On the presence of a critical detachment angle in gecko spatula peeling - a numerical investigation using an adhesive friction model

References

• Autumn, K.; Liang, Y. A.; Hsieh, S. T.; Zesch, W.; Chan, W. P.; Kenny, T. W.; Fearing, R.; Full, R. J. Adhesive Force of a Single Gecko Foot-hair. Nature. 2000, 405, 681–684. DOI:10.1038/35015073.
   PubMed Web of Science ®Google Scholar
• Autumn, K.; Sitti, M.; Liang, Y. A.; Peattie, A. M.; Hansen, W. R.; Sponberg, S.; Kenny, T. W.; Fearing, R.; Israelachvili, J. N.; Full, R. J. Evidence for Van Der Waals Adhesion in Gecko Setae. Proc. Natl. Acad. Sci. 2002, 99, 12252–12256. DOI:10.1073/pnas.192252799.
   PubMed Web of Science ®Google Scholar
• Autumn, K.; Peattie, A. Mechanism of Adhesion in Geckos. Integr. Comp. Biol. 2002, 42, 1081–1090. DOI:10.1093/icb/42.6.1081.
   PubMed Web of Science ®Google Scholar
• Huber, G.; Gorb, S. N.; Spolenak, R.; Arzt, E. Resolving the Nanoscale Adhesion of Individual Gecko Spatulae by Atomic Force Microscopy. Biol. Lett. 2005, 1, 2–4. DOI:10.1098/rsbl.2004.0254.
   PubMed Web of Science ®Google Scholar
• Sun, W.; Neuzil, P.; Kustandi, T. S.; Oh, S.; Samper, V. D. The Nature of the Gecko Lizard Adhesive Force. Biophys. J. 2005, 89, L14– L17. DOI:10.1529/biophysj.105.065268.
   PubMed Web of Science ®Google Scholar
• Autumn, K.; Hansen, W. Ultrahydrophobicity Indicates a Non-adhesive Default State in Gecko Setae. J. Compar. Physio. A. 2006, 192, 1205. DOI:10.1007/s00359-006-0149-y.
   Web of Science ®Google Scholar
• Russell, A. P.;. Integrative Functional Morphology of the Gekkotan Adhesive System (Reptilia: Gekkota). Integr. Comp. Biol. 2002, 42, 1154–1163. DOI:10.1093/icb/42.6.1154.
   PubMed Web of Science ®Google Scholar
• Autumn, K.;. Gecko Adhesion: Structure, Function, and Applications. MRS. Bull. 2007, 32, 473–478. DOI:10.1557/mrs2007.80.
   Web of Science ®Google Scholar
• Pugno, N. M.;. Spiderman Gloves. Nano Today. 2008, 3, 35–41. DOI:10.1016/S1748-0132(08)70063-X.
   Web of Science ®Google Scholar
• Kwak, J. S.; Kim, T. W. A Review of Adhesion and Friction Models for Gecko Feet. Int. J. Precis. Eng. Manuf. 2010, 11, 171–186. DOI:10.1007/s12541-010-0020-5.
   Web of Science ®Google Scholar
• Peng, Z.; Wang, C.; Yang, Y.; Chen, S. Effect of Relative Humidity on the Peeling Behavior of a Thin Film on a Rigid Substrate. Phys. Rev. E. 2016, 94, 032801. DOI:10.1103/PhysRevE.94.032801.
   PubMed Web of Science ®Google Scholar
• Federle, W.; Labonte, D. Dynamic Biological Adhesion: Mechanisms for Controlling Attachment during Locomotion. Phil. Trans. R. Soc. B. 2019, 374, 20190199. DOI:10.1098/rstb.2019.0199.
   PubMed Web of Science ®Google Scholar
• Peng, Z. L.; Chen, S. H.; Soh, A. K. Peeling Behaviour of a Bio-inspired Nano-film on a Substrate. Int. J. Solids Struct. 2010, 47, 1952–1960. DOI:10.1016/j.ijsolstr.2010.03.035.
   Web of Science ®Google Scholar
• Sauer, R. A. Multiscale Modelling and Simulation of the Deformation and Adhesion of a Single Gecko Seta. Comput. Method Biomech. Biomed. Engin. 2009, 12, 627–640. DOI:10.1080/10255840902802917.
