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Research Papers

A Model of a Trapped Particle Under a Plate Adhering to a Rigid Surface

[+] Author and Article Information
George G. Adams

e-mail: adams@coe.neu.edu
Department of Mechanical and Industrial Engineering,
Northeastern University,
Boston, MA, 02115

Manuscript received June 28, 2012; final manuscript received December 17, 2012; accepted manuscript posted February 11, 2013; published online July 12, 2013. Assoc. Editor: George Kardomateas.

J. Appl. Mech 80(5), 051016 (Jul 12, 2013) (6 pages) Paper No: JAM-12-1274; doi: 10.1115/1.4023625 History: Received June 28, 2012; Revised December 17, 2012; Accepted February 11, 2013

Micro and nanomechanics are growing fields in the semiconductor and related industries. Consequently obstacles, such as particles trapped between layers, are becoming more important and warrant further attention. In this paper a numerical solution to the von Kármán equations for moderately large deflection is used to model a plate deformed due to a trapped particle lying between it and a rigid substrate. Due to the small scales involved, the effect of adhesion is included. The recently developed moment-discontinuity method is used to relate the work of adhesion to the contact radius without the explicit need to calculate the total potential energy. Three different boundary conditions are considered—the full clamp, the partial clamp, and the compliant clamp. Curve-fit equations are found for the numerical solution to the nondimensional coupled nonlinear differential equations for moderately large deflection of an axisymmetric plate. These results are found to match the small deflection theory when the deflection is less than the plate thickness. When the maximum deflection is much greater than the plate thickness, these results represent the membrane theory for which an approximate analytic solution exists.

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Figures

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Fig. 1

Perspective view of deflected plate

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Fig. 2

Full clamp plate deflection

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Fig. 3

Partial clamp boundary condition

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Fig. 4

Compliant clamp boundary condition

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Fig. 5

Force versus particle height

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Fig. 6

Contact radius versus particle height

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