高深宽比微纳层次结构仿壁虎脚毛参数优化设计
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摘要
壁虎可以在垂直墙面甚至天花板上自由爬行,他们和未知粗糙表面接触时,能产生牢固的粘附并轻易的脱附,这些特性在MEMS器件可拆卸安装和固定、爬壁机器人等领域有着极为广阔的应用前景。壁虎脚毛的分级层次结构,特别是其微米级刚毛/纳米级绒毛的高深宽比微纳层次结构,是保证壁虎脚毛既产生巨大粘附力又适应不同表面形貌的关键。为此本学位论文开展对壁虎脚毛精细分层结构各参数的优化设计。主要工作如下:
建立微尺度接触的力学模型,解释了壁虎脚毛粘附机理;为了更接近实际情况,考虑表面粗糙度对粘附力的影响,建立了单根绒毛与粗糙表面接触模型,以及单层、双层以及三层粘附阵列与粗糙表面接触模型;进行接触全过程的粘附情况仿真,分析并总结了表面粗糙度、预载荷和结构刚度等因素对粘附能力的影响。
分析壁虎脚毛的各种粘附特性,以及环境适应性要求,提出了强的粘附力、防纠结、防自断裂、快速脱附、较好的粗糙表面适应性等若干设计准则;采用自下而上的设计思想,建立了相应的力学模型;分析并总结约束模型中各参数变化对纤维半径、纤维长度、阵列占空比、阵列对称性、粘附力以及粘附功等参数的影响。
综合考虑上述各约束条件,进行多目标多参数寻优求解,得到仿壁虎脚毛粘附结构的层次性几何特征(分形维数)、阵列几何特征(阵列密度、阵列对称性)以及单根接触几何特征(接触半径、深宽比、倾斜角)等设计参数。设计结果表明,优化设计得到的第一级结构的纤维半径、长度均在壁虎脚绒毛测量值范围内,第二级结构的纤维半径、长度也在壁虎脚刚毛测量值范围内,且具有更好的粘附能力。
Gecko has an extraordinary ability to maneuver on vertical walls and ceilings, for the adhesion is robust enough to function on unknown rough surfaces and also easily releasable on animal movement. The incredible characteristics have a very broad prospect of applications in the deployment and disassembly of MEMS devices, wall-climbing robots, etc. The multi-scale hierarchical structure of the gecko foot-hair, especially the high-aspect-ratio structure of its micro-scale seta and nano-scale spatulae is the critical factor of the gecko’s ability to adopt and stick to any different surface with powerful adhesion force. Accordingly, the optimal design mimicking the finely structured gecko foot-hair has been studied in this degree thesis. The main contents of this thesis comprise:
Analyzing the micro-scale contact mechanics, reveal the mechanism of gecko adhesion. Considering the roughness, set up the contact models between one single spatula, one-, two-, muti-level adhesion arrays and rough surface respectively. Then simulate the adhesion ability through the whole attaching process with rough surfaces and analyze the influence of roughness, the applied force and the stiffness on the adhesion ability.
Analyzing the properties of gecko adhesion at bumpy surfaces, introduce the enquired limitations and modeled to ensure the adhesion is robust and the release is easy, the fibrils are compliant enough to easily deform to mating surface’s roughness profile, yet rigid enough not to collapse under their own weight. And analyze the influence of these constraints to the parameters of optimal design.
Based on these parameters, we have launched a bottom-up design methodology. A procedure is also developed here to find optimum designed parameters considering multi-object/parameter situations that adopt geometrical parameters of hierarchical dimensions (structure) with excellent patterns (density and symmetry) and sizes of single fiber (radius, length and angle). These results show that the optimal designed parameters of fiber structure sizes in both levels are in the scope of gecko spatulae and setae respectively and the simulated adhesion force at the second level is consistent with the observed value of single seta. These provided findings are the strong foundations of bio-inspired dry adhesives.
