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Research Papers: Contact Mechanics

An Efficient Numerical Method With a Parallel Computational Strategy for Solving Arbitrarily Shaped Inclusions in Elastoplastic Contact Problems

[+] Author and Article Information
Zhanjiang Wang

e-mail: wangzhanjiang001@gmail.com

Qinghua Zhou

State Key Laboratory of Mechanical Transmission,
Chongqing University,
Chongqing 400030, China;
Department of Mechanical Engineering,
Northwestern University,Evanston, IL 60208

Xiaolan Ai

The Timken Company,
Canton, OH 44706

Leon M. Keer

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

Qian Wang

State Key Laboratory of Mechanical Transmission,
Chongqing University,
Chongqing 400030, China;
Department of Mechanical Engineering,
Northwestern University, Evanston,
IL 60208

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the Journal of Tribology. Manuscript received October 1, 2012; final manuscript received March 3, 2013; published online March 28, 2013. Assoc. Editor: James R. Barber.

J. Tribol 135(3), 031401 (Mar 28, 2013) (12 pages) Paper No: TRIB-12-1166; doi: 10.1115/1.4023948 History: Received October 01, 2012; Revised March 03, 2013

The plastic zone developed during elastoplastic contact may be effectively modeled as an inclusion in an isotropic half space. This paper proposes a simple but efficient computational method to analyze the stresses caused by near surface inclusions of arbitrary shape. The solution starts by solving a corresponding full space inclusion problem and proceeds to annul the stresses acting normal and tangential to the surface, where the numerical computations are processed by taking advantage of the fast Fourier transform techniques with a parallel computing strategy. The extreme case of a cuboidal inclusion with one facet on the surface of the half space is chosen to validate the method. When the surface truncation domain is extended sufficiently and the grids are dense enough, the results based on the new approach are in good agreement with the exact solutions. When solving a typical elastoplastic contact problem, the present analysis is roughly two times faster than the image inclusion approach and six times faster than the direct method. In addition, the present work demonstrates that a significant enhancement in the computational efficiency can be achieved through the introduction of parallel computation.

Copyright © 2013 by ASME
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Figures

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Fig. 1

New method: the elastic fields caused by an inclusion in a half space are the sum of results due to the inclusion and the surface tractions to create a surface free from their opposite tractions

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Fig. 2

Computational domain, mesh types, and grid points

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Fig. 6

von Mises stress for cases 4 to 6 (the computational domain is fixed but the grid size varies in different cases): (a) along the line passing through point (0, 0.1a, 0) and parallel to the x axis, and (b) along the z axis

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Fig. 5

von Mises stress for case 1 to 3 (the computational domain varies but the grid size is held constant for different cases): (a) along the line passing through point (0, 0.1a, 0) and parallel to the x axis, and (b) along the z axis

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Fig. 3

Image inclusion approach: the elastic fields caused by an inclusion in a half space are the sum of results due to two inclusions with specified eigenstrains and results caused by surface normal stress which makes the surface free from surface tractions

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Fig. 4

Stresses caused by a cuboidal inclusion (2a × 2a × 2a) in the full space, along the x axis in the target plane at different distances h to the cuboidal center: (a) model, (b) h = a, (c) h = 1.5a, and (d) h = 2a

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Fig. 8

Multi-inclusion model and the resultant dimensional von Mises stresses σvonr/ph in the xz plane using different methods: (a) multi-inclusion model, (b) from the new method, (c) based on Zhou et al. [16], and (d) based on Liu et al. [17]

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Fig. 9

Elastoplastic contact model

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Fig. 10

Results from different methods, i.e., the new method, the approach of Zhou et al. [16], and Liu et al. [17]: (a) dimensionless pressure along the x axis, and (b) equivalent plastic strain along the z axis

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Fig. 7

Resultant stresses from different methods, i.e., the analytical solutions, the new method, and the approach of Zhou et al. [16]; (a) along the line passing through point (0, 0.1a, 0) and parallel to the x axis, and (b) along the z axis

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Fig. 11

Dimensional residual von Mises stresses σvonr/ph from different methods: (a) the new method, (b) based on Zhou et al. [16], and (c) based on Liu et al. [17]

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Fig. 12

Computational time with different methods: (a) new method, (b) based on Zhou et al. [16], and (c) based on Liu et al. [17]

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Fig. 13

Parallel strategy for calculating stress caused by eigenstrains in the full space

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Fig. 14

Times for different 3D transform size with double-precision complex data type, where each execution time is obtained through repeating 3D-FFT transforms 10 times

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Fig. 15

Time for calculating the eigenstress by using different numbers of processors and different grid sizes

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Fig. 16

Time for computing an elastoplastic contact case by using different numbers of processors and different grid sizes

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