Published On: Mon, Jan 14th, 2019

Local deformation and stiffness distribution in fly wings [RESEARCH ARTICLE]


Most insect wings are flexible, non-cambered, flat structures, producing aerodynamic forces for locomotion during gliding and wing flapping at elevated frequencies. They consist of thin membranes and ambient, longitudinal and cross veins (Brodsky, 1994; Chapman, 1998). The wing membrane is composed of multiple layers of cuticle that interconnect wing veins (Gorb et al., 2000; Song et al., 2007; Ma et al., 2017). Veins greatly vary in size and shape between animal species and determine the wing’s structure and mechanical behavior under load (Wootton, 1981; Combes and Daniel, 2003a; Appel et al., 2015). Veins may also carry nerves from innervated setae and campaniform sensilla (Gnatzy et al., 1987), situate accessory hearts to supply body appendages with hemolymph (Pass, 2000), and primarily contribute to wing mass.

Flexibility of insect wings prevents mechanical damage and is required in various behaviors, such as grooming and flight. In flight, wings are deformed by inertial-elastic, aerodynamic and viscous forces. Inertial-elastic forces, for example, are prominent at stroke reversals and viscous damping helps to prevent the flexible trailing edge from fluttering (Combes and Daniel, 2003c). Since wing shape determines the wing’s aerodynamic performance, any deformation of the surface during flapping motion may change flow conditions and thus lift and drag production (Young et al., 2009; Zheng et al., 2013). Previous findings on the significance of wing flexing for flight are, however, inconsistent. Compared to rigid wings, flexible wings may change the direction of forces (Zhao et al., 2010), maximize total lift production (Moses et al., 2017) and enhance force production into the downward direction (Mountcastle and Daniel, 2009; Zhao et al., 2010; Nakata and Liu, 2012; Mountcastle and Combes, 2013). By contrast, flexible models of hoverfly wings produce less lift than stiff model wings (Tanaka et al., 2011). In forward flight, flexible wings augment the lift-to-drag ratio mostly owing to wing twist and not changes in wing camber (Zheng et al., 2013). Besides passive deformation, wings of insects such as dragonflies, locusts and flies are thought to be supplemented by a series of muscles that allow some measure of active control of wing deformation (Ellington, 1984).

Computational models of fruit fly wings with reinforced leading edges, moreover, suggest higher lift-to-drag and lift-to-power ratios than wings with uniform stiffness distribution or rigid wings (Nguyen et al., 2016). A recent two-way fluid-structure interactions (FSI) model on bumblebee flight, by contrast, implies that model wings with uniform stiffness produce more lift and thrust than wings with a stiffness distribution similar to a genuine bumblebee wing. This is due to the hyper-compliant wing tip that stabilizes flight but at the cost of elevated aerodynamic power requirements (Tobing et al., 2017). The latter findings were confirmed by an experimental study on bumblebees with artificially stiffened wings that lead to more flight instabilities during forward flight compared to controls (Mistick et al., 2016). Further evidence for the above findings is provided by numerical results on aerodynamic power requirements for flight with flexible wings (Nakata and Liu, 2012). Explanations for the above contradictions have recently been discussed elsewhere (Fu et al., 2018).

The wing’s vein network predominately determines wing bending and twisting behavior. In flies, for example, the v-shaped profile of the leading wing edge resists bending but may easily twist when applying force behind the torsion axis (Ennos, 1988). This twist may propagate to the rest of the wing, resulting in an overall change of camber. Cambering increases with decreasing branching angle between the v-shaped veins, while immobilization of the wing base prevents camber formation under load. Under the latter conditions, torsion is greatly reduced (Ennos, 1988). Change in corrugation is thus thought to be a typical result from bending-torsion control in insect wings (Sunada et al., 1998; Rajabi et al., 2016a).

Wing bending and flexing at vein joints depend on several factors including the shape of veins, the existence of vein spikes and also on the distribution of resilin (Weis-Fogh, 1960). The latter findings have recently been demonstrated in numerical models on vein joint mechanics (Rajabi et al., 2015) and in a study on various types of resilin-mediated wing joint mechanics in the dragonfly Epiophlebia (Appel and Gorb, 2011). Resilin is not only present in wing vein joints but also in the internal cuticle layers of veins (Appel et al., 2015). Besides the number and thickness of cuticle layers, material composition and cross-sectional shape, resilin predominately determines vein material properties and thus the degree of elastic deformation. By contrast, flexible membranes between veins may increase structural stiffness under load and thus the integrity of insect wings (Newman and Wooton, 1986). The latter finding was also demonstrated by finite element modeling of corrugated wings during out-of-plane transversal loading (Li et al., 2009). Other mechanical features of insect wings include dorso-ventral anisotropy (Combes and Daniel, 2003a,b; Ma et al., 2017; Ning et al., 2017) and a gradient in wing stiffness from base to tip (Steppan, 2000; Lehmann et al., 2011; Moses et al., 2017). Since spanwise is typically larger than chordwise stiffness (Combes and Daniel, 2003a; Ning et al., 2017), wings often twist at the stroke reversals when forces peak within the flapping cycle (Ning et al., 2017).

In most previous studies, wing stiffness is quantified by Young’s modulus E, spring constant k and flexural stiffness EI with E the Young’s modulus and I the wing’s second moment of area. While Young’s modulus describes the relationship between tensile stress and tensile strain within the material, the spring constant describes the ratio between the deflection and loading force, and flexural stiffness is a measure that combines material and shape properties. On average, Young’s modulus of insect wings amounts to 5 GPa (Vincent and Wegst, 2004) but may greatly vary from tens to hundreds of Megapascal in flies and dragonflies (leading wing edge, Chen et al., 2013; Tong et al., 2015) and even in different parts of the wing (Haas et al., 2000a,b; Rajabi et al., 2016b). Spring stiffness covers measurements between ∼1 Nm−1 in butterflies (Mengesha et al., 2011) and ∼50 Nm−1 for the wing base of blowflies (Ganguli et al., 2010; Lehmann et al., 2011). Typical measures for flexural stiffness range from ∼10−9 Nm2 at the wing tip of blowflies (Lehmann et al., 2011) to ∼5×10−3 Nm2 at the wing base of moth (Combes and Daniel, 2003b). Although above parameters are mainly species-specific (Combes and Daniel, 2003a), a large part of the variance is explained by dry-out effects during the measurements. Wing stiffness greatly increases as wings desiccate. This leads, for example, to an approximately sixfold increase in flexural stiffness in butterflies (Steppan, 2000), an ∼10-fold increase in shear stiffness of larval fly cuticle (Vincent and Wegst, 2004), an ∼20-fold increase of Young’s modulus in dragonflies (Chen et al., 2013) and an approximately twofold increase in spring stiffness of wings of painted lady butterflies (Mengesha et al., 2011). Altogether, this suggests that measurement conditions are crucial for any reconstruction of complex wing models based on stiffness recordings (Herbert et al., 2000; Combes and Daniel, 2003b).

In this study, we investigate the scaling of mechanical behavior of wings attached to their living bodies in three species of flies, i.e. fruit flies, house flies and blowflies. We quantify the impact of dry-out effects on wing shape, estimate anisotropic deformation and score local deformation of the entire wing surface while loading wings at various sites using a micro-force transducer. From these data, we calculate the wing’s flexural stiffness and spring constants along selected bending lines. The measured data eventually allow us to construct an advanced, numerical model of fly flight using computational fluid dynamics and fluid-structure interaction. This model is currently under development and will provide quantitative results on flow patterns, aerodynamic forces and moments during flapping of model fly wings with a stiffness distribution similar to that of the natural archetype.

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