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Multilayer stag beetle elytra perform better under external loading via non-symmetric bending properties

Lakshminath Kundanati

Lakshminath Kundanati

Laboratory of Bio-inspired and Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano 77, 38123 Trento, Italy

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Stefano Signetti

Stefano Signetti

Laboratory of Bio-inspired and Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano 77, 38123 Trento, Italy

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Himadri S. Gupta

Himadri S. Gupta

School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK

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Michele Menegon

Michele Menegon

MUSE Science Museum, corso del Lavoro e della Scienza 3, 38122 Trento, Italy

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Nicola M. Pugno

Nicola M. Pugno

Laboratory of Bio-inspired and Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano 77, 38123 Trento, Italy

School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK

Ket-Lab, Edoardo Amaldi Foundation, Italian Space Agency, Via del Politecnico snc, 00133 Roma, Italy

[email protected]

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    Abstract

    Insect cuticle has drawn a lot of attention from engineers because of its multifunctional role in the life of insects. Some of these cuticles have an optimal combination of lightweight and good mechanical properties, and have inspired the design of composites with novel microstructures. Among these, beetle elytra have been explored extensively for their multilayered structure, multifunctional roles and mechanical properties. In this study, we investigated the bending properties of elytra by simulating their natural loading condition and comparing it with other loading configurations. Further, we examined the properties of their constitutive bulk layers to understand the contribution of each one to the overall mechanical behaviour. Our results showed that elytra are graded, multilayered composite structures that perform better in natural loading direction in terms of both flexural modulus and strength which is likely an adaptation to withstand loads encountered in the habitat. Experiments are supported by analytical calculations and finite element method modelling, which highlighted the additional role of the relatively stiff external exocuticle and of the flexible thin bottom layer in enhancing flexural mechanical properties. Such studies contribute to the knowledge of the mechanical behaviour of this natural composite material and to the development of novel bioinspired multifunctional composites and for optimized armours.

    1. Background

    Insect cuticle is a biological structure that has been widely investigated for its microstructure because of its crucial role in providing protection and simultaneously permitting locomotion. The composite nature and complex structural design of cuticle determine its mechanical response in terms of strength, bending stiffness, toughness and wear resistance [1]. Insect cuticles are natural fibre-layered composites primarily made of chitin microfibrils and protein, with layers of varying thickness and fibre alignment [2]. The variation in cuticle properties across species is achieved by changing composition, fibre density and orientation, and cross-linking of the protein matrix [3]. Insect cuticle comprises three layers and the outermost epicuticle is a thin wax layer [4]. The other two layers comprise chitin microfibrils embedded in a protein matrix. One of them is the exocuticle which is hardened by sclerotization process [5], and the other is the unsclerotized endocuticle that is tougher and more flexible [6]. Recent studies have reported on how multi-scale elastic gradients in cuticle-based organs like spider fangs enhance their biomechanical functionality [7]. Such structural gradients were also observed in the tarsal setae of seven-spot ladybird (Coccinella septempunctata), which enable contact formation with substrates on which they walk and prevent condensation, resulting in increased pad attachment [8].

    Elytra are a variation of beetle cuticle with a dorsal layer and a ventral layer, which are connected by a haemolymph space and columnar trabecular structures [9]. The mechanical interaction between various bulk layers and the constitutive sublayers together determines the structural performance of the whole elytron. Also, the progressive fibre arrangement in each sublayer of elytra has been shown to be crucial to mechanical performance [9], while the presence of trabecular structures was hypothesized for energy absorbing function [10]. Elytra have drawn a lot of attention because of their light weight in combination with excellent Young's modulus and hardness, and their peculiar surface texturing resulting in specific optical properties and hydrophobicity [11,12]. Elytra play an important role in the survival of some beetles by shielding the insect from damage during battles. In addition, the interaction between the elytron and the flexible wing during flapping has been claimed to improve the aerodynamic force enough to compensate for the weight of the beetle during forward flight [13]. Thus, flexibility of the elytra also plays a role in dynamic interaction with the wind flow during the flight. Such studies based on elytron design led to the development of structural models [10] and novel biomimetic layered composites with specialized microstructures [14,15], and were also employed in building construction [16].

