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Research Papers

Adhesion of a Compliant Cylindrical Shell Onto a Rigid Substrate

[+] Author and Article Information
Jiayi Shi, Kai-tak Wan

 Department of Mechanical and Industrial Engineering, Northeastern University,Boston, MA 02115

Sinan Müftü1

 Department of Mechanical and Industrial Engineering, Northeastern University,Boston, MA 02115s.muftu@neu.edu

Note that in this work the distance z is measured along the normal to the surface of the shell.

This is an allusion to linear elastic fracture mechanics where the crack profile and the associated stress field ahead of a crack front are invariant as the crack propagates into a continuum solid.

1

Corresponding author.

J. Appl. Mech 79(4), 041015 (May 11, 2012) (7 pages) doi:10.1115/1.4005555 History: Received December 12, 2010; Revised June 23, 2011; Posted January 30, 2012; Published May 11, 2012; Online May 11, 2012

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of a cylindrical shell deformed by an external load coupled with intersurface attraction or disjoining pressure

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Figure 2

Coordinate system for the deformed shell

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Figure 3

Lennard–Jones potential for the disjoining pressure and the Dugdale–Barenblatt–Maugis cohesive zone approximation

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Figure 4

Cylindrical shell adhering to a rigid substrate under zero external load, F = 0: (a) deformed profile in the vicinity of the contact edge and inset showing the global deformation and (b) pressure at equilibrium. The adhesion force range z*/R is allowed to vary as indicated, while the adhesion energy is maintained at p*z*/ER = 1 × 10−8 .

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Figure 5

Delamination trajectory for different adhesion force range z*/R values and fixed adhesion energy p*z*/ER = 1 × 10−8 . Contact width as a function of applied load for fixed adhesion energy and a range of disjoining pressure. Delamination follows trajectory ABCDGHP and pull-off occurs at P when the contact reduces to a centerline.

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Figure 6

Shell profiles for a range of external loads FR as indicated, and for z*/R = 2/50 and fixed adhesion energy p*z*/ER = 10−8 . Curves are labeled according to Fig. 5.

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Figure 7

Shell profiles close to the contact edge for z*/R = 2/50 and fixed adhesion energy p*z*/ER = 10−8 . Curves are labeled according to Fig. 5.

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Figure 8

Delamination trajectory for different adhesion force range z*/R values and fixed adhesion energy p*z*/ER = 1 × 10−8 . (a) Applied load as a function of approach displacement. The curves terminate at the maximum allowable pull-off force. (b) Diminishing contact width as the external load turns tensile. Pull-off occurs at a†  = 0. Points labeled A to P correspond to those shown in Fig. 5.

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Figure 9

Incremental deformation of the shell

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Figure 10

Flow chart for the solution algorithm

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