建立微尺度接触的力学模型,解释了壁虎脚毛粘附机理;为了更接近实际情况,考虑表面粗糙度对粘附力的影响,建立了单根绒毛与粗糙表面接触模型,以及单层、双层以及三层粘附阵列与粗糙表面接触模型;进行接触全过程的粘附情况仿真,分析并总结了表面粗糙度、预载荷和结构刚度等因素对粘附能力的影响。
分析壁虎脚毛的各种粘附特性,以及环境适应性要求,提出了强的粘附力、防纠结、防自断裂、快速脱附、较好的粗糙表面适应性等若干设计准则;采用自下而上的设计思想,建立了相应的力学模型;分析并总结约束模型中各参数变化对纤维半径、纤维长度、阵列占空比、阵列对称性、粘附力以及粘附功等参数的影响。
综合考虑上述各约束条件,进行多目标多参数寻优求解,得到仿壁虎脚毛粘附结构的层次性几何特征(分形维数)、阵列几何特征(阵列密度、阵列对称性)以及单根接触几何特征(接触半径、深宽比、倾斜角)等设计参数。设计结果表明,优化设计得到的第一级结构的纤维半径、长度均在壁虎脚绒毛测量值范围内,第二级结构的纤维半径、长度也在壁虎脚刚毛测量值范围内,且具有更好的粘附能力。
Gecko has an extraordinary ability to maneuver on vertical walls and ceilings, for the adhesion is robust enough to function on unknown rough surfaces and also easily releasable on animal movement. The incredible characteristics have a very broad prospect of applications in the deployment and disassembly of MEMS devices, wall-climbing robots, etc. The multi-scale hierarchical structure of the gecko foot-hair, especially the high-aspect-ratio structure of its micro-scale seta and nano-scale spatulae is the critical factor of the gecko’s ability to adopt and stick to any different surface with powerful adhesion force. Accordingly, the optimal design mimicking the finely structured gecko foot-hair has been studied in this degree thesis. The main contents of this thesis comprise:
Analyzing the micro-scale contact mechanics, reveal the mechanism of gecko adhesion. Considering the roughness, set up the contact models between one single spatula, one-, two-, muti-level adhesion arrays and rough surface respectively. Then simulate the adhesion ability through the whole attaching process with rough surfaces and analyze the influence of roughness, the applied force and the stiffness on the adhesion ability.
Analyzing the properties of gecko adhesion at bumpy surfaces, introduce the enquired limitations and modeled to ensure the adhesion is robust and the release is easy, the fibrils are compliant enough to easily deform to mating surface’s roughness profile, yet rigid enough not to collapse under their own weight. And analyze the influence of these constraints to the parameters of optimal design.
Based on these parameters, we have launched a bottom-up design methodology. A procedure is also developed here to find optimum designed parameters considering multi-object/parameter situations that adopt geometrical parameters of hierarchical dimensions (structure) with excellent patterns (density and symmetry) and sizes of single fiber (radius, length and angle). These results show that the optimal designed parameters of fiber structure sizes in both levels are in the scope of gecko spatulae and setae respectively and the simulated adhesion force at the second level is consistent with the observed value of single seta. These provided findings are the strong foundations of bio-inspired dry adhesives.
引文
[1] Autumn K, Liang Y A, Hsieh S T, et al. Adhesive force of a single gecko foot-hair [J]. Nature, 2000, 405 (6787): 681~685.
[2] Johnson K, Kendall K, Roberts A. Surface energy and the contact of elastic solids [J]. Proceedings of the Royal Society of London, 1971, 324(1558): 301~313.
[3] Autumn K, Sitti M, Liang Y A, et al. Evidence for van der Waals adhesion in gecko setae [J]. Proceedings of the National Academy of the United States of America, 2002, 99(19): 12252~12256.
[4] Autumn K, Peattie A M. Mechanisms of adhesion in geckos [J]. Integrative and Comparative Biology, 2002, 42(6): 1081~1090.
[5] Persson B.N.J. On the mechanism of adhesion in biological systems [J]. Journal of Chemical Physics, 2003, 118(16): 22.