    In this study, we chose male stag beetles (Lucanus cervus) because of their large size and their battle behaviour using large puncturing mandibles. Earlier studies on stag beetles were focused on determining bite forces of the mandible and modelling the bites during fights to understand the biomechanical aspects of their mandible movement and its properties [17]. In some instances, the elytron comes in contact with the mandible during battle and the elytron's bending response plays a crucial role in preventing damage. In principle, the elytra of beetles should be resistant to fracture and be rigid enough to sustain bending loads without internal damage to help in the beetle's survival. Overall, elytra play a multifunctional role in resisting wear from outside environment and protecting the fragile wings when they are folded. Most earlier studies dealing with elytra characterization primarily focused on tensile testing, on dynamic mechanical analysis and, in some cases, on nano-indentation [1820]. Very few studies have explored the more physiologically relevant bending properties of elytra, which closely simulate natural loading scenario that a beetle experiences in its habitat. Thus, elytron with its multilayered complex microstructure requires a more detailed investigation of its multifunctional mechanical performance. The goal of our study is to provide comprehensive structural and mechanical characterization of the composite elytra in physiological deformation modes and also to investigate the contribution of each layer. Initially, tensile tests were performed on two sample sizes to examine the size effects in the elytra mechanical strength, followed by bending experiments. We then performed tensile tests on each layer to determine their material constitutive properties and to quantitatively assess their contribution to the overall mechanical behaviour. The determined layer properties were used to carry out analytical predictions of the overall bending behaviour of elytra and also as input for finite element method (FEM) simulation to better understand the deformation mechanisms, delamination and fracture behaviour of the multilayer composite structure. The understanding of the role of different layers with different mechanical properties and of the overall elytron structure in its deformation and fracture behaviour will also help in more detailed design of bioinspired lightweight composites and structures, e.g. for impact resistance in advanced applications.

    2. Material and methods

    2.1. Optical and electron microscopy

    The male stag beetle specimens were acquired in dehydrated state from the collection of the MUSE Science Museum of Trento (Trento, Italy). Images of insects were captured using a camera (Sony HDR XR500) as shown in figure 1a. Scanning electron microscopy (SEM) imaging was performed directly on samples without any preparation because of the relative dryness of elytra samples. Prepared elytra sections from the dissection and mechanical tests were carefully mounted on double-sided carbon tape, stuck on an aluminium stub followed by sputter coating (Manual Sputter Coater, AGAR SCIENTIFIC) with gold. Imaging was carried out using an SEM (EVO 40 XVP, ZEISS, Germany) with accelerating voltages between 5 and 10 kV. ImageJ software was used for all dimensional quantification reported in this study [21].

    Figure 1.

    Figure 1. Sample preparation for mechanical testing: (a) image of the stag beetle species used in the study, (b) details of representative size and location of extracted samples (red = tension samples, green = samples used for in-plane anisotropy, blue = samples used for testing asymmetry in the out of plane direction). (c) SEM image of whole elytron cross section showing the constitutive bulk layers, void space and trabecular structures. (d) SEM image of the elytron cross section showing the endocuticle constitutive sublayers. (e) SEM image of the fractured elytron showing the macro-fibril orientation in endocuticle. (f) Schematic of procedures used for separation of bulk layers and (g) final separation of sublayers from the middle layer.

    2.2. Mechanical testing

    Mechanical tests were performed on the sample sections (figure 1b), using a Messphysik MIDI 10 (MESSPHYSIK, Germany) universal testing machine and forces were obtained using transducers of two ranges (LEANE Corp., ±10 N and METTLER TOLEDO, ±200 N). In monotonic tension, specimens were tested in displacement control mode at a rate of 0.01 mm s−1. Engineering stresses were calculated as ratio of applied load to the nominal specimen cross-sectional area. Axial strains were defined as ratio of change in displacement to initial specimen length. Tensile tests were performed on two sets of samples (three samples from mid location of elytra of each beetle as shown in figure 1b) with different sizes: large size samples (length = 6.59 ± 1.8 mm, width = 2.62 ± 0.6 mm) and small size samples (length = 1.79 ± 0.26 mm, width = 0.98 ± 0.23 mm).

    Bending experiments were performed using the same machine with a custom built three-point bending set-up machined out of hard plastic material on which blunted blades are mounted to achieve line contact during loading. The rate of testing in three-point bending tests was 0.01 mm s−1. In order to observe and ensure the tests were done without any significant slipping of the sample, all the mechanical tests were monitored using a video camera (Sony HDR XR500) with an objective lens (Olympus 1.5XPF) kept at a distance of approximately 5 cm from the samples. First set of bending tests (four samples in each direction, from four beetles) on elytra were performed from the hinge location to examine in-plane anisotropy at a given location in the longitudinal and transverse directions, orthogonal to each other, as shown in figure 1b. We then performed a second set of bending tests using samples from middle region of elytra to compare the response of elytra to opposite bending directions (three samples each from four beetles). In this study, the combined epicuticle and exocuticle layers are referred to as the top layer, the endocuticle is referred to as middle layer and the lower lamination is referred to as bottom layer, which is the thinnest of all layers (figure 1c). The endocuticle primarily consists of stacked sublayers (figure 1d) and the fibre orientation changes from layer to layer (figure 1e). Constitutive bulk layers were separated using various procedures (figure 1f). Top layer was separated by mechanically peeling the bottom layer and carefully scraping the middle layer using a scalpel blade. The bulk middle layer was isolated after soaking the elytron with bottom layer removed, in 10% NaOH solution for 4 h that enabled easy removal of the top layer. The bottom layer was carefully peeled off from the whole elytron after soaking in water overnight. All the layers were allowed to dry for 24 h before testing to minimize the hydration effects during the separation processes. Tensile tests (two samples each from four beetles) and bending tests (three samples each from four beetles) on bulk layers were performed on the sections cut from the middle region of elytra as shown in figure 1b. Sublayers of the middle layer were also separated one by one after soaking the elytra in 10% NaOH for 2 days, which was proved to dissolve the protein matrix to an extent making the separation easy (figure 1g).

