Mechanical Simulation of Hierarchical Micro-Nano Structure of Butterfly Wings

SHI Shunjie GE Dengteng JIN Junhong LI Guang YANG Shenglin

State Key Laboratory for Modification of Chemical Fibers and Polymer Materials,College of Materials Science and Engineering,Donghua University,Shanghai 201620,China

Abstract:The ridge-cross rib microstructures of Carystoides escalantei butterfly wing scales have been reproduced by 2D and 3D models via the ANSYS software,and the structural analyses under tensile and bending deformation,as well as the relative failure analyses are performed for those models. It has been found that the curved model in which the ridges acted as triangular prisms while the cross-ribs acted as bend cuboids could simulate the real scale configuration more accurately. Besides,it also shows much more even stress distribution under deformation and better mechanical properties than the rectangular one,in which both ridges and cross-ribs are modeled as regular cuboids.

Key words:butterfly scales;multilevel structure;bionic model;mechanical simulation

Introduction

The wings of Lepidopterans such as butterflies are composed of membrane tissue densely covered by scales of various morphologies and structures[1].Furthermore,butterfly scales still consist of precise and complex substructures with dimensions ranging from tens of nanometers to hundreds of micrometers[2-3],which endow the butterfly wings with some amazing characteristics such as gorgeous physical color,superhydrophobicity and self-cleaning properties[4-5].

The multilevel structure of butterfly scales has inspired many researchers to make novel devices through the so-called bionics design[6-7].Morpho sulkowskyi scales,composed of multiple nanostructures with high ratio of depth to width and surface area,have been replicated in the solar energy and photocatalytic nanostructure templates through depositing process to improve the photocatalysis efficiency[8].The bionic sensors based on photonic microstructure of Morpho have been used in the fields of infrared radiation,radiative cooling,thermal radiation,air pressure and so on[9-11].The sensitive discoloring mechanism of micro-nano structures of Trogonoptera brookiana butterfly scales in specific liquid media has also been reproduced in the applications of water quality detection and analysis systems or biodegradation[12].Up to now,most considerations have been focused on the optical characteristics of the complicated structures exhibited by wing scales[13-16],but few researches are aimed to explore the mechanical properties of this special nature structures.

Carystoides escalantei,native to Costa Rica,is one kind of dusk-active butterflies.This butterfly has two types of white spots in its wings,including angle dependent whiteness and angle independent one.The scales in angle independent white spots are laid down in stacks on the membrane,while scales in angle dependent white spots stand at different angles from the membrane[17].In the latter case,it has been found that the main body of the scale is like a crinkled flake and in the both sides of the flake there are periodic ridges attached by curved cross-rib array.Because of this kind of microstructure,the standing angles of those scales will be disturbed by the airflow caused by wing flapping,resulting in the brightness changing of white spots.In this procedure,the force acting on the scales is alternated and sophisticated.However,the ridge-cross rib structure of the scales appears to be fairly stable.In this study,several structural models imitating the ridge-cross rib configuration of Carystoides escalantei scales with different accuracise has been established,and the mechanical behaviors of those models have also been predicted by using the ANSYS software.

1 Modeling

The configuration and the dimension of ridge-cross rib microstructure in Carystoides escalantei scales were demonstrated by means of the scanning electron microscope (SEM) and the atomic force microscope (AFM) images in Fig.1,which were reported by Geetal.[17]It could be found that the longitudinal ridges have a shape of curved triangular prism while the cross ribs are like bent cuboid.In the ANSYS software,a 2D model was firstly set up to investigate the structural effect of ridges and then a 3D model was used to check the combination effect of ribs.Moreover,the simple rectangular model (easy to coarse meshing and reducing calculation) and the more accurate curved model were put forward simultaneously (shown in Fig.2,unit:mm).

Fig.1 SEM and AFM photographs of the ridge-cross rib microstructures of Carystoides escalantei scale:(a) SEM image of the scales from the angle-independent white spot;(b) AFM image;(c)-(d) corresponding 3D scan profiles of the scale from the angle-dependent white spot (scan directions are shown in (b) as black and red solid lines)

Fig.2 Two structural models with different rib shapes:(a) 2D rectangular model;(b) 3D rectangular model; (c) 2D curved model;(d) 3D curved model

The geometric dimensions of those models demonstrated in Fig.2 were estimated from the AFM photograph [shown in Figs.1 (b)-(d)] and enlarged in proportion for simplicity because a linear elastic material would be adopted.It should also be declared that just a part of scale structure has been modeled and the periodic boundary condition is applied to simplify the calculation.

2 Finite Element Simulation

In this study,ANSYS,the finite element software was applied to the nonlinear static analysis,in which a four-node SHELL181 element and a SOLID185 element were chosen to mesh the 2D and 3D models mentioned above,respectively.The main component of the butterfly scales is chitin,so the mechanical properties are based on natural chitin films obtained from the wing of cockroach[18],which is similar to those of the butterfly scales.

