DP included smoothing and remeshing the surface to eliminate the mesh distortions, which were present in the model due to the localized polygon offset (figure 3b,d ). The edited mesh was then imported into ZPrint 7.10 software for 3DP using a ZCorp Spectrum Z510 printer and zp150 high-performance powder (calcium sulfate hemihydrate particles (ranging in size from 10 to 100 mm in diameter and variable length) with a polyvinylpyrrolidone adhesive binder). This powder is characterized with a higher green strength compared with other generation ZCorp powders, which makes it suitable for handling of complex printed structures which consist of numerous thin struts. A further consideration when generating 3D printed architectures concerns the print layer orientation and the influence this will exert on the mechanical properties of the final part [10,11]. The closed cell models were oriented with the longest axis along the y-direction of the build bed, which is the printer head's direction of travel (figure 4a). The orientation was chosen according to the recommendations for the highest ultimate green strength for 3D printed parts, the direction of the applied uniaxial compression load and the longest dimension of the models (figure 4a,b). In the 3DP process, the print orientation governs the mechanical performance of the part; where the strongest performance is oriented along the y-and x-axes with the least along the z-axis. After printing, the sample was depowdered to remove the loose material, deposited around it during printing (figure 4c). To improve the comprehensive strength of the sample, the porous architecture was subsequently infiltrated and stabilized with ZMax epoxy resin using a highvolume, low-pressure spray gun (figure 4d ). Three coats were applied in the direction of the vertical beams and two in the direction of the horizontal beams on each side of the sample to ensure efficient resin penetration through the thickness of the struts; followed by a cure for 2 h at 718C. In a similar manner to the biological samples, the ends were cast in epoxy resin (EPON 828) with DETA as curing agent using a silicon mould (figure 4e). The sample was subjected to a compression loading on a Shimadzu Autograph AGS-X Series testing machine with a loading rate of 1 mm min 21 , connected to an Imetrum video extensometer (figure 4f,g) with a resolution of 2.8 mm + 5% [12]. The latter is an efficient non-contact method for strain/ displacement measurement, operating by precisely tracking the position of specific features or predefined targets on the specimen's surface in video images. The video records the movement of the target during test, while the software extracts the strain or displacement values by measuring the target movement.

Finite-element analysis
The FE model was based on surface topology of the 3 Â 3 Closed Cell 1 (figure 2a) for the manufacture of the physical samples. The FE simulation was performed with explicit LS-DYNA code, version LS971vR6.0.0 (Livermore Software Technology Corporation, Livermore, USA). LS-DYNA provides a wide range of material models to capture different types of material behaviour, offering highly nonlinear, robust and computationally efficient contact algorithms. Furthermore, within LS-DYNA several constitutive models are employed to capture the fundamental behaviour of multiphase materials, for example, post-peak softening, shear dilation, strain rate and confinement effects. In this study, the parts were assembled in Oasys PRIMER 10.2 64bit (Ove Arup SYStems) pre-processing software.  [14], which falls under the generalized isotropic plasticity theory, and comprises elastic and plastic updates, strength surface formulations, rate and scale effects and damage accumulation parameters [15]. It differentiates the deviatoric and volumetric responses and also requires an equation of state. KCC uses a three-surface plasticity formulation which incorporates a material damage evaluation algorithm to compute, at each time step of the simulation, a new failure surface. To calculate the failure response, the KCC model requires the experimentally defined unconfined uniaxial compression strength and the material density. The compression strength was obtained from the authors' uniaxial compression testing of 3D printed cylinders. The obtained values for the uniaxial compression strength and the density are 39.7 + 4.5 MPa and 1.60 + 0.02 g mm 23 , respectively. In LS-DYNA, these experimentally derived data are directly included as *MAT CONCRETE DAMAGE REL3 [15] with the default parameters being obtained from an extensive range of experimental tests, including unconfined uniaxial compression and tension tests, triaxial compression tests and a number of strain path tests [16,17]. The author defined data in conjunction with the default parameters allow the KCC model, with a mesh element size of 1.5 mm, to accurately capture post-peak softening, shear dilation, confinement and strain rate effects of the closed cell system. The reader is referred to the electronic supplementary material for full breakdown of the derived and default parameters used within the FE simulation.