    For this study, ‘natural’ loading condition was defined as the scenario in which the elytra would be subjected to forces on the outermost epicuticular layer, either by the mandible of an opponent beetle during a fight or at the time of impact due to fall from a tree on the dorsal side (figure 2a). ‘Unnatural’ loading condition was defined as elytra being subjected to hypothetical loads from inside by the abdomen expansion, which is unlikely (figure 2b). The words ‘natural’ and ‘unnatural’ thus have been adopted to specify the loading direction. The flexural stress (σ) and strain (ɛ) from bending experiments were calculated using the following equations from the theory of beams, respectively:

    Display Formula
    2.1a
    and
    Display Formula
    2.1b
    Figure 2.

    Figure 2. Schematic of three-point bending for testing (a) the natural loading condition and (b) the unnatural loading condition.

    where F is the applied bending force and δ is deflection at the midspan (from the measurements), w is the beam width, l is the span and t is the thickness. The above calculations were made assuming that the multilayer is homogeneous and thus that the maximum stress values occur at the bottom and top chords of the cross section.

    2.3. Analytical modelling

    The global tensile properties, i.e. stiffness and strength, of the multilayer system obtained from experiments were verified by a simple rule of mixtures taking into account the contribution of each layer, assuming perfect bonding between them:

    Display Formula
    2.2a
    and
    Display Formula
    2.2b
    where fi is the volume fraction of each layer, that is, the ratio of their thickness over the overall thickness of the elytron. The derivation of bending properties for a multilayer beam is described in the following [22]. Assuming all material laws as linear elastic and isotropic, a homogenization factor Ei(y)/Er, defined as the ratio of elastic modulus of each material layer to an arbitrary reference modulus Er, is used to determine the homogenized cross-section geometrical properties. The stress distribution along the thickness coordinate y of a beam subjected to axial load N and bending moment M can be evaluated according to the classical Navier's formula, under the hypothesis of planar deformation of bent sections
    Display Formula
    2.3
    where (Inline Formula) is the coordinate with respect to the level of elastic centroid Inline Formula, A* is the homogenized cross-section area defined as
    Display Formula
    2.4
    and I* is the homogenized beam moment of inertia with respect to the beam elastic centroid Inline Formula:
    Display Formula
    2.5
    where w is the beam section width, yi, ye are the coordinates of the bottom and top chords of the beam, respectively, with respect to the position of the elastic centroid Inline Formula which can be calculated by the following expression:
    Display Formula
    2.6
    where Ei, ti are the Young's moduli and thicknesses of each layer, respectively, and yG,i is the coordinate of the centroid of each layer with respect to an arbitrary reference origin. Equation (2.6) is obtained by posing the beam homogenized static moment equal to zero:
    Display Formula
    2.7
    Accordingly, the flexural modulus of the whole elytra can be calculated as
    Display Formula
    2.8
    where t is the total height of the beam. Finally, in accordance with the three-point bending scheme, the maximum transversal force at failure is
    Display Formula
    2.9
    which is obtained by imposing that the maximum bending moment that the beam is able to carry under the three-point bending scheme (Mmax = Fmaxl/4, at the midspan section) is reached when the current flexural stress (equation (2.1a)) reaches the failure strength of the corresponding materials σf at the bottom or top chords of the beam (yi and ye coordinates, respectively).

    2.4. Computation modelling

    A FEM model was developed to simulate three-point bending tests and elucidate the deformation/failure mechanism in the elytra. The multilayer was modelled assuming that the constitutive materials of the layers follow a linear elastic and isotropic law, having the same behaviour in tension and in compression, as assumed in the analytical model. The average tensile mechanical and geometrical properties of each layer determined from the experimental tests, i.e. elastic modulus, failure strength and strain, and thickness were used as input for simulations. Two cylindrical rigid bars are used to support the elytron beam and a third one at the midspan moves from the top under displacement control (same rate as experiments) in order to apply deflection. The simulated sample has the same dimension of the experiments. Details of the geometry can be found in electronic supplementary material, figures S2–S3. The top layer and trabecular structures were modelled with under-integrated solid elements with hourglass (spurious deformation modes) controlled. Middle and bottom layers are modelled with strain reduced integrated thick shell elements. These elements are specifically suitable for low thickness layers because they have the same degrees of freedom as a shell element but a physical thickness in place of a mathematical one. This allows a better treatment of contact, especially when the plies are subjected to out of plane compression, such as in our experiments. The details of the contact model are explained in the electronic supplementary material (finite element modelling details S1).