[6] Huber G, Gorb S N, Spolenak R, et al. Resolving the nanoscale adhesion of individual gecko spatulae by atomic force microscopy [J]. Biology Letters, 2005, 1(1): 2~4.
[7] Huber G, Mantz H, Spolenak R, et al. Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements [J]. Proceedings of the National Academy of the United States of America, 2005, 102(45): 16293~16296.
[8] Kim T.W. and Bhushan B. The adhesion model considering capillarity for gecko attachment system [J]. Journal of the Royal Society Interface, 2007, 5(20): 319-327.
[9] Hansen W R, Autumn K. Evidence for self-cleaning in gecko setae [J]. Proceedings of the National Academy of the United States of America, 2005, 102(2): 385~389.
[10] Autumn K, Majidi C, Groff R E, et al. Effective elastic modulus of isolated gecko setal arrays [J]. Journal of Experimental Biology, 2006, 209(18): 3558~3568.
[11] Hui C.Y, Shen L and Autumn K, et al. Mechanics of anti-fouling or self-cleaning in Geckos [C]. //Proceedings of the 29th Annual Meeting of The Adhesion Society, 2006, Blacksburg, VA. New York: Adhesion society, 2004: 29~31.
[12] Tsai Y. C., Shih P. J. and W.-P. Shih et al. Self-cleaning efects of biomimetic dry adhesives [C]. Proceedigns of the 1st IEEE International Conference on Nano/Micro Engineered and Molecular Systems, January 18~21, 2006, Zhuhai, China. New York: IEEE-NEMS, 2004: 1388~1391.
[13] Autumn K, Hansen W. Ultrahydrophobicity indicates a non-adhesive default state in gecko setae [J]. Journal of Comparative Physiology A, 2006, 192(11): 1205~1212.
[14] Gao H J, Yao H M. Shape insensitive optimal adhesion of nanoscale fibrillar structures [J]. Proceedings of the National Academy of the United States of America, 2004, 101(21): 7851~7856.
[15] Shah G J, Sitti M. Modeling and design of biomimetic adhesives inspired by gecko foot-hairs [C] //Proceedings of the 2004 IEEE International Conference on Robotics and Biomimetics, August 22~26, 2004, Shenyang, China. New York: PNAS, 2004: 873~878.
[16] Takahashi K, Berengueres J.O.L., and S. Saito. Gecko's foot hair structure and their ability to hang from rough surfaces and move quickly [J]. Journal of Adhesion and Adhesives, 2006, 26(8): 639~643.
[17] Glassmaker N J, Jagota A, Hui C Y, et al. Design of biomimetic fibrillar interfaces: 1. making contact [J]. Journal of the Royal Society Interface, 2004, 1(1): 23~33.
[18] Spolenak R, Gorb S, Gao H J, et al. Effects of contact shape on the scaling of biological attachments [J]. Proceedings of the Royal Society of London A, 2005, 461(2054): 305~319.
[19] Gao H J, Wang X, Yao H M, et al. Mechanics of hierarchical adhesion structures of geckos [J]. Mechanics of Materials, 2005, 37 (2~3): 275~285.
[20] Tian Y, Pesika N and Zeng H, et al. Adhesion and friction in gecko toe attachment and detachment [J]. Proceedings of the National Academy of the United States of America, 2006, 103(51): 19320-19325.
[21] Autumn K, Dittmore A and Santos D, et al. Frictional adhesion: a new angle on gecko attachment [J]. Journal of Experimental Biology, 2006, 209 (18): 3569-3579.
[22] Sitti M, Fearing R S. Synthetic gecko foot-hair micro/nano-structures as dry adhesives [J]. Journal of Adhesion Science and Technology, 2003, 17 (8): 1055~1073.
[23] Kim T. W. and Bhushan B. Optimazation of biomimetic attachment system contacting with a rough surface [J]. 2007, 25(4): 1003~1012.
