Use of a Digital Image Correlation Technique for Measuring the Material Properties of Beetle Wing

Beetle wings are very specialized flight organs consisting of the veins and membranes.Therefore it is necessary from abionic view to investigate the material properties of a beetle wing experimentally.In the present study,we have used a DigitalImage Correlation (DIC) technique to measure the elastic modulus of a beetle wing membrane.Specimens were prepared bycarefully cutting a beetle hind wing into 3.0 mm by 7.0 mm segments (the gage length was 5 mm).We used a scanning electronmicroscope for a precise measurement of the thickness of the beetle wing membrane.The specimen was attached to a designedfixture to induce a uniform displacement by means of a micromanipulator.We used an ARAMISTM system based on the digitalimage correlation technique to measure the corresponding displacement of a specimen.The thickness of the beetle wing variedat different points of the membrane.The elastic modulus differed in relation to the membrane arrangement showing a structuralanisotropy;the elastic modulus in the chordwise direction is approximately 2.65 GPa,which is three times larger than the elasticmodulus in the spanwise direction of 0.84 GPa.As a result,the digital image correlation-based ARAMIS system was suc-cessfully used to measure the elastic modulus of a beetle wing.In addition to membrane’s elastic modulus,we considered thePoisson’s ratio of the membrane and measured the elastic modulus of a vein using an Instron universal tensile machine.Theresult reveals the Poisson’s ratio is nearly zero and the elastic modulus of a vein is about 11 GPa.     

A modified blade element theory for estimation of forces generated by a beetle-mimicking flapping wing system

We present an unsteady blade element theory (BET) model to estimate the aerodynamic forces produced by a freely flying beetle and a beetle-mimicking flapping wing system. Added mass and rotational forces are included to accommodate the unsteady force. In addition to the aerodynamic forces needed to accurately estimate the time history of the forces, the inertial forces of the wings are also calculated. All of the force components are considered based on the full three-dimensional (3D) motion of the wing. The result obtained by the present BET model is validated with the data which were presented in a reference paper. The difference between the averages of the estimated forces (lift and drag) and the measured forces in the reference is about 5.7%. The BET model is also used to estimate the force produced by a freely flying beetle and a beetle-mimicking flapping wing system. The wing kinematics used in the BET calculation of a real beetle and the flapping wing system are captured using high-speed cameras. The results show that the average estimated vertical force of the beetle is reasonably close to the weight of the beetle, and the average estimated thrust of the beetle-mimicking flapping wing system is in good agreement with the measured value. Our results show that the unsteady lift and drag coefficients measured by Dickinson et al are still useful for relatively higher Reynolds number cases, and the proposed BET can be a good way to estimate the force produced by a flapping wing system.     

The Role of Soft Vein Joints in Dragonfly Flight

Dragonflies are excellent flyers among insects and their flight ability is closely related to the architecture and material properties of their wings.The veins are main structure components of a dragonfly wing,which are found to be connected by resilin with high elasticity at some joints.A three-dimensional (3D) finite element model of dragonfly wing considering the soft vein joints is developed,with some simplifications.Passive deformation under aerodynamic loads and active flapping motion of the wing are both studied.The functions of soft vein joints in dragonfly flight are concluded.In passive deformation,the chordwise flexibility is improved by soft vein joints and the wing is cambered under loads,increasing the action area with air.In active flapping,the wing rigidity in spanwise direction is maintained to achieve the required amplitude.As a result,both the passive deformation and the active control of flapping work well in dragonfly flight.The present study may also inspire the design of biomimetic Flapping Micro Air Vehicles (FMAVs).     

Role of Soft Matter in the Sandwich Vein of Dragonfly Wing in Its Configuration and Aerodynamic Behaviors

The microstructure of the main longitudinal veins of the dragonfly wing and the aerodynamic behaviors of the wing were investigated in this paper.The microstructure of longitudinal vein presents two circumferential chitin layers and a protein-fiber soft layer.The dragonfly wing is corrugated due to the spatial arrangement of longitudinal veins.It was found that the corrugation angle could significantly influence the lift/drag ratio across a range of attack angles by the wind tunnel experiments.The results of the finite element analysis indicate that the protein soft layer of vein facilitates the change of the corrugation angle by allowing substantial relative twisting deformation between two neighboring veins,which is not possible in veins without a soft sandwich layer.     

A Model for Selection of Eyespots on Butterfly Wings

Unsolved Problem

The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not.