    The FEM model to study the cushioning effect replaces the two rigid supports with a continuous elastic substrate, composed of two layers simulating the wing and the body of the animal. The mechanical properties of the body were assumed to be the same as that of the top layer of the elytra, because the abdominal external cuticle has similar multilayer structure. The single layer of wing has thickness of 4.4 µm and an elastic modulus E = 3 GPa [23]. The load application follows the same procedure described for the three-point bending set-up.

    3. Results and discussion

    3.1. Microstructure of elytra

    Microstructural examination showed that elytra are multilayered composites primarily comprising three bulk layers of different thickness. The exocuticle is just below the epicuticle that is exposed to the environment and the middle bulk layer comprised sublayers including microfibres (figure 3a). The tanned exocuticle consists of chitin microfibrils embedded helicoidally in a sclerotized protein matrix [24]. Fibre cross-section shape changes from nearly circular to square section from top to the bottom, along with reduction in the layer thickness (figure 3a). The fibre orientation in endocuticle gradually changes from the top to the bottom sublayer (figure 3b). This is similar to observation made in Japanese rhinoceros beetles, Allomyrina dichotoma [25]. The ventral layer referred to as bottom layer also has similar structure to that of endocuticle but with thinner sublayers (figure 3c). These fibres are bundles made up of thin chitin nano-fibres cross-linked with protein matrix (figure 3d). Thickness of each bulk layer was quantified for use in our theoretical and numerical modelling. The top layer has a thickness of 45 ± 4 µm and major contribution to the elytron thickness comes from the middle layer, with a thickness of 67 ± 5 µm. Elytron cross section obtained by fracturing showed a change in orientation of fibres between each layer (figure 3b). Such microstructural organization with changing fibre orientation in consecutive sublayers is referred to as the Bouligand structure and has been observed in elytra of other beetles [9], crab exoskeletons [26] and also in scales of fish dermal armours [27]. The change in angle of fibre alignment between consecutive sublayers in the middle layer is of about 78°. The bottom layer is the thinnest of all layers with a thickness of 8 ± 4 µm (figure 3c). We also observed interconnections between fibre bundles in a single sublayer that are crucial for inter fibre bundle bonding (figure 3e). These interconnections also enhance the interlaminar shear strength [28]. The microstructure of a single separated sublayer showed the out of plane interconnections that might play an important role in the overall mechanical response (figure 3f). Trabecular structures are pillar-like connections between the bottom and middle layers that are placed in rows along with pore canals (figure 4a). These trabecular structures have tapered cylindrical shape with higher diameter at the bottom and the top, when compared to the middle (figure 4b). The empty space between the bottom and the middle layers is the void space created by the loss of haemolymph after resorption [29]. After mechanically removing three sublayers from the middle layer, trabecular structure shows a reduced diameter (figure 4c) and its fractured structure show the spiral winding of the layers around the core (figure 4d). The observed interconnections (figure 3f) are similar to the ribbon-shaped pore canal tubules in crab exoskeletons that were hypothesized to function as a ductile component connecting the fibre bundles to improve the toughness in the thickness direction [26]. In the mineralized shell of windowpane oyster (Placuna placenta), a different type of screw dislocation-like connection centre was observed to enhance the interface toughness by reducing the delamination [30].

    Figure 3.

    Figure 3. SEM images showing the microstructure of elytra. (a) Fractured cross section showing the exocuticle with relatively smooth surface and the endocutilce with change in fibre diameter and layer thickness from top to bottom sublayers. (b) Top view of fractured surface of elytron shows fibre rotation in sublayers. (c) Lower lamination made by a composite layer with sublayers made of relatively smaller fibre cross section. (d) Fractured fibre bundle showing its constitutive nano-fibres (arrows). (e) Interconnections (arrows) between fibre bundles in a layer. (f) A single separated sublayer shows the broken fibrillar connections (arrows) between two adjacent sublayers.

    Figure 4.

    Figure 4. Elytra microstructure. (a) Large scanned area showing distribution pattern of trabecular structures of elytron (white arrows) and pore canals (yellow arrows). (b) Cross section showing how trabecular structure connects the middle and bottom layers. (c) Trabecular structure showing inner substructure after peeling of three layers as described in §2. (d) Top cross-sectional view of a trabecular structure showing concentric layers and their spiral woven structure.