The failure behaviour of the Euplectella aspergillum 3 Â 3 unit cell
The average failure for all three 3 Â 3 specimens was determined as 14.3 N with a standard deviation of 2.8 N. The average extension at the onset of catastrophic failure was recorded as 1.1 mm with a standard deviation of 0.2 mm. Figure 5 shows the reconstructed images at four different loading points illustrating the failure behaviour of Closed Cell 1 specimen during the in situ compression testing. The description of the failure response, given below, is typical of all the specimens. The lattice initially exhibits an initial stiff linear response characterized with no visible damage to the main struts. The first fracture occurs in the right reinforcing vertical strut and in a diagonal beam near the bottom section (figure 5b, white arrows). Although, the main beams remain intact, the deformation of the upper parts of the outer vertical struts was readily observed during this phase of the test. The yield point (the onset of strut buckling or crushing at the peak load, figure 5c) is followed by a load drop, post-yield softening and load plateau. The observed progressive nature of the fracture corresponds to the failure of the lattice components, crack deviation and arrest in the silica cement and strut-beam connection point failure (see figure 6a-f indicating the different failure modes). As the compressive load progresses towards final failure (lattice densification), the shear fracture of the main vertical beams was clearly observed in each experimental sample. This led to the failure of the diagonal reinforcing struts, breaking away from the main vertical beams (figure 6a), which the authors deemed responsible for the loss of stability and subsequent fracture of the main vertical beams (figure 6bd) and the delamination of the horizontal beams. In all specimens, the brittle crushing of the longitudinal beams takes place near the nodes between the mid and lower cell rows and the mid and upper rows. It is noticeable that the fracture develops in shear pattern, predominantly in the cells with lower connectivity, i.e. the open cells.
According to Maxwell's rule [18], a square lattice with rigid nodes is characterized with a failure in bending of the constituent struts, hence the lattice behaves as a bendingdominated structure. The introduction of diagonal elements increases the nodal connectivity, resulting in a lattice with royalsocietypublishing.org/journal/rsif J. R. Soc. Interface 16: 20180965 stretching-dominated failure mode [10,19,20]. The role of the diagonal elements, whether under tension or compression loading, is to redistribute the loads. In hexactinellid sponges with main quadrate skeletons, the introduction of long diagonal elements that intersect the nodes appears to be in conflict with sponge hydrodynamic efficiency. Nonetheless, the diagonal beams still re-channel the loads and are under tension or compression depending on the load direction. They also act to reduce the stresses away from the nodal intersections by delocalizing the stress to neighbouring beams. This arrangement is highly beneficial for rigid frameworks since most of the stresses are concentrated at the nodes and in the middle of the beams. In addition, this configuration decreases the effective length of the longitudinal beams, thus preventing buckling of the latter under compressive loading [20]. Force -displacement plots are available as open data at doi.org/10.5061/dryad.ns7n1/1. Experimentally, it is clear that this strategy is adopted by E. aspergillum sponges resulting in a damage tolerant and rigid supportive skeleton.

The failure behaviour of the 3D printed engineering analogue
The load-strain and failure sequence of the 3D printed specimen is shown in figures 7 and 8. The steep gradient of the elastic region corresponds to the stiff response of the 3D printed sample when subjected to compression loading. Such a response is observed in stretching-dominated lattices [12]. As noted in figure 7, initial failure was followed by a very sharp load drop in the outer beams (1 and 4) and subsequent load redistribution in the inner beams (2 and 3) near the yield point of the lattice framework. The sequence of photographs in figure 8 shows the failure sequence of the lattice. The first macroscopic fracture event took place at   8e, red arrow). Densification of the lattice was not observed after post-yield softening. The 3D printed samples resulted in three distinct types of response to uniaxial compression: defined as predominantly brittle, predominantly quasi-brittle and soft quasi-brittle. A typical failure pattern of one of the 3D printed spicules is given in figure 9. Figure 9a illustrates the granular nature of the spicule architecture encapsulated with an epoxy resin infused skin. While, figure 9b,c highlights the prevalence of intergranular fracture as the primary deformation mechanism in these synthetic specimens. Fracture was initiated through the existence of voids within the 3D printed architecture, despite the addition of the infused resin present in the microstructure. All samples exhibited similar behaviour in

Failure simulation of the 3D printed engineering analogue
The FE model was based on surface topology of the 3 Â 3 Closed Cell 1 ( figure 2a) incorporating the mechanical properties of the material used for the manufacture of the 3D printed physical samples. To enhance the prediction quality of the model, local topological transformations and automatic mesh optimization techniques were implemented to substantially reduce the number of distorted elements. This resulted in the elimination of any potential numerical instabilities occurring during the analysis.