Key Idea and Model

We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature.

Result

We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell.     

Sexual Dichromatism of the Damselfly Calopteryx japonica Caused by a Melanin-Chitin Multilayer in the Male Wing Veins

Mature male Calopteryx japonica damselflies have dark-blue wings, due to darkly coloured wing membranes and blue reflecting veins. The membranes contain a high melanin concentration and the veins have a multilayer of melanin and chitin. Female and immature C. japonica damselflies have brown wings. We have determined the refractive index of melanin by comparing the differently pigmented wing membranes and applying Jamin-Lebedeff interference microscopy. Together with the previously measured refractive index of chitin the blue, structural colour of the male wing veins could be quantitatively explained by an optical multilayer model. The obtained melanin refractive index data will be useful in optical studies on melanized tissues, especially where melanin is concentrated in layers, thus causing iridescence.     

An interspecific QTL study of Drosophila wing size and shape variation to investigate the genetic basis of morphological differences

The Drosophila wing has been used as a model in studies of morphogenesis and evolution; the use of such models can contribute to our understanding of mechanisms that promote morphological divergence among populations and species. We mapped quantitative trait loci (QTL) affecting wing size and shape traits using highly inbred introgression lines between D. simulans and D. sechellia, two sibling species of the melanogaster subgroup. Eighteen QTL peaks that are associated with 12 wing traits were identified, including two principal components. The wings of D. simulans and D. sechellia significantly diverged in size; two of the QTL peaks could account for part of this interspecific divergence. Both of these putative QTLs were mapped at the same cytological regions as other QTLs for intraspecific wing size variation identified in D. melanogaster studies. In these regions, one or more loci could account for intra- and interspecific variation in the size of Drosophila wings. Three other QTL peaks were related to a pattern of interspecific variation in wing size and shape traits that is summarized by one principal component. In addition, we observed that female wings are significantly larger and longer than male wings and the second, fourth and fifth longitudinal veins are closer together at the distal wing area. This pattern was summarized by another principal component, for which one QTL was mapped.     

Wing cross veins: an efficient biomechanical strategy to mitigate fatigue failure of insect cuticle

Locust wings are able to sustain millions of cycles of mechanical loading during the lifetime of the insect. Previous studies have shown that cross veins play an important role in delaying crack propagation in the wings. Do cross veins thus also influence the fatigue behaviour of the wings? Since many important fatigue parameters are not experimentally accessible in a small biological sample, here we use the finite element (FE) method to address this question numerically. Our FE model combines a linear elastic material model, a direct cyclic approach and the Paris law and shows results which are in very good agreement with previously reported experimental data. The obtained results of our study show that cross veins indeed enhance the durability of the wings by temporarily stopping cracks. The cross veins further distribute the stress over a larger area and therefore minimize stress concentrations. In addition, our work indicates that locust hind wings have an endurance limit of about 40% of the ultimate tensile strength of the wing material, which is comparable to many engineering materials. The comparison of the results of the computational study with predictions of two most commonly used fatigue failure criteria further indicates that the Goodman criterion can be used to roughly predict the failure of the insect wing. The methodological framework presented in our study could provide a basis for future research on fatigue of insect cuticle and other biological composite structures.     

Characteristics of a Beetle's Free Flight and a Flapping-Wing System that Mimics Beetle Flight

In this work, we first present a method to experimentally capture the free flight of a beetle (Allomyrina dichotoma), which is not an active flyer. The beetle is suspended in the air by a hanger to induce the free flight. This flight is filmed using two high-speed cameras. The high speed images are then examined to obtain flapping angle, flapping frequency, and wing rotation of the hind wing. The acquired data of beetle free flight are used to design a motor-driven flapper that can approximately mimic the beetle in terms of size, flapping frequency and wing kinematics. The flapper can create a large flapping angle over 140° with a large passive wing rotation angle. Even though the flapping frequency of the flapper is not high enough compared to that of a real beetle due to the limited motor torque, the flapper could produce positive average vertical force. This work will provide important experience for future development of a beetle-mimicking Flapping-Wing Micro Air Vehicle (FWMAV).     