    3.2. Mechanical testing and modelling

    3.2.1. Tensile strength and Young's modulus of the elytra

    Stress–strain curves from these experiments showed repeatability in terms of a sudden drop in load that is representative of a brittle-like fracture of the cuticle (figure 5a,b). In large samples, the average values of fracture strength and modulus of elytra were 65.0 ± 25.5 MPa and 1.9 ± 0.6 GPa, as reported in table 1. In the case of small size samples, the average values of fracture strength and modulus of elytra were 81.7 ± 35.1 MPa and 1.29 ± 0.5 GPa, as shown in table 1. This sample-size-dependent variation can be attributed to the presence of trabecular structures and pore canals acting as defects. So, the density and distribution of these structures could be a significant factor. If we consider the surface area of the samples, the larger samples have an average surface area of 17.3 mm2 and the smaller samples have an average surface area of 1.75 mm2. We investigated the scaling effects in tensile strength of the specimens. According to Weibull's (weakest link) theory, we expect:

    Display Formula
    3.1
    where σ and V are the tensile strength and volume of the specimens, respectively. The estimated value of the Weibull modulus m is 10.25. Similarly, according to an energy dissipation on a fractal volume of dimension D [31], we expected
    Display Formula
    3.2
    Figure 5.

    Figure 5. Stress–strain relationships showing mechanical behaviour from tension experiments of elytra: (a) larger samples showing brittle like fracture and (b) smaller size samples showing similar behaviour. (c) Top layer having a linear response with sudden failure, (d) middle layer also showing linear response with a drop due to initiation of fibre delamination followed by sudden failure, and (e) bottom layer also showing linear response with a sudden failure.

    Table 1.Tensile mechanical properties of elytron and of its constitutive layers (in brackets: standard mean of error).

    tensile mechanical properties
    cuticle/layer Young's modulus (GPa) fracture strength (MPa)
    elytron (large) 1.90 ± 0.6 (0.23) 65.0 ± 25.5 (10.1)
    elytron (small) 1.29 ± 0.5 (0.32) 81.7 ± 35.1 (21.4)
    top layer 4.14 ± 0.46 (0.33) 203.5 ± 62.2 (63.1)
    middle layer 2.73 ± 0.77 (0.19) 124.5 ± 37.4 (25.2)
    bottom layer 2.62 ± 0.92 (0.93) 101.6 ± 46.6 (36.5)

    The estimated value of D is 2.41 confirming a fractal domain intermediate between an Euclidean surface (D = 2) and volume (D = 3). Our whole elytron experimental results were comparable to those of other beetle species [17], in particular, Hercules beetle (Dynastes hercules) with elastic modulus and strength values in the range of 3.1–14 GPa and 26.8–62.9 GPa, respectively [32]. The large variability observed in fracture strength could be attributed to the biological variation, density and distribution of observable defects such as pore canals and trabecular structures, and in addition the effects introduced from the sample preparation. During preparation, it is difficult to create samples which are identical in terms of distribution and density of trabecular structures and of pore canals. In addition, the location of these structures has a significant effect depending on whether the cut was made through them or close to them. In such cases, these defects could possibly act as cracks and notches, if they are located on the edges of the sample (along the length) and close to the stress concentration regions, resulting in a significant reduction of fracture strength. By contrast, if these structures are not located at the edges, the sample could result in higher fracture strength. Such variations were also observed in the tanned elytra of Tribolium castaneum [33]. To understand the detailed contribution of various bulk layers, we have performed tensile tests on separated layers. The top layer has a nearly linear stress–strain response and failed suddenly with the load dropping to zero (figure 5c). Middle layer also displayed a linear stress–strain response but towards the end showed a slight drop in load corresponding to initiation of fibre delamination followed by a sudden failure (figure 5d). Bottom layer also displayed a linear stress–strain response and load dropped to zero with sudden failure (figure 5e). The top layer has a Young's modulus of 4.14 ± 0.46 GPa and a fracture strength of 203.5 ± 62.2 MPa. Whereas, the middle layer has a modulus of 2.73 ± 0.77 GPa and fracture strength of 124.5 ± 37.4 MPa. The bottom layer has a modulus of 2.62 ± 0.92 GPa and fracture strength of 101.6 ± 46.6 MPa. Thus, top layer has stiffer response and also higher failure strength, as compared to other bulk layers. Using the measured mechanical properties of single layers, by a classical rule of mixture (equations (2.2a,b), see Materials and methods section), we estimated Young's modulus and tensile strength of multilayer to be 2.1 GPa and 85.8 MPa, respectively. These estimates are comparable with the experimentally measured values of the whole elytron.

