Viscoelastic Constitutive Model Related to Deformation of Insect Wing Under Loading in Flapping Motion

BAO Lin; HU Jin-song; YU Yong-liang; CHENG Peng; XU Bo-qing; TONG Bing-gang

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Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(6): 655-662

BAO Lin, HU Jin-song, YU Yong-liang, CHENG Peng, XU Bo-qing, TONG Bing-gang. Viscoelastic Constitutive Model Related to Deformation of Insect Wing Under Loading in Flapping Motion[J]. Applied Mathematics and Mechanics, 2006, 27(6): 655-662.

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Viscoelastic Constitutive Model Related to Deformation of Insect Wing Under Loading in Flapping Motion

1.
Laboratory for Biomechanics of Animal Locomotion, Graduate University of the Chinese Academy of Sciences, Beijing 100049, P. R. China;

Received Date: 2005-10-17
Rev Recd Date: 2006-02-10
Publish Date: 2006-06-15

Abstract

Abstract

Flexible insect wings deform passively under periodic loading during flapping flight.The wing flexibility is considered as one of the specific mechanisms on improving insect flight perfor mance.The constitutive relation of the insect wing material plays a key role on the wing deformation, but has not been clearly understood yet.A viscoelastic constitutive relation model was established based on the experimental results:the stress relaxation experiment of a dragonfly wing(in vitro). This model was examined by the finite element analysis of the dynamic deformation response for a model insect wing under the action of the periodical inertial force in flapping.It is revealed that the viscoelastic constitutive relation is rational to characterize the biomaterial property of insect wings in contrast to the elastic one.The amplitude and form of the passive viscoelastic deformation of the wing is evidently dependent on the viscous parameters in the constitutive relation.
- constitutive relation,
- viscoelasticity,
- stress relaxation,
- finite element analysis,
- insect wing,
- passive deformation

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References(24)

References

[1]	Ellington C P,Van den Berg C,Willmott A P,et al.Leading-edge vortices in insect flight[J].Nature,1996,384(6610):626—630. doi: 10.1038/384626a0
[2]	Dickinson M H,Lehmann F-O,Sane S P. Wing rotation and the aerodynamic basis of insect flight[J].Science,1999,284(5422):1954—1960. doi: 10.1126/science.284.5422.1954
[3]	SUN Mao,TANG Jian.Lift and power requirements of hovering flight in Drosophila virilis[J].J Exp Biol,2002,205(16):2413—2427.
[4]	YU Yong-liang,TONG Bing-gang.A flow control mechanism in wing flapping with stroke asymmetry during insect forward flight[J].Acta Mech Sinica,2005,21(3):218—227. doi: 10.1007/s10409-005-0032-z
[5]	Ennos A R.The kinematics and aerodynamics of the free flight of diptera[J].J Exp Biol,1989,142(1):49—85.
[6]	Willmott A P,Ellington C P.The mechanics of flight in the hawkmoth Manduca sexta Ⅰ—Kinematics of hovering and forward flight[J].J Exp Biol,1997,200(21):2705—2722.
[7]	WANG Hao,ZENG Li-jiang,LIU Hao,et al.Measuring wing kinematics, flight trajectory and body attitude during forward flight and turning maneuvers in dragonflies[J].J Exp Biol,2003,206(4):745—757. doi: 10.1242/jeb.00183
[8]	Mueller T J.Fixed and Flapping Wing Dynamics for MAV Applications[M].AIAA Progress in Astron and Aeron,Massachusetts:AIAA,2001,195.
[9]	Alexander R M.Winging their way[J].Nature,2000,405(6782):17—18.
[10]	Wootton R J.From insects to microveechicles[J].Nature，2000,403(6766):144—145. doi: 10.1038/35003074
[11]	Dudley R. Unsteady aerodynamics[J].Science,1999,284(5422):1937—1938. doi: 10.1126/science.284.5422.1937
[12]	童秉纲，陆夕云.关于飞行和游动的生物力学研究[J].力学进展,2004,34(1):1—8.
[13]	Wootton R J.Functional morphology of insect wings[J].Annu Rev Entomol,1992,37:113—140. doi: 10.1146/annurev.en.37.010192.000553
[14]	Antonia B K,Ute P,Werner N.Biomechanical aspects of the insect wing: an analysis using the finite element method[J].Computers in Biology and Medicine,1998,28(4):423—437. doi: 10.1016/S0010-4825(98)00018-3
[15]	Herbert R C,Young P G,Smith C W,et al.The hind wing of the desert locust (Schistocerca gregaria Forskal)Ⅲ—A finite element analysis of a deployable structure[J].J Exp Biol,2000,203(19):2945—2955.
[16]	Combes S A,Daniel T L.Into thin air: contributions of aerodynamic and inertial-elastic forces to wing bending in the hawkmoth Manduca sexta[J].J Exp Biol,2003,206(17):2999—3006. doi: 10.1242/jeb.00502
[17]	Vincent J F V.Insect cuticle: a paradigm for natural composites[J].Symp Soc Exp Biol,1980,34(1):183—210.
[18]	Ellington C P. The aerodynamics of hovering insect flight Ⅱ—Morphological parameters[J].Phil Trans R Soc Lond B,1984,305(1122):17—40. doi: 10.1098/rstb.1984.0050
[19]	Wootton R J,Evans K E,Herbert R,et al. The hind wing of the desert locust (Schistocerca gregaria Forskal) Ⅰ—Functional morphology and mode of operation[J].J Exp Biol,2000,203(19):2921—2931.
[20]	Combes S A,Daniel T L.Flexural stiffness in insect wings Ⅰ—Scaling and the influence of wing venation[J].J Exp Biol,2003,206(17):2979—2987. doi: 10.1242/jeb.00523
[21]	周光泉,刘孝敏.粘弹性理论[M].合肥：中国科学技术大学出版社,1996.
[22]	Newman D J S,Wootton R J. An approach to the mechanics of pleating in dragonfly wings[J].J Exp Biol,1986,126(1):361—372.
[23]	Smith C W,Herbert R H,Wootton R J,et al.The hind wing of the desert locust (Schistocerca gregaria Forskal) Ⅱ—Mechanical properties and functioning of the membrane[J].J Exp Biol,2000,203(19):2933—2943.
[24]	Cheng J Y,Pedley T J,Altringham J D.A continuous dynamic beam model for swimming fish[J].Phil Trans R Soc Lond B,1998,353(1371):981—997. doi: 10.1098/rstb.1998.0262