The simulation results are captured in figure 10 for different simulation times, i.e. prior to loading, after 1 s and after 1.5 s. The simulation captures the initial linear response up to the first yield point, and subsequent strain hardening (hardening plasticity response) of the lattice framework until the maximum strength is attained. In the post-peak region, softening takes place until the residual strength of the material is reached [21]. It should be noted that while the KCC failure criteria have been developed specifically for the quasi-static and high strain blast response of concrete [22 -24], the simulation was sufficiently robust to capture the elastic deformation mechanisms, and the quasi-brittle softening behaviour of the epoxy infused Zcorp zp150 powder.
This success is despite the dimensions of the micro-and the mesoscale structural features differing significantly. A key feature arising from the FE simulations was their effectiveness at representing the observed macroscopic failure behaviour of the closed cell 3D printed samples. However, a difference of approximately 1500 N occurred between the maximum load values predicted by the FE simulations and the experimental results. The authors believe this was largely due to the employment of 4-node linear tetrahedral elements which exhibit a considerably stiffer behaviour compared to the quadratic solid tetrahedra [25]. Moreover, the applied conservative boundary conditions, and the contact modelling definitions (see the electronic supplementary material) were also accountable for the higher peak load values.
While acknowledging the limitation of capturing the precise failure load of the 3D printed architectures, the simulation results have shown that there is indeed a synergy between the biological sample (figure 5d ) and its engineered equivalent (figure 10c) in terms of global compression response and the locations of damage initiation and evolution. The new scientific understanding of the architecture, connectivity and failure response developed through the simulation of the biological system can now be extracted and employed in the development of a bioinspired engineering equivalent lattice structures. In this regard, the role of structural topology and multi-layered structs and joints has been shown to be critical in the design of closed cell configurations when subjected to compression loading.

Discussion
As detailed in the hypothesis, the overarching goal of this study was to investigate the translation of a biological lattice framework (siliceous skeleton of E. aspergillum) to an engineering analogue. This was achieved through the application of m-CT imaging which was used to generate both an FE model and a scaled 3D printed construct.
A state-of-the art additive layer manufacturing technique employing fused ceramic particulate was used to construct global architecture. This methodology was pursued to determine if the deformation mechanisms of the biological 3 Â 3 unit cell translate to its engineering scaled equivalent and whether the compressive failure behaviour of the lattice can be defined as 'material or structure' dominated. The siliceous skeleton of E. aspergillum is characterized with an elaborate hierarchical organization, in which each hierarchy is tuned to a specific function. The multi-layered arrangement of the struts and the fusion strategies between individual struts (figure 1d) improve the local energy-absorbing capabilities, while the subsequent sub-structural design of irregular spicule-nodal point overlap (figure 1b,c) imparts global strength and stiffness across the whole structure.
In comparison, the 3D printed sample is constructed with a homogeneous material (comprising bonded ceramic granular particles with an outer epoxy infused shell), with limited hierarchical organization, triggering the assumption that the mechanical response of the sample would follow conventional understanding and would follow a brittle and less damage tolerant failure response. However, the engineering analogues showed a very similar initiation and propagation failure pattern to the biological specimen when subjected to compression loading (figure 11). These experimental results suggest that the complex biological lattice design strategy can be adopted and will 'operate' at an engineering length scale. For this philosophy to be fully successful, improved material science understanding of the ceramic materials for AM is also required. It is through this new understanding, and the ability to manipulate and tailor the engineering materials and structure at different length scales which can 'control' the macroscopic deformation behaviour of the synthetic specimens (from predominantly brittle to quasi-brittle failure mode).