[24] Jagota A. and Bennison S. J. Mechanics of adhesion through a fibrillar microstructure [J]. Integrative and Comparative Biology, 2002, 42 (6): 1140~1145.
[25] Arzt E., Gorb S. and Spolenak R. From micro to nano contacts in biological attachment devices [J]. Proceedings of the National Academy of Sciences of the United States of America, 2003, 100 (19): 10603~10606.
[26] Peressadko A. and Gorb S.N. When less is more: experimental evidence for tenacity enhancement by division of contact area [J].The Journal of Adhesion, 2004, 80 (4): 247~261.
[27] Chung J.Y. and Chaudhury M. K. Roles of discontinuities in bio-inspired adhesive pads [J]. Royal Society Interface, 2005, 2 (2): 55~61.
[28] Chan E. P., Greiner C., Arzt E.,et al. Crosby. Designing Model Systems for EnhancedAdhesion [J]. Mrs bulletin, 2007, 32: 496~503.
[29] Thomas T.; Alfred J. and Crosby A. J.. Controlling Adhesion with Surface Hole Patterns [J]. The Journal of Adhesion, 2006, 82(3):311~329.
[30] Varenberg M., Peressadko A., Gorb S.and Arzt E. Effect of real contact geometry on adhesion [J]. Appl. Phys. Lett. 2006, 89(12): 121905.
[31] Tang T., Hui C.Y. and Glassmaker N.J. Can a fibrillar interface be stronger and tougher than a non-fibrillar one? [J] Royal Society Interface, 2005, 2 (5): 505~516.
[32] Campo A. D., Greiner C. and Arzt E. Contact shape controls adhesion of bioinspired fibrillar surfaces [J]. Langmuir, 2007, 23: 10235~10243.
[33] Crosby A.J., Hageman M. and Duncan A. Controlling Polymer Adhesion with ``Pancakes'' [J]. Langmuir, 2005, 21 (25): 11738~11743.
[34] Gorb S. N, Varenberg M. and J. Tuma. Biomimetic mushroom-shaped fibrillar adhesive microstructure [J]. Journal of The Royal Society Interface, 2006, 4 (13): 271~275.
[35] Gorb, S.N.; Varenberg, M. Mushroom-shaped geometry of contact elements in biological adhesive systems [J]. Journal of Adhesion Science and Technology, 2007, 21 (12~13): 1175~1183.
[36] Greiner C., Spolenak R., and Arzt E. Adhesion design maps for fibrillar adhesives: The effect of shape [J]. Acta Biomaterialia, 2009, 5 (2): 597~606.
[37] Greiner C., Campo A.D. and Arzt E. Adhesion of bioinspired micropatterned surfaces: effects of pillar radius, aspect ratio, and preload [J]. American Chemical Society, 2007, 23(7): 3495~3502.
[38] Majidi C. S., Groff R.E., and Fearing R.S. Attachment of Fiber Array Adhesive through Side Contact [J]. Journal of Applied Physics, 2005, 98 (10): 103521~5.
[39] Glassmaker N.J., Jagota, C.Y. Hui N.J., et al. Biologically inspired crack trapping for enhanced adhesion [J]. Proc. National Academy of Sciences, 2007, 104(26): 10786~10791.
[40] Wang. M, Wang, L. Interaction and Simulation Analysis between the Biomimetic Gecko Adhesion Array and Rough Surface. [C].//IEEE International Conference Mechatronics and Automation, July, 2005, Niagara Falls, Canada. 2005, 2 (2): 1063~1068.
[41] Bhushan B. and Sayer R. A. Surface characterization and friction of a bio-inspired reversible adhesive tape [J]. Microsystem Technologies, 2007, 13 (1): 71~78.
[42] Huber G., Gorb S.N., N. and E. Arzt. Influence of surface roughness on gecko adhesion [J]. Acta Biomaterialia, 2007, 3 (4): 607~610.
[43] Kim T.W., and Bhushan B. Optimization of Biomimetic Attachment System Contacting with a Rough Surface [J]. Journal of Vacuum Science and Technology A, 2007, 20(13): 1003~1012.