基于四种金龟的昆虫后翅关节骨片三维形态复杂性研究

【目的】昆虫的翅非常精巧与灵活,翅脉及翅关节的形态及功能长久以来受到众多领域科学家的广泛关注。由于历史条件的限制,昆虫翅的研究主要集中在翅脉,即使少量的有关翅关节形态的研究也主要是停留在二维形态数据分析的层面上。更重要的是,各骨片内部形态结构还未见报道。本研究的目的就是为了重建翅关节骨片内部和外部复杂的三维形态结构,全面呈现利用传统形态学方法无法获得的形态学信息,进而深入探究昆虫翅的形态与功能的关系。【方法】本文利用显微CT对鞘翅目4种金龟进行了扫描,通过计算机三维重建技术,对折叠和展开状态时后翅关节各个骨片（第1, 2和3腋片及中片）的内部和外部的三维形态进行研究,展示和分析昆虫翅关节内部与外部形态结构和空间运动的复杂性。【结果】翅关节骨片的三维重建模型及虚拟切面图展示了其复杂的外部形态,主要表现在表面曲率的不均匀变化和部分结构的互相遮挡两个方面。前者主要表现骨片表面具有突起、沟槽、弯折以及外长物等。后者指各骨片均呈现了不同程度的弯折,有的弯折还会互相接触,最终形成筒状结构,这样不可避免造成部分结构被遮挡或包裹。三维重建模型的断层图显示了翅关节骨片并非是实心的结构,而是分为两层：靠近表皮的为高度骨化的外骨骼,而靠近骨片核心则为疏松的类似海绵状结构。本文还展示了各个骨片在后翅折叠状和展开状态下的空间位置,并对所研究的4个科的翅关节骨片的三维形态进行了比较。【结论】翅关节骨片具有复杂的内部和外部形态结构。关节骨片的内部海绵结构和外层强烈骨化的双层结构,可能与其尽量减小骨片的重量和节约运动能量,同时又尽量保持骨片的刚性结构的形态适应策略有关。此类形态适应在材料学、空气动力学等领域具有重要的仿生学意义。     

Effects of grid dimensions on finite element models of an articular surface

Recent activity in finite element analysis of articular joints has emphasized refinements in geometry and material properties. In the implementation of such models, it is necessary to ensure that grid dimensions are optimal for suitable solutions of displacements, strains and stresses. A method of grid optimization was developed to ensure that for typical material properties, finite element models of an articular surface agree with known analytical solutions. The layered axisymmetric model presented by Askew and Mow (J. biomech. Engng 100, 105-115, 1978) was used as a reference. From this reference, an STZ of 0.2 mm, middle and deep zones of 0.8 mm and tidemark region of 0.2 mm were chosen. Cancellous bone was an infinite elastic half space under these layers. Loading was a parabolic distribution over a 10 mm radius having a peak of 1 MPa. Agreement was obtained between analytical solutions and finite element solutions when the finite element model had a radial boundary of 30 mm radius and a bone depth of 32 mm. These results suggested that in models of real joints, care must be taken to ensure the boundaries are reasonably represented and that sufficient bone is modelled for adequate solutions.     

Development and experimental validation of a finite element model of total ankle replacement

Total ankle replacement remains a less satisfactory solution compared to other joint replacements. The goal of this study was to develop and validate a finite element model of total ankle replacement, for future testing of hypotheses related to clinical issues. To validate the finite element model, an experimental setup was specifically developed and applied on 8 cadaveric tibias. A non-cemented press fit tibial component of a mobile bearing prosthesis was inserted into the tibias. Two extreme anterior and posterior positions of the mobile bearing insert were considered, as well as a centered one. An axial force of 2 kN was applied for each insert position. Strains were measured on the bone surface using digital image correlation. Tibias were CT scanned before implantation, after implantation, and after mechanical tests and removal of the prosthesis. The finite element model replicated the experimental setup. The first CT was used to build the geometry and evaluate the mechanical properties of the tibias. The second CT was used to set the implant position. The third CT was used to assess the bone-implant interface conditions. The coefficient of determination (R-squared) between the measured and predicted strains was 0.91. Predicted bone strains were maximal around the implant keel, especially at the anterior and posterior ends. The finite element model presented here is validated for future tests using more physiological loading conditions.     