   PubMed Web of Science ®Google Scholar
• Sauer, R. A.;. A Computational Model for Nanoscale Adhesion between Deformable Solids and Its Application to Gecko Adhesion. J. Adhes. Sci. Tech. 2010, 24, 1807–1818. DOI: 10.1163/016942410X507588.
   Web of Science ®Google Scholar
• Sauer, R. A. The Peeling Behaviour of Thin Films with Finite Bending Stiffness and the Implications on Gecko Adhesion. J. Adhes. 2011, 87, 624–643. DOI: 10.1080/00218464.2011.596084.
   Web of Science ®Google Scholar
• Gautam, S. S.; Sauer, R. A. A Composite Time Integration Scheme for Dynamic Adhesion and Its Application to Gecko Spatula Peeling. Int. J. Comput. Methods. 2014, 11, 1350104. DOI: 10.1142/S0219876213501041.
   Web of Science ®Google Scholar
• Asbeck, A.; Dastoor, S.; Parness, A.; Fullerton, L.; Esparza, N.; Soto, D.; Heyneman, B.; Cutkosky, M. Climbing Rough Vertical Surfaces with Hierarchical Directional Adhesion. Proc. - IEEE Int. Conf. Robot. Autom. Kobe, Japan, 2009; pp. 2675–2680. DOI:10.1109/ROBOT.2009.5152864
   Google Scholar
• Drotlef, D. M.; Amjadi, M.; Yunusa, M.; Sitti, M. Bioinspired Composite Microfibers for Skin Adhesion and Signal Amplification of Wearable Sensors. Adv. Mater. 2017, 29, 1701353–1—-1701353–8. DOI: 10.1002/adma.201701353.
   PubMed Web of Science ®Google Scholar
• Hou, X.; Su, Y.; Jiang, S.; Li, L.; Chen, T.; Sun, L.; Deng, Z. Adhesion Mechanism of Space-climbing Robot Based on Discrete Element and Dynamics. Adv. Mech. Eng. 2018, 10, 1–15. DOI: 10.1177/1687814018772934.
   Web of Science ®Google Scholar
• Sitti, M.; Fearing, R. S. Synthetic Gecko Foot-hair Micro/nano-structures as Dry Adhesives. J. Adhes. Sci. Technol. 2003, 17, 1055–1073. DOI: 10.1163/156856103322113788.
   Web of Science ®Google Scholar
• Gao, H.; Wang, X.; Yao, H.; Gorb, S.; Arzt, E. Mechanics of Hierarchical Adhesion Structures of Geckos. Mech. Mater. 2005, 37, 275–285. DOI: 10.1016/j.mechmat.2004.03.008.
   Web of Science ®Google Scholar
• Chen, S.; Gao, H. Bio-inspired Mechanics of Reversible Adhesion: Orientation-dependent Adhesion Strength for Non-slipping Adhesive Contact with Transversely Isotropic Elastic Materials. J. Mech. Phys. Solids. 2007, 55, 1001–1015. DOI: 10.1016/j.jmps.2006.10.008.
   Web of Science ®Google Scholar
• Autumn, K.; Dittmore, A.; Santos, D.; Spenko, M.; Cutkosky, M. Frictional Adhesion: A New Angle on Gecko Attachment. J. Exp. Biol. 2006, 209, 3569–3579. DOI: 10.1242/jeb.02486.
   PubMed Web of Science ®Google Scholar
• Majidi, C.; Groff, R.-E.; Maeno, Y.; Schubert, B.; Baek, S.; Bush, B.; Maboudian, R.; Gravish, N.; Wilkinson, M.; Autumn, K.; et al. High Friction from a Stiff Polymer Using Microfiber Arrays. Phys. Rev. Lett. 2006, 97, 076103–1—-076103–4. DOI: 10.1103/PhysRevLett.97.076103.
   PubMed Web of Science ®Google Scholar
• Tian, Y.; Pesika, N.; Zeng, H.; Rosenberg, K.; Zhao, B.; McGuiggan, P.; Autumn, K.; Israelachvili, J. N. Adhesion and Friction in Gecko Toe Attachment and Detachment. Proc. Natl. Acad. Sci. 2006, 103, 19320–19325. DOI: 10.1073/pnas.0608841103.