[44] Porwal P.K. and Hui C. Y. Strength statistics of adhesive contact between a fibrillar structure and a rough substrate [J]. Royal Society Interface, 2007, 5(21): 441~448.
[45] Spolenak R, Gorb S, Arzt E. Adhesion design maps for bio-inspired attachment systems [J]. Acta Biomaterialia, 2005, 1(1): 5~13.
[46] Persson B. N. J. and Gorb S. The effect of surface roughness on the adhesion of elastic plates with application to biological systems [J]. Chemical physics, 2003, 119 (21):11437~11444.
[47] Johonson K L著,徐秉业等译,接触力学[M],高等教育出版社, 1992: 31~78.
[48] Chang Y, I. and Wang Y,. F. Adhesion of an elastic particle to a plane surface: effects of the inertial force and the van der Walls force [J]. Colloids and Surfaces, 1996: 21~28.
[49] Derjaguin B. V., Muller V. M. and Toporov Y. P. Effect of contact deformations on the adhesion of particles [J]. Journal of Colloid and Interface Science, 1975, 53 (2): 314~326.
[50] Kim T.W. and Bhushan B. Adhesion analysis of multi-level hierarchical attachment system contacting with a rough surface [J]. Journal of Adhesion Science and Technology, 2007, 21 (1): 1~20.
[51] Bhushan B. Adhesion and stiction: mechanism, measurement techniques, and methods for reduction [J]. The Journal of Vacuum Science and Technology B, 2003, 21 (6): 2262~2296.
[52]陈隆德,赵福令,互换性与测量技术基础(修订版)[M],大连:大连理工大学出版社, 1997: 123~125.
[53] Glassmaker N J, Jagota A and Hui C Y, et al. Design of biomimetic fibrillar interfaces: 1. making contact [J]. Journal of the Royal Society Interface, 2004, 1(1): 23~33.
[54] Yao H. M. and Gao H. J. Bio-inspired mechanics of bottom-up designed hierarchical materials: robust and releasable adhesion systems of gecko [J]. Bulletin of the Polish Academy of Sciences Technical Sciences, 2007, 55(2): 141～150.
[2] Johnson K, Kendall K, Roberts A. Surface energy and the contact of elastic solids [J]. Proceedings of the Royal Society of London, 1971, 324(1558): 301~313.
[3] Autumn K, Sitti M, Liang Y A, et al. Evidence for van der Waals adhesion in gecko setae [J]. Proceedings of the National Academy of the United States of America, 2002, 99(19): 12252~12256.
[4] Autumn K, Peattie A M. Mechanisms of adhesion in geckos [J]. Integrative and Comparative Biology, 2002, 42(6): 1081~1090.
[5] Persson B.N.J. On the mechanism of adhesion in biological systems [J]. Journal of Chemical Physics, 2003, 118(16): 22.
[6] Huber G, Gorb S N, Spolenak R, et al. Resolving the nanoscale adhesion of individual gecko spatulae by atomic force microscopy [J]. Biology Letters, 2005, 1(1): 2~4.
[7] Huber G, Mantz H, Spolenak R, et al. Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements [J]. Proceedings of the National Academy of the United States of America, 2005, 102(45): 16293~16296.
[8] Kim T.W. and Bhushan B. The adhesion model considering capillarity for gecko attachment system [J]. Journal of the Royal Society Interface, 2007, 5(20): 319-327.
[9] Hansen W R, Autumn K. Evidence for self-cleaning in gecko setae [J]. Proceedings of the National Academy of the United States of America, 2005, 102(2): 385~389.
[10] Autumn K, Majidi C, Groff R E, et al. Effective elastic modulus of isolated gecko setal arrays [J]. Journal of Experimental Biology, 2006, 209(18): 3558~3568.
[11] Hui C.Y, Shen L and Autumn K, et al. Mechanics of anti-fouling or self-cleaning in Geckos [C]. //Proceedings of the 29th Annual Meeting of The Adhesion Society, 2006, Blacksburg, VA. New York: Adhesion society, 2004: 29~31.