    It emerges that tensile strength gradually decreases from top layer to bottom layer and stiffness also followed a similar trend which could be an optimization for puncturing resistance. In tension, failure was observed as a brittle fracture propagating in the top hard layer, pull-out and breaking of fibres in the other layers. The observed bridging fibres between adjacent fibre bundles and also between sublayers aid in increasing the fracture resistance (figure 3e,f). Overall, the Bouligand (helicoidal) structure of the layers is known to increase the fracture toughness [34,35].

    3.2.2. Flexural modulus and flexural strength of elytra

    Experimental flexural stress–strain curves showed a nearly linear response up to failure and the dispersion in the mechanical properties is significant (figure 6a,b). Flexural strength and flexural modulus were 312 ± 103 MPa and 451 ± 91 MPa, respectively, in the longitudinal direction. A similar range of values of flexural strength (333 ± 94 MPa) and flexural modulus (421 ± 59 MPa) was observed in the orthogonal transverse direction. These results demonstrate that there is no significant anisotropy in the bending response of elytra at a given location. To examine the dependency of loading condition on bending behaviour of elytra, we performed a second set of bending experiments. Stress–strain curves from these experiments were observed to be significantly different (figure 6c,d). In natural loading condition, some specimens failed suddenly and some failed gradually with progressive damage. In the case of unnatural loading condition, step-wise load drop was observed with increasing strain after a certain deflection. Flexural strength and flexural modulus in natural loading direction were 222 ± 172 MPa and 811 ± 650 MPa, respectively. In unnatural loading direction, the values of flexural strength and flexural modulus were 73 ± 39 MPa and 455 ± 287 MPa, respectively, i.e. nearly one-half with respect to the real operating scenario (table 2). Such high variability in modulus and strength for each configuration can be attributed to the inherent biological differences in our extracted beetle samples, regional variation in the elytra and the limited availability because of their endangered status. The variation in properties from hinge location to mid location was in agreement with earlier observations made on five species of beetles [36]. Flexural modulus values are lower than that of tensile modulus, and this is also affected by the void space in elytra. By contrast, flexural strength is nearly three times that of the tensile strength. This is a noteworthy observation in elytra mechanics, with a higher mechanical strength in bending with respect to tension, due to the smaller high-stress regions in bending. Such observations were also made in glass fibre-reinforced polyamide composite materials [37]. The observed higher bending performance in elytra natural loading condition is similar to the behaviour of functionally graded ceramic engineering materials [38], where the asymmetric bending behaviour is achieved by varying the composition of the ceramic components.

    Figure 6.

    Figure 6. Bending stress–strain curves from elytra along (a) longitudinal direction and (b) transversal direction. Second set of experiments on elytra under (c) natural loading condition and (d) unnatural loading condition. Natural bending in longitudinal direction of (e) top layer and (f) middle layer.

    Table 2.Flexural mechanical properties of elytron and of its constitutive layers (in brackets: standard mean of error).

    bending mechanical properties
    layer flexural strength (MPa) flexural modulus (MPa)
    elytron natural direction 222 ± 172 (138) 811 ± 650 (420)
    elytron unnatural direction 73 ± 39 (17) 455 ± 287 (135)
    top layer 392 ± 178 (99) 8295 ± 4745 (1543)
    middle layer 221 ± 85 (52) 3952 ± 1452 (612)

    Stress–strain curves of top layer displayed behaviour similar to that of a brittle material and that of the middle layer were similar to a ductile material (figure 6e,f). Results from these tests showed that the top layer has a flexural strength of 392 ± 178 MPa and flexural modulus of 8.29 ± 4.74 GPa, while the flexural strength and flexural modulus of middle layer were measured to be 221 ± 85 MPa and 3.95 ± 1.45 GPa, respectively (table 2). The exocuticle of elytra of giant water bugs (Hydrocyrius columbiae) was observed to have microfibrils of diameter approximately 45 Å and centre to centre distance of approximately 65 Å, and to be arranged helicoidally with a rotation of 6–7° per plane [39]. These densely packed chitin microfibrils embedded in tanned protein matrix might act as reinforcements and the helicoidal arrangement results in isotropic and enhanced stiffness of the exocuticle. Such improvement in mechanical properties due to the presence of the helicoidal fibre arrangement has been proved by testing bioinspired laminate composites [40]. Flexural modulus of these layers was an order of magnitude higher and flexural strength was of the same order, as compared to the whole elytron. It was not possible to measure flexural properties of the bottom layer using the current experimental set-up, because of its extremely low thickness and bending stiffness, thus negligible here.