   PubMed Web of Science ®Google Scholar
• Chen, B.; Wu, P.; Gao, H. Pre-tension Generates Strongly Reversible Adhesion of a Spatula Pad on Substrate. J. R. Soc. Interface. 2009, 6, 529–537. DOI: 10.1098/rsif.2008.0322.
   PubMed Web of Science ®Google Scholar
• Kendall, K. Thin-film Peeling-the Elastic Term. J. Phys. D. Appl. Phys. 1975, 8, 1449–1452. DOI: 10.1088/0022-3727/8/13/005.
   Web of Science ®Google Scholar
• Schubert, B.; Lee, J.; Majidi, C.; Fearing, R. S. Sliding-induced Adhesion of Stiff Polymer Microfibre Arrays. II. Microscale Behaviour. J. R. Soc. Interface. 2008, 5, 845–853. DOI: 10.1098/rsif.2007.1308.
   PubMed Web of Science ®Google Scholar
• Jagota, A.; Hui, C. H. Adhesion, Friction, and Compliance of Bio-mimetic and Bio-inspired Structured Interfaces. Mater. Sci. Eng. R Rep. 2011, 72, 253–292. DOI: 10.1016/j.mser.2011.08.001.
   Web of Science ®Google Scholar
• Cheng, Q. H.; Chen, B.; Gao, H. J.; Zhang, Y. W. Sliding-induced Non-uniform Pretension Governs Robust and Reversible Adhesion: A Revisit of Adhesion Mechanisms of Geckos. J. R. Soc. Interface. 2012, 9, 283–291. DOI: 10.1098/rsif.2011.0254.
   PubMed Web of Science ®Google Scholar
• Peng, Z.; Chen, S. Effect of Pre-tension on the Peeling Behavior of a Bio-inspired Nano-film and a Hierarchical Adhesive Structure. Appl. Phys. Lett. 2012, 101, 163702. DOI: 10.1063/1.4758481.
   Web of Science ®Google Scholar
• Begley, M. R.; Collino, R. R.; Israelachvili, J. N.; McMeeking, R. M. Peeling of a Tape with Large Deformations and Frictional Sliding. J. Mech. Phys. Solid. 2013, 61, 1265–1279. DOI: 10.1016/j.jmps.2012.09.014.
   Web of Science ®Google Scholar
• Afferrante, L.; Carbone, G.; Demelio, G.; Pugno, N. Adhesion of Elastic Thin Films: Double Peeling of Tapes versus Axisymmetric Peeling of Membranes. Tribol. Lett. 2013, 52, 439–447. DOI: 10.1007/s11249-013-0227-6.
   Web of Science ®Google Scholar
• Collino, R. R.; Philips, N. R.; Rossol, M. N.; McMeeking, R. M.; Begley, M. R. Detachment of Compliant Films Adhered to Stiff Substrates via Van Der Waals Interactions: Role of Frictional Sliding during Peeling. J. R. Soc. Interface. 2014, 11, 20140453. DOI: 10.1098/rsif.2014.0453.
   PubMed Web of Science ®Google Scholar
• Labonte, D.; Federle, W. Biomechanics of Shear-sensitive Adhesion in Climbing Animals: Peeling, Pre-tension and Sliding-induced Changes in Interface Strength. J. R. Soc. Interface. 2016, 13, 20160373. DOI: 10.1098/rsif.2016.0373.
   PubMed Web of Science ®Google Scholar
• Mergel, J. C.; Sahli, R.; Scheibert, J.; Sauer, R. A. Continuum Contact Models for Coupled Adhesion and Friction. J. Adhes. 2019, 95, 1101–1133. DOI: 10.1080/00218464.2018.1479258.
   Web of Science ®Google Scholar
• Sauer, R. A.; Li, S. A Contact Mechanics Model for Quasi-continua. Int. J. Numer. Methods Eng. 2007, 71, 931–962. DOI: 10.1002/nme.1970.
   Web of Science ®Google Scholar
• Gouravaraju, S.; Sauer, R. A.; Gautam, S. S. Investigating the Normal and Tangential Peeling Behaviour Ofgecko Spatulae Using a Couple Adhesion-friction Model. J. Adhes. 2020. DOI: 10.1080/00218464.2020.1719838.