[12] Tsai Y. C., Shih P. J. and W.-P. Shih et al. Self-cleaning efects of biomimetic dry adhesives [C]. Proceedigns of the 1st IEEE International Conference on Nano/Micro Engineered and Molecular Systems, January 18~21, 2006, Zhuhai, China. New York: IEEE-NEMS, 2004: 1388~1391.
[13] Autumn K, Hansen W. Ultrahydrophobicity indicates a non-adhesive default state in gecko setae [J]. Journal of Comparative Physiology A, 2006, 192(11): 1205~1212.
[14] Gao H J, Yao H M. Shape insensitive optimal adhesion of nanoscale fibrillar structures [J]. Proceedings of the National Academy of the United States of America, 2004, 101(21): 7851~7856.
[15] Shah G J, Sitti M. Modeling and design of biomimetic adhesives inspired by gecko foot-hairs [C] //Proceedings of the 2004 IEEE International Conference on Robotics and Biomimetics, August 22~26, 2004, Shenyang, China. New York: PNAS, 2004: 873~878.
[16] Takahashi K, Berengueres J.O.L., and S. Saito. Gecko's foot hair structure and their ability to hang from rough surfaces and move quickly [J]. Journal of Adhesion and Adhesives, 2006, 26(8): 639~643.
[17] Glassmaker N J, Jagota A, Hui C Y, et al. Design of biomimetic fibrillar interfaces: 1. making contact [J]. Journal of the Royal Society Interface, 2004, 1(1): 23~33.
[18] Spolenak R, Gorb S, Gao H J, et al. Effects of contact shape on the scaling of biological attachments [J]. Proceedings of the Royal Society of London A, 2005, 461(2054): 305~319.
[19] Gao H J, Wang X, Yao H M, et al. Mechanics of hierarchical adhesion structures of geckos [J]. Mechanics of Materials, 2005, 37 (2~3): 275~285.
[20] Tian Y, Pesika N and Zeng H, et al. Adhesion and friction in gecko toe attachment and detachment [J]. Proceedings of the National Academy of the United States of America, 2006, 103(51): 19320-19325.
[21] Autumn K, Dittmore A and Santos D, et al. Frictional adhesion: a new angle on gecko attachment [J]. Journal of Experimental Biology, 2006, 209 (18): 3569-3579.
[22] Sitti M, Fearing R S. Synthetic gecko foot-hair micro/nano-structures as dry adhesives [J]. Journal of Adhesion Science and Technology, 2003, 17 (8): 1055~1073.
[23] Kim T. W. and Bhushan B. Optimazation of biomimetic attachment system contacting with a rough surface [J]. 2007, 25(4): 1003~1012.
[24] Jagota A. and Bennison S. J. Mechanics of adhesion through a fibrillar microstructure [J]. Integrative and Comparative Biology, 2002, 42 (6): 1140~1145.
[25] Arzt E., Gorb S. and Spolenak R. From micro to nano contacts in biological attachment devices [J]. Proceedings of the National Academy of Sciences of the United States of America, 2003, 100 (19): 10603~10606.
[26] Peressadko A. and Gorb S.N. When less is more: experimental evidence for tenacity enhancement by division of contact area [J].The Journal of Adhesion, 2004, 80 (4): 247~261.
[27] Chung J.Y. and Chaudhury M. K. Roles of discontinuities in bio-inspired adhesive pads [J]. Royal Society Interface, 2005, 2 (2): 55~61.
[28] Chan E. P., Greiner C., Arzt E.,et al. Crosby. Designing Model Systems for EnhancedAdhesion [J]. Mrs bulletin, 2007, 32: 496~503.
[29] Thomas T.; Alfred J. and Crosby A. J.. Controlling Adhesion with Surface Hole Patterns [J]. The Journal of Adhesion, 2006, 82(3):311~329.