However, a key caveat should be acknowledged before AM is considered as the champion of bioinspired design; namely, the application of the AM process permits user selection and alignment of the printing pathways to match the primary structural loads. In this study, the printing layer orientation at the macroscale was selected to ensure the maximum performance of the printed samples under uniaxial compression. While this has maximized the uniaxial performance of the lattice framework, the off-axis performance (i.e. diagonal reinforcing struts) may have been compromised, triggering the observed quasi-brittle response. While an artefact of the engineering manufacturing process, ironically this is exactly the observed mechanism (i.e. decoupling of the fused secondary structs) which provides the damage tolerant response observed in siliceous skeleton of E. aspergillum. In this regard, the response has not been designed or optimized but rather an artefact of the engineering manufacturing process. The generation of the FE simulation was very challenging. This stems from the architectural complexity and the material model to predict failure. The selection of the material model for the FE analysis was of fundamental importance to correctly capture the damage evolution, the transition from linear elastic to nonlinear elastic response and the strain-softening behaviour, exhibited by the 3D printed samples. To achieve this goal, the KCC damage model [17] was selected for the FE simulations, to capture the quasi-brittle behaviour of the closed cell 3D printed samples. KCC model is a damage plasticity model that incorporates three fixed surfaces, elastic and plastic updates, strength surface formulations and damage evolution parameters. The inherent advantage of this approach is its capability to generate fit parameters for different strength concrete material solely based on the compression strength and the density. It should be noted that despite the similarities in the quasi-brittle compression response between concrete and the resin-infused Zcorp zp150 powder, there are significant differences in their structure at micro and meso levels. These differences are directly related to the size of the aggregate and thus the deformation mechanisms responsible for the initiation and development of damage. Therefore, it was expected that the default input materials have a certain effect on the transition between the initial yield, maximum strength and residual surfaces as well as on plasticity behaviour of the closed cell FE model. Critically, the mesh density, the implemented failure criterion, the aggregate size and the contact stiffness were shown to have an effect on the plasticity and the maximum load. The difference in the response of the FE model compared to the 3D samples in terms of peak load and compressive strain can be attributed to the more conservative boundary conditions, the incorporation of linear solid tetrahedrons (which are generally stiffer compared to quadratic tetrahedrons), the default input material parameters, the failure criteria and the strain extraction techniques.
Despite the aforementioned differences, the FE simulation and the experimental results of the 3D printed samples showed good agreement in terms of the location of damage initiation and progression of failure. It was shown that the FE model efficiently represented the macroscopic failure behaviour observed in the closed cell 3D printed samples, despite the significant differences in the compression response of the latter. The simulation results showed that there is indeed overall agreement between the biological sample and its engineered equivalent, in terms of global compression response and the locations of damage initiation and evolution ( figure 11). However, the rate of failure and the deformation mechanisms, controlling the accumulation of damage in each configuration, have been observed to be principally governed by the material phases and their geometrical arrangement at the smaller length scales. Realistically, until the current AM processes can actively construct a multi-material, multi-stiffness, multi-layered hierarchical architecture, rather than generating an isotropic construct with fully rigid structural linkages, the ability to mimic the tailored structural strut and joint connectivity, as observed in E. aspergillum, as an efficient energy-absorbing mechanism for lattice frameworks remains aspirational.

Conclusion
In the hypothesis, we set out the challenge of the current work; namely can current engineering materials in conjunction with a 'bioinspired design philosophy' develop the products of the future? In our efforts to answer this question, the authors have employed the latest state-ofthe-art developments in m-CT characterization, 3D AM techniques with ceramic materials and FE simulation capabilities with user derived failure criteria. A number of key conclusions have arisen from this methodology.
The structural efficiency of the lattice skeleton of hexactinellid sponge Euplectella aspergillum was evaluated to extract its design principles, and to translate this methodology to a commercial engineering environment. The siliceous skeleton of E. aspergillum is characterized with an elaborate hierarchical organization, in which each hierarchy is tuned to a specific function. While the multi-layered arrangement of the struts, consisting of hard and soft phases, and the fusion strategies improve the energy-absorbing capabilities, the subsequent levels impart strength and stiffness to the whole structure.
Notwithstanding the less elaborate structural hierarchy of the 3DP samples, comprising brittle particulate phase reinforced with another brittle phase, the experimental results clearly demonstrated that the manipulation of material and structure at different length scales altered the macroscopic deformation behaviour from predominantly brittle to quasibrittle. The imparted enhanced damage tolerance and the subsequent 'graceful' failure were largely a result of the material and structural gradation of the lattice components. The observed trend strongly suggests that the compression response of the closed cell lattice arrangement was largely governed by the structure. This highlights the potential of biomimicry of the global architecture (and not biomimicry of the local material constituents) where the failure behaviour is dominated by the structure rather than a material-dominated response. Competing interests. We declare we have no competing interests. Funding. This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) through an ACCIS Doctoral Training Centre grant (grant no. EP/G036772/1) and R.S.T. †s fellowship under EPSRC 'Engineering Fellowships for Growth' (grant no. EP/M002489/1).