   Web of Science ®Google Scholar
• Mergel, J. C.; Scheibert, J.; Sauer, R. A. Contact with Coupled Adhesion and Friction: Computational Framework, Applications, and New Insights. arXiv. 2001, 06833.
   Google Scholar
• Israelachvili, J. N. Intermolecular and Surface Forces, 3rd ed.; Elsevier: London, 2011.
   Google Scholar
• Sauer, R. A.; Wriggers, P. Formulation and Analysis of a Three-dimensional Finite Element Implementation for Adhesive Contact at the Nanoscale. Comput. Methods Appl. Mech. Eng. 2009, 198, 3871–3883. DOI: 10.1016/j.cma.2009.08.019.
   Web of Science ®Google Scholar
• Bonet, J.; Wood, R. D. Nonlinear Continuum Mechanics for Finite Element Analysis, 2nd ed.; Cambridge University Press: Cambridge, 2008.
   Google Scholar
• Sauer, R. A.; Holl, M. A Detailed 3D Finite Element Analysis of the Peeling Behaviour of A Gecko Spatula. Comput. Methods Biomech. Biomed. Engin. 2013, 16, 577–591. DOI: 10.1080/10255842.2011.628944.
   PubMed Web of Science ®Google Scholar
• Peng, Z.; Chen, S. Effect of Bending Stiffness on the Peeling Behavior of an Elastic Thin Film on a Rigid Substrate. Phys. Rev. E. 2015, 91, 042401. DOI: 10.1103/PhysRevE.91.042401.
   Web of Science ®Google Scholar
• Sauer, R. A.;. Enriched Contact Finite Elements for Stable Peeling Computations. Int. J. Numer. Methods Eng. 2011, 87, 593–616. DOI: 10.1002/nme.3126.
   Web of Science ®Google Scholar
• Autumn, K.; Majidi, C.; Gro, R. E.; Dittmore, A.; Fearing, R. Effective Elastic Modulus of Isolated Gecko Setal Arrays. J. Exp. Biol. 2006, 209, 3558–3568. DOI: 10.1242/jeb.02469.
   PubMed Web of Science ®Google Scholar
• Hu, C.; Greaney, P. A. Role of Seta Angle and Flexibility in the Gecko Adhesion Mechanism. J. Appl. Phys. 2014, 116, 074302. DOI: 10.1063/1.4892628.
   Web of Science ®Google Scholar
• Sekiguchi, Y.; Takahashi, K.; Sato, C. Adhesion Mechanism of a Gecko-inspired Oblique Structure with an Adhesive Tip for Asymmetric Detachment. J. Phys. D Appl. Phys. 2015, 48, 475301. DOI: 10.1088/0022-3727/48/47/475301.
   Web of Science ®Google Scholar
• Autumn, K.; Hsieh, S. T.; Dudek, D. M.; Chen, J.; Chitapahan, C.; Full, R. J. Dynamics of Geckos Running Vertically. J. Exp. Biol. 2006, 209, 260–272. DOI: 10.1242/jeb.01980.
   PubMed Web of Science ®Google Scholar
• Rizzo, N. W.; Gardner, K. H.; Walls, D. J.; Keiper-Hrynko, N. M.; Ganzke, T. S.; Hallahan, D. L. Characterization of the Structure and Composition of Gecko Adhesive Setae. J. R. Soc. Interface. 2006, 3, 441–451. DOI: 10.1098/rsif.2005.0097.
   PubMed Web of Science ®Google Scholar
• Persson, B. N. J.; Gorb, S. The Effect of Surface Roughness on the Adhesion of Elastic Plates with Application to Biological Systems. J. Chem. Phys. 2003, 119, 11437–11444. DOI: 10.1063/1.1621854.
   Web of Science ®Google Scholar
• Peng, Z.; Yin, H.; Yao, Y.; Chen, S. Effect of Thin-film Length on the Peeling Behavior of Film-substrate Interfaces. Phys. Rev. E. 2019, 100, 032804. DOI: 10.1103/PhysRevE.100.032804.
   PubMed Web of Science ®Google Scholar