Symbolic and numerical solution of the axisymmetric indentation problem for a multilayered elastic coating

•A semi-analytical approach for the indentation of a multilayered solid is presented.•The method of solution is based on the Hankel transform and the transfer matrix.•The implementation is done with Mathematica under the form of a fast and efficient code.•The procedure is valid for a large wide mate...

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Bibliographic Details
Published in:International journal of solids and structures Vol. 50; no. 18; pp. 2798 - 2807
Main Authors: Constantinescu, A., Korsunsky, A.M., Pison, O., Oueslati, A.
Format: Journal Article
Language:English
Published: Elsevier Ltd 15.08.2013
Elsevier
Subjects:
Axisymmetric
Condensed Matter
Engineering Sciences
Exact solutions
Half spaces
Indentation
Indenters
Integral equation
Materials Science
Mathematica
Mathematical analysis
Mathematical models
Mechanics
Mechanics of materials
Multilayer
Numerical analysis
Physics
Solid mechanics
Transfer matrix
Mathematica
Transfer matrix
Integral equation
Multilayer
Indentation
ISSN:0020-7683, 1879-2146
Online Access:Get full text
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Summary:•A semi-analytical approach for the indentation of a multilayered solid is presented.•The method of solution is based on the Hankel transform and the transfer matrix.•The implementation is done with Mathematica under the form of a fast and efficient code.•The procedure is valid for a large wide material combinations and arbitrary layer’s thickness.•A series of results for flat, conical, spherical and blunted punches is given. This paper is concerned with a semi-analytical approach to the solution of the axisymmetric indentation problem for a multilayered elastic half-space. The stress and displacement fields for each layer and the substrate are derived in closed form by using the Papkovich–Neuber potentials and the Hankel transform. The bonded or sliding interface conditions between the sub-layers are handled by the use of the appropriate transfer matrix, and then the mixed boundary value problem is reduced to a Fredholm integral equation. Symbolic and numerical computations of the solution are implemented in the symbolic software Mathematica in the form of a fast and efficient numerical algorithm, allowing rapid determination of the load–displacement curves and composite elastic properties for an arbitrary rigid indenter shape. A series of results for different indenters (flat, conical, spherical and blunted conical punch shapes) and different multilayered composites is presented and discussed. The complete set of symbolic and numerical computations are provided as supplementary resources with the paper.
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ISSN:0020-7683
1879-2146
DOI:10.1016/j.ijsolstr.2013.04.017