A 3D graded coating/substrate model based on multigrid techniques within a finite difference frame work is presented. Localized refinement is implemented to optimize memory requirement and computing time. Validation of the solver is performed through a comparison with analytical results for (i) a homogeneous material and (ii) a graded material. The algorithm performance is analyzed through a parametric study describing the influence of layer thickness (0.01 < t/a < 10) and mechanical properties (0.005 < Ec/Es < 10) of the coating on the contact parameters (Ph, a). Three-dimensional examples are then presented to illustrate the efficiency and the large range of possibilities of the model. The influence of different gradations of Young’s modulus, constant, linear and sinusoidal, through the coating thickness on the maximum tensile stress is analyzed, showing that the sinusoidal gradation best accommodates the property mismatch of two successive layers. A final case is designed to show that full 3D spatial property variations can be accounted for. Two spherical inclusions of different size made from elastic solids with Young’s modulus and Poisson’s ratio are embedded within an elastically mismatched finite domain and the stress field is computed.
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e-mail: hugo.boffy@insa-lyon.fr
e-mail: marie-christine.baietto@insa-lyon.fr
e-mail: philippe.sainsot@insa-lyon.fr
e-mail: ton.lubrecht@insa-lyon.fr
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April 2012
Contact Mechanics
An Efficient 3D Model of Heterogeneous Materials for Elastic Contact Applications Using Multigrid Methods
Hugo Boffy,
Hugo Boffy
Ph.D. Student
LaMCoS, CNRS UMR 5259,
e-mail: hugo.boffy@insa-lyon.fr
Université de Lyon
, INSA-Lyon, Villeurbanne, F69621, France
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Marie-Christine Baietto,
Marie-Christine Baietto
CNRS Research Director
LaMCoS, CNRS UMR 5259,
e-mail: marie-christine.baietto@insa-lyon.fr
Université de Lyon
, INSA-Lyon, Villeurbanne, F69621, France
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Philippe Sainsot,
Philippe Sainsot
Assistant Professor
LaMCoS, CNRS UMR 5259,
e-mail: philippe.sainsot@insa-lyon.fr
Université de Lyon
, INSA-Lyon, Villeurbanne, F69621, France
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Antonius A. Lubrecht
Antonius A. Lubrecht
Professor
LaMCoS, CNRS UMR 5259,
e-mail: ton.lubrecht@insa-lyon.fr
Université de Lyon
, INSA-Lyon, Villeurbanne, F69621, France
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Hugo Boffy
Ph.D. Student
LaMCoS, CNRS UMR 5259,
Université de Lyon
, INSA-Lyon, Villeurbanne, F69621, France
e-mail: hugo.boffy@insa-lyon.fr
Marie-Christine Baietto
CNRS Research Director
LaMCoS, CNRS UMR 5259,
Université de Lyon
, INSA-Lyon, Villeurbanne, F69621, France
e-mail: marie-christine.baietto@insa-lyon.fr
Philippe Sainsot
Assistant Professor
LaMCoS, CNRS UMR 5259,
Université de Lyon
, INSA-Lyon, Villeurbanne, F69621, France
e-mail: philippe.sainsot@insa-lyon.fr
Antonius A. Lubrecht
Professor
LaMCoS, CNRS UMR 5259,
Université de Lyon
, INSA-Lyon, Villeurbanne, F69621, France
e-mail: ton.lubrecht@insa-lyon.fr
J. Tribol. Apr 2012, 134(2): 021401 (8 pages)
Published Online: April 12, 2012
Article history
Received:
June 9, 2011
Revised:
February 17, 2012
Published:
April 10, 2012
Online:
April 12, 2012
Citation
Boffy, H., Baietto, M., Sainsot, P., and Lubrecht, A. A. (April 12, 2012). "An Efficient 3D Model of Heterogeneous Materials for Elastic Contact Applications Using Multigrid Methods." ASME. J. Tribol. April 2012; 134(2): 021401. https://doi.org/10.1115/1.4006296
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