    The position Inline Formula of the neutral axis, that is the level at which the bending stresses and strains change sign, is calculated to be approximately 12 µm below the interface between the top and the middle layers, using average values of each layer's elastic modulus and thickness. To analyse the role of trabecular structures, in particular of their height, we analysed the role of the void space between middle and bottom layers by varying it in the analytical calculations from 0 to 80 µm. According to equation (2.3), we obtained that the distance of neutral axis would be in the range of 9 to 13 µm, thus the relative position of the elastic centroid is nearly constant within the endocuticle, suggesting another role for the void space other than optimizing bending properties. On the other hand, the position of neutral axis is significantly affected by the variation in elastic modulus and thickness of each layer, as expected for a composite multilayer. This indicates that the multilayer grading sequence of thickness and elastic moduli is optimized for better mechanical performance in bending. In particular, the elytron multilayer combination is a suitable design for the natural loading conditions, because the position of the elastic centroid confines compression stresses in the top brittle layer and tension in the tough composite middle layer, optimizing the local stress state for the specific constitutive laws of materials. This results in a ratio of about 3 between the bending mechanical properties in the two opposite directions (table 3).

    Table 3.Summary and comparison of experimental, analytical and simulation results of elytra mechanical properties.

    experiments analytical FEM simulations
    tensile properties σ (MPa) 81.7 ± 35.1 85.8
    E (GPa) 1.29 ± 0.50 2.10
    bending properties Ef,n (GPa) 0.81 ± 0.65 1.46 0.94
    Ef,u (GPa) 0.46 ± 0.28 0.96 0.83
    σf,n (GPa) 0.22 ± 0.14 0.14 0.26
    σf,u (GPa) 0.07 ± 0.04 0.07 0.09
    Fmax,n (N mm−1) 2.98 ± 1.82 2.31 3.31
    Fmax,u (N mm−1) 1.20 ± 0.64 1.15 1.15

    The FEM simulations resembling three-point bending tests (figures 7 and 8) were performed to closely understand the mechanics of bending deformation and fracture behaviour. Results were consistent with experiments predicting the variation in flexural modulus and flexural strength in different loading conditions, despite the approximation of linear elastic isotropic material and same constitutive behaviour in tension and compression for each layer. In natural loading condition, an initial load drop (figure 7, point 2) was observed due to delamination in the middle layer and failure of the bottom layer, which suggests an optimized design of the bottom layer and interlamellar strength. The latter, assumed as a free parameter, allowed us to obtain the closest response with respect to the average force displacement bending curve of elytra (see electronic supplementary material, figure S4). The results suggest optimal interface shear strength (τlim = 5.5 MPa) in the elytron multilayers. Similar findings were observed in impact simulations based on composite armours [41]. The final drop occurs when the whole elytron fails (figure 7a). After the first drop (point 2), a recovery of the load with reduced stiffness at point 3 is attributed to the bending resistance from the intact top layer and middle layer. The deformation sequence is shown using snapshots of simulation corresponding to various stages of deformation and complete failure (figure 7b). In the unnatural loading condition, buckling of bottom layer was observed as it experiences compression and its contribution to flexural modulus and strength becomes nearly negligible (figure 8a), causing the first drop in the force (point 2). Delamination within the middle layer results in second load drop (figure 8b, point 3) and a consequent further flexural stiffness reduction. Complete fracture of the whole elytron starts from the failure of the hard layer at the bottom in this configuration (point 4). Thus, failure in this condition initiates from top layer depending on its tensile properties, followed by delamination in the middle layer and final overall collapse. Thus, we claim that the bottom layer is able to play a crucial role only in natural loading bending response. Simulations are in good quantitative agreement with experimental results.

    Figure 7.

    Figure 7. FEM simulation results of bending in natural loading condition showing (a) the force displacement relationship and (b) snapshots of the corresponding stages of bending.

    Figure 8.

    Figure 8. FEM simulation results of bending in unnatural loading condition showing (a) the force displacement relationship and (b) snapshots of the corresponding stages of bending.

    It should be noted that all the experiments were performed on dehydrated specimens because of the near threatened (IUCN Red List) state of the selected species. As described in earlier studies, dehydration may significantly increase the mechanical properties of the cuticle [40]. So the mechanical properties of the whole elytron specimens must be considered in our study as related to the dried samples and as upper bound of living samples. Also an artificial rehydration cannot be considered representative of the living material, for which in any case the non-symmetric bending properties are also expected as confirmed by the related nonlinear mechanism (buckling of the bottom layer). Moreover, the sublayer separation methods could have affected their mechanical properties, i.e. by damaging layers and thus reducing the properties as compared to the properties in the native state. However, the numerical and analytical comparisons (which use single layer properties as inputs) with the experimental measurements on the multilayered elytra suggest a limited alteration of properties during the layer separation process.