[30] Varenberg M., Peressadko A., Gorb S.and Arzt E. Effect of real contact geometry on adhesion [J]. Appl. Phys. Lett. 2006, 89(12): 121905.
[31] Tang T., Hui C.Y. and Glassmaker N.J. Can a fibrillar interface be stronger and tougher than a non-fibrillar one? [J] Royal Society Interface, 2005, 2 (5): 505~516.
[32] Campo A. D., Greiner C. and Arzt E. Contact shape controls adhesion of bioinspired fibrillar surfaces [J]. Langmuir, 2007, 23: 10235~10243.
[33] Crosby A.J., Hageman M. and Duncan A. Controlling Polymer Adhesion with ``Pancakes'' [J]. Langmuir, 2005, 21 (25): 11738~11743.
[34] Gorb S. N, Varenberg M. and J. Tuma. Biomimetic mushroom-shaped fibrillar adhesive microstructure [J]. Journal of The Royal Society Interface, 2006, 4 (13): 271~275.
[35] Gorb, S.N.; Varenberg, M. Mushroom-shaped geometry of contact elements in biological adhesive systems [J]. Journal of Adhesion Science and Technology, 2007, 21 (12~13): 1175~1183.
[36] Greiner C., Spolenak R., and Arzt E. Adhesion design maps for fibrillar adhesives: The effect of shape [J]. Acta Biomaterialia, 2009, 5 (2): 597~606.
[37] Greiner C., Campo A.D. and Arzt E. Adhesion of bioinspired micropatterned surfaces: effects of pillar radius, aspect ratio, and preload [J]. American Chemical Society, 2007, 23(7): 3495~3502.
[38] Majidi C. S., Groff R.E., and Fearing R.S. Attachment of Fiber Array Adhesive through Side Contact [J]. Journal of Applied Physics, 2005, 98 (10): 103521~5.
[39] Glassmaker N.J., Jagota, C.Y. Hui N.J., et al. Biologically inspired crack trapping for enhanced adhesion [J]. Proc. National Academy of Sciences, 2007, 104(26): 10786~10791.
[40] Wang. M, Wang, L. Interaction and Simulation Analysis between the Biomimetic Gecko Adhesion Array and Rough Surface. [C].//IEEE International Conference Mechatronics and Automation, July, 2005, Niagara Falls, Canada. 2005, 2 (2): 1063~1068.
[41] Bhushan B. and Sayer R. A. Surface characterization and friction of a bio-inspired reversible adhesive tape [J]. Microsystem Technologies, 2007, 13 (1): 71~78.
[42] Huber G., Gorb S.N., N. and E. Arzt. Influence of surface roughness on gecko adhesion [J]. Acta Biomaterialia, 2007, 3 (4): 607~610.
[43] Kim T.W., and Bhushan B. Optimization of Biomimetic Attachment System Contacting with a Rough Surface [J]. Journal of Vacuum Science and Technology A, 2007, 20(13): 1003~1012.
[44] Porwal P.K. and Hui C. Y. Strength statistics of adhesive contact between a fibrillar structure and a rough substrate [J]. Royal Society Interface, 2007, 5(21): 441~448.
[45] Spolenak R, Gorb S, Arzt E. Adhesion design maps for bio-inspired attachment systems [J]. Acta Biomaterialia, 2005, 1(1): 5~13.
[46] Persson B. N. J. and Gorb S. The effect of surface roughness on the adhesion of elastic plates with application to biological systems [J]. Chemical physics, 2003, 119 (21):11437~11444.
[47] Johonson K L著,徐秉业等译,接触力学[M],高等教育出版社, 1992: 31~78.
[48] Chang Y, I. and Wang Y,. F. Adhesion of an elastic particle to a plane surface: effects of the inertial force and the van der Walls force [J]. Colloids and Surfaces, 1996: 21~28.
[49] Derjaguin B. V., Muller V. M. and Toporov Y. P. Effect of contact deformations on the adhesion of particles [J]. Journal of Colloid and Interface Science, 1975, 53 (2): 314~326.
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