The mechanical deformation of an ideal thin-walled cylindrical shell is investigated in the presence of intersurface interactions with a planar rigid substrate. A Dugdale–Barenblatt–Maugis (DBM) cohesive zone approximation is introduced to simulate the convoluted surface force potential. Without loss of generality, the repulsive component of the surface forces is approximated by a linear soft-repulsion, and the attractive component is described by two essential variables, namely, surface force range and magnitude, which are allowed to vary. The nonlinear problem is solved numerically to generate the pressure distribution within the contact, the deformed membrane profiles, and the adhesion-delamination mechanics, which are distinctly different from the classical solid cylinder adhesion models. The model has wide applications in cell adhesion and nanostructures.
Issue Section:
Research Papers
References
1.
Hertz
, H.
, 1896, miscellaneous papers
, Macmillian
, London
.2.
Johnson
, K. L.
, Kendall
, K.
, and Roberts
, A. D.
, 1971, “Surface Energy and the Contact of Elastic Solids
,” Proc. R. Soc. London, Ser. A
, 324
, pp. 301
–313
.3.
Derjaguin
, B. V.
, Muller
, V. M.
, and Toporov
, Y. P.
, 1975, “Effect of Contact Deformations on the Adhesion of Particles
,” J. Colloid Interface Sci.
, 53
(2
), pp. 314
–326
.4.
Tabor
, D.
, 1977, “Surface Forces and Surface Interactions
,” J. Colloid Interface Sci.
, 58
(1
), pp. 2
–13
.5.
Maugis
, D.
, 1992, “The JKR-DMT Transition Using a Dugdale Model
,” J. Colloid Interface Sci.
, 150
, pp. 243
–269
.6.
Chaudhury
, M. K.
, Weaver
, T.
, Hui
, C. Y.
, and Kramer
, K. J.
, 1996, “Adhesive Contact of Cylindrical Lens and a Flat Sheet
,” J. Appl. Phys.
, 80
(1
), pp. 30
–37
.7.
Johnson
, K. L.
, and Greenwood
, J. A.
, 2008, “A Maugis Analysis of Adhesive Line Contact
,” J. Phys. D
, 41
, p. 155315
.8.
Wu
, J.-J.
, 2009, “Adhesive Contact Between a Cylinder and a Half-Space
,” J. Phys. D: Appl. Phys.
, 42
, p. 155302
.9.
Plaut
, R. H.
, 2009, “Linearly Elastic Annular and Circular Membranes Under Radial, Transverse, and Torsional Loading. Part I: Large Unwrinkled Axisymmetric Deformations
,” Acta Mech.
, 202
, pp. 79
–99
.10.
Plaut
, R. H.
, Suherman
, S.
, Dillard
, D. A.
, Williams
, B. E.
, and Watson
, L. T.
, 1999, “Deflections and Buckling of a Bent Elastica in Contact With a Flat Surface
,” Int. J. Solids Struct.
, 36
, pp. 1209
–1229
.11.
Plaut
, R. H.
, White
, S. A.
, and Dillard
, D. A.
, 2003, “Effect of Work of Adhesion on Contact of a Pressurized Blister With a Flat Surface
,” Int. J. Adhes. Adhes.
, 23
, pp. 207
–214
.12.
Tang
, T.
, Jogota
, A.
, and Hui
, C.-Y.
, 2005, “Adhesion Between Single-Walled Carbon Nanotubes
,” J. Appl. Phys.
, 97
, p. 074304
.13.
Majidi
, C.
, and Wan
, K.-T.
, 2010, “Adhesion Between Thin Cylindrical Shells With Parallel Axes
,” J. Appl. Mech.
, 77
(5
), p. 041013
.14.
Maugis
, D.
, 2000, Contact, Adhesion and Rupture of Elastic Solids
, Springer
, New York
.15.
Seifert
, U.
, 1997, “Configurations of Fluid Membranes and Vesicles
,” Adv. Phys.
, 46
(1
), pp. 1
–137
.16.
Yao
, X.
, Walter
, J.
, Burke
, S.
, Stewart
, S.
, Jericho
, M. H.
, Pink
, D.
, Hunter
, R.
, and Beveridge
, T. J.
, 2002, “Atomic Force Microscopy and Theoretical Considerations of Surface Properties and Turgor Pressures of Bacteria
,” Colloids Surf., B
, 23
, pp. 213
–230
.17.
Tran-Son-Tay
, R.
, Sutera
, S. P.
, Zahalak
, G. I.
, and Rao
, P. R.
, 1987, “Membrane Stress and Internal Pressure in a Red Blood Cell Freely Suspended in a Shear Flow
,” Biophys. J.
, 51
, pp. 915
–924
.18.
Lin
, Y.
, and Freund
, L. B.
, 2007, “Forced Detachment of a Vesicle in Adhesive Contact With a Substrate
,” Int. J. Solids Struct.
, 22
, pp. 1927
–1938
.19.
Blokhius
, E. M.
, and Sager
, W. F. C.
, 1999, “Vesicle Adhesion and Microemulsion Droplet Dimerization: Small Bending Rigidity Regime
,” J. Chem. Phys.
, 111
(15
), pp. 7062
–7074
.20.
Lan
, G.
, Wolgemuth
, C. W.
, and Sun
, S. X.
, 2007, “Z-Ring Force and Cell Shape During Division in Rod-Like Bacteria
,” Proc. Natl. Acad. Sci. U.S.A.
, 104
(41
), pp. 16110
–16115
.21.
Zhao
, L.
, Schaefer
, D.
, Xu
, H.
, Modi
, S.
, LaCourse
, W.
, and Marten
, M.
, 2005, “Elastic Properties of the Cell Wall of Aspergillus Nidulans Studied With Atomic Force Microscopy
,” Biotechnol. Prog.
, 21
(1
), pp. 292
–299
.22.
Ghatak
, A.
, Mahadevan
, L.
, Chung
, J. Y.
, Chaudhury
, M. K.
, and Shenoy
, V.
, 2004, “Peeling From a Biomimetically Patterned Thin Elastic Film
,” Proc. R. Soc. Ser. A
, 460
, pp. 2725
–2735
.23.
Wan
, K.-T.
, Lawn
, B. R.
, and Horn
, R. G.
, 1992, “Repulsive Interaction Between Co-Planar Cracks in the Double-Cantilever Geometry
,” J. Mater. Res.
, 7
(6
), pp. 1584
–1588
.24.
Barenblatt
, G. I.
, 1962, “The Mathematical Theory of Equilibrium Cracks in Brittle Fracture
,” Adv. Appl. Mech.
, 7
, pp. 55
–129
.25.
Cook
, R.
, Malkus
, D.
, Plesha
, M.
, and Witt
, R.
, 2002, Concepts and Applications of Finite Element Analysis
, Wiley
, New York
.Copyright © 2012
by American Society of Mechanical Engineers
You do not currently have access to this content.