A simplified model of scar contraction

The healing of wounds is a complex process and the contraction of the resulting scar can have a negative impact on the neighbouring skin. A finite element model of skin simulating the contraction of a scar and deformation of the surrounding skin is presented. The skin is represented by an orthotropic–viscoelastic constitutive law, which is validated against experimental data in the literature. A simplified experimental model of a contracting scar in real skin is also developed. The pattern and size of the wrinkles formed around the contracting scar in the finite element model compare favourably with those formed in the experimental model. The orthotropic nature of skin plays a significant role in the behaviour of skin around scars—the wrinkles have a preferential orientation that corresponds to a direction perpendicular to the Langer's lines in the skin. The pre-stress in skin (a property that is ignored in many skin models) is shown to be an important factor in wrinkle formation around scars. The proposed model can be used to analyse the suturing and closure of wounds of various shapes.     

A Simulation of the Flight Characteristics of the Deployable Hindwings of Beetle

An insect is an excellent biological object for the bio-inspirations to design and develop a MAV.This paper presents the simulation study of the flight characteristics of the deployable hindwings of beetle,Dorcustitanus platymelus.A 3D geometric model of the beetle was obtained using a 3D laser scanning technique.By studying its hindwings and flight mechanism,the mathematical model of the flapping motion of its hindwings was analyzed.Then a simulation analysis was carried out to analyze and evaluate the flapping flying aerodynamic characteristics.After that,the flow of blood in the hindwing veins was studied through simulation to determine the maximum pressure on a vein surface and the minimum blood flow in flight.A number of interesting bio-inspirations were obtained.It is believed that these findings can be used for the design and development of a MAV with similar flying capabilities to a natural beetle.     

Physical Constraint Finite Element Model for Medical Image Registration

Due to being derived from linear assumption, most elastic body based non-rigid image registration algorithms are facing challenges for soft tissues with complex nonlinear behavior and with large deformations. To take into account the geometric nonlinearity of soft tissues, we propose a registration algorithm on the basis of Newtonian differential equation. The material behavior of soft tissues is modeled as St. Venant-Kirchhoff elasticity, and the nonlinearity of the continuum represents the quadratic term of the deformation gradient under the Green- St.Venant strain. In our algorithm, the elastic force is formulated as the derivative of the deformation energy with respect to the nodal displacement vectors of the finite element; the external force is determined by the registration similarity gradient flow which drives the floating image deforming to the equilibrium condition. We compared our approach to three other models: 1) the conventional linear elastic finite element model (FEM); 2) the dynamic elastic FEM; 3) the robust block matching (RBM) method. The registration accuracy was measured using three similarities: MSD (Mean Square Difference), NC (Normalized Correlation) and NMI (Normalized Mutual Information), and was also measured using the mean and max distance between the ground seeds and corresponding ones after registration. We validated our method on 60 image pairs including 30 medical image pairs with artificial deformation and 30 clinical image pairs for both the chest chemotherapy treatment in different periods and brain MRI normalization. Our method achieved a distance error of 0.320±0.138 mm in x direction and 0.326±0.111 mm in y direction, MSD of 41.96±13.74, NC of 0.9958±0.0019, NMI of 1.2962±0.0114 for images with large artificial deformations; and average NC of 0.9622±0.008 and NMI of 1.2764±0.0089 for the real clinical cases. Student’s t-test demonstrated that our model statistically outperformed the other methods in comparison (p-values <0.05).     

An augmented Lagrangian finite element formulation for 3D contact of biphasic tissues

Biphasic contact analysis is essential to obtain a complete understanding of soft tissue biomechanics, and the importance of physiological structure on the joint biomechanics has long been recognised; however, up to date, there are no successful developments of biphasic finite element contact analysis for three-dimensional (3D) geometries of physiological joints. The aim of this study was to develop a finite element formulation for biphasic contact of 3D physiological joints. The augmented Lagrangian method was used to enforce the continuity of contact traction and fluid pressure across the contact interface. The biphasic contact method was implemented in the commercial software COMSOL Multiphysics 4.2^® (COMSOL, Inc., Burlington, MA). The accuracy of the implementation was verified using 3D biphasic contact problems, including indentation with a flat-ended indenter and contact of glenohumeral cartilage layers. The ability of the method to model multibody biphasic contact of physiological joints was proved by a 3D knee model. The 3D biphasic finite element contact method developed in this study can be used to study the biphasic behaviours of the physiological joints.     

