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Experimental preparations.
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1. Materials and instrument The experiments were conducted with Bamboo Beetles Otidognathus Davidis Fairs (it will be shorted as Bamboo Beetles hereinafter) showed in Fig. 1 which belong to coleopteran and curculionidae. We captured 10 Bamboo Beetles whose weights range from 2. 5g to 3. 0g and body-lengths range from 3. 4cm to 3. 8cm in Leshan, Sichuan. Figure 1 The Bamboo Beetle Otidognathus davidis Fair A nano-indenter (SA2, MTS, USA) were introduced in this manuscript (Fig. 2). It possesses a 15μm maximum indentation depth, a 2mm maximum indenter motion with a 0. 0002nm solution and a 10mN maximum load whose solution is 1mN. It's worth noting that the specimens should so smooth that the nano-indenter could be used easily. Figure 2 The nano-indenter. 1is the load windings; 2 is the capacitance type displace sensor; 3 is the supporting spring; 4 is the substrate; 5 is the load rod; 6 is the specimen.
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2. The specimens Now that the nano-indenter was introduced before, the specimen should be prepared. The Bamboo Beetle was chosen as the experimental subject. The Bamboo Beetle's abdominal shell (it will be shorted as abdominal shell hereinafter) was selected as the original specimen because the other parts of Bamboo Beetle are too rough or bend with large curvatures. The original specimens with 3mm×3mm dimensions were cleaned by ultrasonic washer for 5 minutes and natural withered before tests (Fig. 3).
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3. The experiments The specimens were adhered to 30mm×15mm×5mm steel plates with solid-state hot-melt adhesive when they were tested. The environmental temperature was 27℃±0. 5℃ and the moisture capacity was 65%±1%. The passion ratio was set as 0. 35 the thermal drift rate was 0. 15nm/s according to usual practice for biomaterials. What's more, the depths of indentations were controlled in 500nm to 800nm. When it comes to the results, the averages of the mechanical parameters at valuable points were calculated for the 5-8 points on the specimens were investigated. Even 10 specimens were tested total, those experiments have a valuable loads-depths curve were employed. Figure 3 The detected areas on a specimen. The mechanical performances, especially the hardness and Yong's modulus, are of great significance in materials evaluations, are also the major foundation of structure designs and calculations. An advanced material superficial mechanical properties detecting instrument, the nano-indenter, were introduced to research the mechanical performances of the Bamboo Beetles' abdominal shells. Because high solution brake and sensors were used, we not only can control and check the indenter accurately when it's forced pass in and out the surfaces of materials, but also can detect with continuous loads and displacements by using nano-indenter. Apart from this, some advantages should be mentioned here, i. e. i) we can obtain the real contact areas from loads-displacements curves with smaller errors, releasing experimenters from cockamamie works such as seek indentations and measure residuary proportions; ii) we can obtain multi-parameter contemporaneously such as the hardness and the modulus from the dynamical curves of mechanical performances.
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Results and discussions The mechanical tests and investigations of the abdominal shells are of great potential in bionic designing aerial materials for it's a kind typical lightweight and high-strength biomaterial in micro-level. As we all know, the mechanical performances change rapidly from microscopic and nasoscopic to macroscopic levels because of nano-particles' surface actions, dimensional effects and quantum effects. Nano-materials perform peculiarly in many fields such as mechanics, electromagnetism, thermo and chemistry because of the nanometer effects. We investigated the nano-mechanical properties of the abdominal shells using the nano-indenter to understand its role in flights. There is a layer of black tight waxiness about 15μm thickness, i. e. collagen, at the outermost layer of specimen. And there are 5-10 layers of fibers connect with the collagen layer. The fiber layers may share the results for they are made by collagen both even the outermost layer was tested in fact. Especially, the mechanical properties of fibers can be used to predict those of the whole abdominal shell. Four test areas along the centerline of the abdominal shell were selected on very specimen for experiments (Fig. 3). One of the loads-depths curves is showed in Fig. 4 and the average values of valuable experiments are listed in Table 1. The experiments showed that the mechanical performances of points at the same latitude resemble each other much, e. g. area III and IV in Fig. 3, while they decreased from the head to the tail and got minimums at the tail, i. e. area I, indicating that the mechanical performances of the abdominal shells distribute in topology. This result demonstrates the structural optimizations of the abdominal shells. In fact, the abdominal shell can be divided into two functional fields. One is to extend or to shrink actively and the other one is used as load-supporting. The mobilizable part close to chest needs better mechanical performances for it's used to connect to the chest wall and keep a hermetical thorax mainly while the mobilizable part close to tail needs better elasticity and flexibility to protect wings from injuries when the Bamboo Beetle flap its wings by shrinking the abdominal shell. In the next place, the large Yong's modulus of the abdominal shell provides the necessary conditions for that the abdominal shell can be regard as the rigid support of flapping wings. What should not been ignored is that the large modulus ensures the abdominal shell can provide enough restoring forces to the deformed dorsal muscles and the deformed abdominal shell to achieve continuous flapping. Figure 4 The loads-depths curve. Table 1 The statistical values of Yong's modulus Area Ⅰ Ⅱ Ⅲ Ⅳ The Yong's modulus(GPa).
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21±1. 15 N=6, n=30, where N is the number of specimen while n is the number of total valuable indentation.
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Conclusions The mechanical performances distribute in topology. The excellent mechanical performances of the abdominal shell provide the necessary conditions for that the abdominal shell can be regard as the rigid support of flapping wings. And the abdominal shell plays a notable role in flapping. It provides enough restoring forces to the deformed dorsal muscles and the deformed abdominal shell to achieve continuous flapping, which is referential to ornithopter designs.
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Acknowledgements This work was supported by the National Basic Research Program of China (973 Program) (Grant no. 2011CB302106), the National Natural Science Foundation of China（Grant No. 50975140 and 31070344）.
DOI: 10.1016/j.ifacol.2015.12.208
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