    According to the experimental and simulation observations we can define two mechanisms in relation to the direction of bending. Under natural loading all the layers contribute to bending stiffness, whereas in the unnatural bending the contribution of the bottom layer can be neglected as it experiences buckling in compression due to its low thickness. Thus, in the natural loading case, the total thickness of the multilayer enters into play, while in the unnatural loading case, only the thickness of top and the middle layers could be considered. According to equation (2.8), we estimate the flexural moduli in the two loading conditions Ef,n = 1.46 GPa and Ef,u = 0.96 GPa, where the subscripts n and u denote the natural and unnatural loading conditions, respectively. From equation (2.9), in the case of natural bending, first failure occurs in the bottom layer, corresponding to a bending force Fmax,n = 2.98 N mm−1. After that, the reactive section is composed by just the top and middle layers and the overall failure of the multilayer occurs for the rupture in tension of the middle layer. In the unnatural bending case, the maximum force at failure is given by the rupture of top layer at Fmax,u = 1.15 N mm−1. Both analytical and simulation results are in good agreement with experiments. The final plateau region obtained both in FEM simulation and experiments corresponds to the friction slipping of the sample at the contact points (figure 8b). Results from experiments, simulation and analytical calculation are summarized for comparison in table 3.

    In the real situation, the elytron and the folded wing underneath it are continuously supported by the body. The trabecular structures with the void space between them may provide a cushioning effect to further protect the fragile wing and the body from external loads. The supports of the three-point bending set-up are substituted by a continuous substrate simulating the insect wing and body under the protective elytra. In electronic supplementary material, figure S5, the distribution of stresses in the wing and the body under the same concentrated load (Fmax,n, previously determined) is depicted. Simulation results showed that elytron structure is subjected to local higher stresses due to the presence of void space inside as compared to the case without it (3.9 MPa versus 2.9 MPa), because trabecular structures concentrate the load, but performed better in absorbing the energy. Indeed, under the same external load F, the total strain energy in the body was less than one-half compared to the elytron model without void space (2.2 µJ versus 4.92 µJ). This is a good indication that the presence of the void space in elytra helps in mitigating the energy transfer to the body by allowing higher deformation of the top layers and spreading the load over a larger area (electronic supplementary material, figure S5). In some beetles, the void space could be filled haemolymph but because we are not sure of its occurrence in the natural state of our study species, we have not considered this complex scenario.

    4. Conclusion

    Characterization of stag beetle elytra by means of mechanical experiments, theory and simulations gave a new insight into the role of microstructure in their mechanical behaviour. Particularly, the synergy between materials and structural arrangement by combination of layer stacking results in enhanced stiffness and load bearing capacity upon bending. The combination of hard top layer performing better in compression and the flexible bottom layer that contributes only in tension is optimized to provide higher bending stiffness in natural loading condition. Also, the position of flexible bottom layer far away from the centroid of the cross section with the aid of connecting trabecular structures allows the beetle to reduce the cuticle weight by maximizing the moment of inertia, and thus flexural strength and modulus. At the same time, this structure provides cushioning capability, reducing the energy transfer to the beetle body and internal organs. FEM simulations developed in this study have the capability of modelling fracture and large deformations and could be extended to other biological structures similar to elytra or to their engineering bioinspired designs. These results could help in designing structures such as body armours with asymmetric bending properties tuned to perform better in terms of energy absorption and strength in a particular loading condition, with improved ergonomics and flexibility together with external rigidity.

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    Authors' contributions

    L.K. and N.M.P. designed the study. M.M. helped in acquiring the samples. H.S.G. contributed in technical discussions and manuscript editing. L.K. performed the mechanical experiments. S.S. performed the FEM simulations. L.K. and S.S. wrote the first draft of the manuscript (corresponding sections). N.M.P. supervised the study and developed the analytical model. All authors approved the contents of the article.

    Competing interests

    The authors declare no conflict of interest.

    Funding

    N.M.P. is supported by the European Commission H2020 under the Graphene Flagship Core 2 grant no. 785219 (WP14, Composites) and under the FET Proactive (‘Neurofibres’ no. 732344), as well as by the Italian Ministry of Education, University and Research (MIUR) under the ‘Departments of Excellence’ grant no. L.232/2016. N.M.P is also supported by Fondazione Caritro under ‘Self-Cleaning Glasses’ no. 2016.0278, as L.K. S.S. acknowledges financial support from Ermenegildo Zegna Founder's Scholarship 2017–2018.

    Acknowledgement

    The authors thank Nicola Angeli (MUSE, Trento) for the help with SEM imaging and Ludovic Taxis for his guidance and help with the initial experiments.

    Footnotes

    Electronic supplementary material is available online at https://dx.doi.org/10.6084/m9.figshare.c.4150937.

    Published by the Royal Society. All rights reserved.

    References