肱骨有限元模型建立及生物力学分析

目的:以成人肱骨为例,将医学图像三维重建技术和有限元方法结合应用于正骨手法研究,建立正常肱骨有限元模型,验证模型的有效性并进行生物力学分析。方法:选择一位青年男性志愿者,对其上肢自尺桡骨上端至肱骨头进行连续断层扫描,得到CT图像,将CT数据导入MIMICS软件中,通过图像分割、三维重建和材料属性赋值,构建正常肱骨有限元模型,利用ANSYS软件进行力学分析,与文献中肱骨的生物力学数据相比较,以此验证模型的有效性。结果:建立了正常肱骨三维几何模型和有限元模型。利用ANSYS软件,对模型进行了有效性验证。所建模型物理特性与真实骨骼相近,能很好地反映骨骼的力学变化,实现手法的定量分析。结论:所建立的肱骨模型外形逼真、在不同载荷下的应力值与相关文献一致,可用作中医仿真系统中的虚拟骨折模型。     

Do dung beetles show interrelated evolutionary trends in wing morphology,flight biomechanics and habitat preference?

In flying organisms, wing shape and biomechanical properties are recognized as key traits related to dispersal, foraging behavior, sexual selection and habitat preferences. To determine if differences in dung beetle wing shape and flight biomechanics are consistent with habitat preferences in a phylogenetic context, we examined how wing morphology varied in a set of 18 Mozambique forest and grassland dung beetle (Scarabaeinae) species, representing nine genera and six tribes. Geometric morphometric measurements were taken of entire wings, as well as two additional shape characters comprising the RA4 and CuA to J regions of veins. Ordination (Principal Components Analysis and Canonical Variate Analysis) of landmark data revealed three different trends in wing shape related to expansion or contraction in external wing margins. These trends were consistent with published dung beetle phylogenies and a phylogenetic reconstruction of ancestral morphological changes using parsimony analysis of wing landmark configurations. Analysis of variance showed that the Procrustes distances between wing shapes were significantly correlated to species identity (~?48% of variance), wing size (~?27%), habitat (~?11%) and two of the three, tested, biomechanical variables (wing loading, wing aspect ratio: ~?1%). However, while a phylogenetic generalized least squares analysis confirmed a strongly significant phylogenetic signal for wing shape, it found no significant effect of any other variable. Therefore, wing shape evolution in dung beetles appears to have been phylogenetically constrained and habitat may constitute only a weak selective pressure for changes in wing shape.     

Evaluation of accuracy of non-linear finite element computations for surgical simulation: study using brain phantom

In this paper, the accuracy of non-linear finite element computations in application to surgical simulation was evaluated by comparing the experiment and modelling of indentation of the human brain phantom. The evaluation was realised by comparing forces acting on the indenter and the deformation of the brain phantom. The deformation of the brain phantom was measured by tracking 3D motions of X-ray opaque markers, placed within the brain phantom using a custom-built bi-plane X-ray image intensifier system. The model was implemented using the ABAQUS(TM) finite element solver. Realistic geometry obtained from magnetic resonance images and specific constitutive properties determined through compression tests were used in the model. The model accurately predicted the indentation force-displacement relations and marker displacements. Good agreement between modelling and experimental results verifies the reliability of the finite element modelling techniques used in this study and confirms the predictive power of these techniques in surgical simulation.     

Influence of transmucosal height in abutments of single and multiple implant-supported prostheses: a non-linear three-dimensional finite element analysis

The aim of this study was to analyze the influence of three different transmucosal heights of the abutments in single and multiple implant-supported prostheses through the finite element method. External hexagon implants, MicroUnit, and EsthetiCone abutments were scanned and placed in an edentulous maxillary model obtained from a tomography database. The simulations were divided into two groups: (1) one implant with 3.75 × 10 mm placed in the upper central incisor, simulating a single implant-supported fixed prosthesis with an EsthetiCone abutment; and (2) two implants with 3.75 × 10 mm placed in the upper lateral incisors with MicroUnit abutments, simulating a multiple implant-supported prosthesis. Subsequently, each group was subdivided into three models according to the transmucosal height (1, 2, and 3 mm). A static oblique load at an angle of 45 degrees to the long axis of the implant in palatal-buccal direction of 150 and 75 N was applied for multiple and single implant-supported prosthesis, respectively. The implants and abutments were assessed according to the equivalent Von Mises stress analyses while the bone and ceramics were analyzed through maximum and minimum principal stresses. The total deformation values increased in all models, while the transmucosal height was augmented. The transmucosal height of the abutments influences the stress values at the bone, ceramics, implants, and abutments of both the single and multiple implant-supported prostheses, with the transmucosal height of 1 mm showing the lowest stress values.