For predicting the tensile strength and bending strength of biomimetic construction,and understanding the difference in mechanical properties by structural changes,the proposed models are applied in a quasi-static failure analysis (determined via Tsai-Wu failure criteria) using the ANSYS Parametric Design Language (APDL) codes.

During the failure analysis,the structure was subjected to a cumulative small strain step by step.At first,there was no failure in the model.By the increasing number of cycles,the local failure led to the global stiffness degeneration as a result of the cumulative loading,which would bring about stress redistribution[19].Considering the influence on the prediction of strength,the elements judged by Tsai-Wu failure criteria in each sub-step of loading were dealt with by “birth and death”.The elements killed indicate that the initial stiffness matrix in the damaged region should be reduced if the failure criteria for the element exceed 1[20-21],and then the stress will be redistributed until the structure collapses.

Final failure criterion was the key to decide the point of catastrophic destruction.In this work,considering the convergence of computation,the final failure criterion was assumed conservatively that the sudden degradation came to 5%.In other words,the structures would collapse when the number of failure elements reached 5% of the total in this work.The sudden degradation was acted on the element whose stiffness matrix was regulated by a reduced factor[22].The stresses in a thin lamina with any orientation could be derived in terms of the global deformation as

The flow chart of the strength prediction was depicted in Fig.3.

Fig.3 Flow chart of algorithm for strength simulation of the scale-like structure model

The stress and strain data were recorded and stored during the whole procedure,and the difference in strength of two models would be obtained by the stress-strain curve.On the other hand,a series of contour maps such as axial stress and axial displacement could also be derived to analyze the diversity and characteristic of those two types of the scale-like structure.

3 Results and Discussion

Firstly,the methodology was applied to tensile and bending simulation for the 2D model,and the tensile direction was parallel to thex-axis and the strain direction of bending was along they-axis.Figures 4-6 showed the tensile analysis of 2D models.Since the ridges were asymmetrically distributed on the main body of scales,the torque will be produced in the process of tensile,leading to a certain bending deformation just demonstrated in those figures.

Fig.4 Strain distribution of tensile simulation

Figure 4 showed the contour maps of axial strain.The tensile strain distribution of the curved structure was more uniform than that of the rectangular enhanced structure,especially in the bottom of ridges.The similar situation could also be observed in the distribution of shear stress(shown in Fig.5).There were more stress concentration regions at the junction parts of ridges,while the shear stress value of the curved structure was much smaller,implying the much more stabilities in the curved structure.

The total stress intensity distributions were shown in Fig.6.

Fig.5 Shear stress of tensile simulation

Fig.6 Stress intensity of tensile simulation

It could be found again that the distribution was much even in the curved model,whereas the rectangular model showed a steep intensity gradient.Moreover,the results of bending simulation gave a similar phenomenon (shown in Fig.7),i.e.,the curved model possessed a better distributed stress intensity.

Fig.7 Stress intensity of bending simulation

Moreover,Fig.8 showed the 3D tensile and bending stress intensity contour maps,from which it could be found that the cross-ribs played a reinforcing role because they had gained the most stress concentration.3D models also showed that the stress distribution would be more smooth in curved ridge-cross rib structures than in rectangular ones.

Finally,the simulated tensile and bending stress-strain curves are shown in Fig.9.The curved structure possessed a higher apparent elastic modulus and a higher strength,whereas a smaller elongation at break than the rectangular one.The similar results appeared in the bending simulation,and it was worth mentioning that the stiffness of the film standing with rectangle ribs showed no difference between the tensile and bending simulation,while the curved reinforcing ribs made the axial stiffness slightly larger than the transverse stiffness.Combined with tensile and bending analyses,the shape transition of ridges and ribs could raise the capability of anti-deformation in both tensile and bending directions of the membrane,which keep the stability of structural color.Despite the higher elastic modulus,the stress intensity distribution of curved structures was similar to the rectangular structures in bending process.In other words,this special curved structure could improve the stiffness and strength more obviously in the axial direction of ribs than those in its vertical direction.

Fig.8 Stress intensity distribution:tensile stress intensity of (a) plate model,(b) rectangular model and (c) curved model;bending stress intensity of (d) plate model,(e) rectangular model and (f) curved model

Fig.9 Strength prediction of two models for (a) stress-strain for tensile strength prediction and (b) stress-strain for bending strength prediction

4 Conclusions

The results of the simulation by imitating the scale structure of Carystoides released that different cross-section would change the stress intensity distribution and mechanical properties of the structure.Compared with the rectangular rib,the curved rib was much conducive to the dispersion of stress and increased the stress intensity.From the stress-strain curves of the tensile simulation and the bending simulation,it was obvious that the rectangular rib could improve the toughness and elongation,while the curved rib could enhance the stiffness and strength of the structure.

Therefore,there may be an appropriate curvature shape that can not only maximize the strength but also eliminate the stress at the connection of ridges and ribs.The excellent mechanical properties of bionic butterfly scale structure in theory are constructive to the structure design.In addition to the optical characteristics,the hierarchical structure shows better mechanical properties than the single structure.Consequently,various special butterfly scales may be worth exploring for structural-functional integrated materials research.