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Semi-Analytic Iterative Solution for the Adhesive Contact Between a Micro-Indenter and a Graded Elasticity Coating

[+] Author Affiliations
Stewart J. Chidlow

Oxford Brooks University, Oxford, UK

William W. F. Chong

Southampton University, Malaysia Campus, Nusajaya, Johor, Malaysia

Mircea Teodorescu

University of California Santa Cruz, Santa Cruz, CA

Paper No. DETC2014-35110, pp. V004T09A026; 5 pages
doi:10.1115/DETC2014-35110
From:
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 19th Design for Manufacturing and the Life Cycle Conference; 8th International Conference on Micro- and Nanosystems
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4635-3
  • Copyright © 2014 by ASME

abstract

This paper proposes a hybrid (semi-analytic) solution for determining the contact footprint and subsurface stress field in a two-dimensional adhesive problem involving a multi-layered elastic solid loaded normally by a rigid indenter. The subsurface stress field is determined using a semi-analytic solution and the footprint using a fast converging iterative algorithm. The solid to be indented consists of a graded elasticity coating with exponential increase of decay of its shear modulus bonded on a homogeneously elastic substrate. By applying the Fourier Transform to the governing boundary value problem, we formulate expressions for the stresses and displacements induced by the application of line forces acting both normally and tangentially at the origin. The superposition principle is then used to generalize these expressions to the case of distributed normal pressure acting on the solid surface. A pair of coupled integral equations are further derived for the parabolic stamp problem which are easily solved using collocation methods.

Copyright © 2014 by ASME

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