Numerical Implementation of the Equivalent Inclusion Method for 2D Arbitrarily Shaped Inhomogeneities

Qinghua Zhou; Xiaoqing Jin; Zhanjiang Wang; Jiaxu Wang; Leon M. Keer; Qian Wang

doi:10.1007/s10659-014-9477-2

Numerical Implementation of the Equivalent Inclusion Method for 2D Arbitrarily Shaped Inhomogeneities

Qinghua Zhou, Xiaoqing Jin^*, Zhanjiang Wang, Jiaxu Wang, Leon M. Keer, Qian Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

Abstract

A new numerical method for solving two-dimensional arbitrarily shaped inhomogeneity problems is demonstrated in the present work. Solution is achieved through a discretization consisting of rectangular elements using newly formulated closed-form solutions. An iterative scheme for implementing the numerical equivalent inclusion method, i.e., determining the equivalent eigenstrains, is proposed. Comprehensive benchmarks on numerical convergence with respect to mesh size and iterative number are conducted to demonstrate the performance of the new numerical method. Comparative studies among results are obtained by the proposed iterative scheme, the Gaussian elimination method, and the Hutchinson approximation and show superiority of the iterative scheme. Simulations for material combinations utilizing the Dundurs α–β plane reveal its capability. A double-inhomogeneity model illustrates the ability of the new numerical method to predict the stress concentration factor for closely distributed multiple inhomogeneities.

Original language	English (US)
Pages (from-to)	39-61
Number of pages	23
Journal	Journal of Elasticity
Volume	118
Issue number	1
DOIs	https://doi.org/10.1007/s10659-014-9477-2
State	Published - Jan 2015

Funding

The authors would like to acknowledge the supports from Center for Surface Engineering and Tribology at Northwestern University, USA, and State Key Laboratory of Mechanical Transmission at Chongqing University (No. 0301002109162), China. The authors are grateful to Prof. Volodymyr Kushch for providing the source code of their paper. Qinghua Zhou would like to thank the scholarship support from China Scholarship Council (No. 2011605076). Zhanjiang Wang would also like to acknowledge the support from National Science Foundation of China under Grant No. 51105391.

Keywords

Inclusion solution
Inhomogeneity
Numerical equivalent inclusion method
Stress concentration factor

ASJC Scopus subject areas

General Materials Science
Mechanics of Materials
Mechanical Engineering

Access to Document

10.1007/s10659-014-9477-2

Cite this

@article{f2f28e6dc778460abe702956ca5b551b,

title = "Numerical Implementation of the Equivalent Inclusion Method for 2D Arbitrarily Shaped Inhomogeneities",

abstract = "A new numerical method for solving two-dimensional arbitrarily shaped inhomogeneity problems is demonstrated in the present work. Solution is achieved through a discretization consisting of rectangular elements using newly formulated closed-form solutions. An iterative scheme for implementing the numerical equivalent inclusion method, i.e., determining the equivalent eigenstrains, is proposed. Comprehensive benchmarks on numerical convergence with respect to mesh size and iterative number are conducted to demonstrate the performance of the new numerical method. Comparative studies among results are obtained by the proposed iterative scheme, the Gaussian elimination method, and the Hutchinson approximation and show superiority of the iterative scheme. Simulations for material combinations utilizing the Dundurs α–β plane reveal its capability. A double-inhomogeneity model illustrates the ability of the new numerical method to predict the stress concentration factor for closely distributed multiple inhomogeneities.",

keywords = "Inclusion solution, Inhomogeneity, Numerical equivalent inclusion method, Stress concentration factor",

author = "Qinghua Zhou and Xiaoqing Jin and Zhanjiang Wang and Jiaxu Wang and Keer, {Leon M.} and Qian Wang",

note = "Funding Information: The authors would like to acknowledge the supports from Center for Surface Engineering and Tribology at Northwestern University, USA, and State Key Laboratory of Mechanical Transmission at Chongqing University (No. 0301002109162), China. The authors are grateful to Prof. Volodymyr Kushch for providing the source code of their paper. Qinghua Zhou would like to thank the scholarship support from China Scholarship Council (No. 2011605076). Zhanjiang Wang would also like to acknowledge the support from National Science Foundation of China under Grant No. 51105391. Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media Dordrecht.",

year = "2015",

month = jan,

doi = "10.1007/s10659-014-9477-2",

language = "English (US)",

volume = "118",

pages = "39--61",

journal = "Journal of Elasticity",

issn = "0374-3535",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Numerical Implementation of the Equivalent Inclusion Method for 2D Arbitrarily Shaped Inhomogeneities

AU - Zhou, Qinghua

AU - Jin, Xiaoqing

AU - Wang, Zhanjiang

AU - Wang, Jiaxu

AU - Keer, Leon M.

AU - Wang, Qian

N1 - Funding Information: The authors would like to acknowledge the supports from Center for Surface Engineering and Tribology at Northwestern University, USA, and State Key Laboratory of Mechanical Transmission at Chongqing University (No. 0301002109162), China. The authors are grateful to Prof. Volodymyr Kushch for providing the source code of their paper. Qinghua Zhou would like to thank the scholarship support from China Scholarship Council (No. 2011605076). Zhanjiang Wang would also like to acknowledge the support from National Science Foundation of China under Grant No. 51105391. Publisher Copyright: © 2014, Springer Science+Business Media Dordrecht.

PY - 2015/1

Y1 - 2015/1

N2 - A new numerical method for solving two-dimensional arbitrarily shaped inhomogeneity problems is demonstrated in the present work. Solution is achieved through a discretization consisting of rectangular elements using newly formulated closed-form solutions. An iterative scheme for implementing the numerical equivalent inclusion method, i.e., determining the equivalent eigenstrains, is proposed. Comprehensive benchmarks on numerical convergence with respect to mesh size and iterative number are conducted to demonstrate the performance of the new numerical method. Comparative studies among results are obtained by the proposed iterative scheme, the Gaussian elimination method, and the Hutchinson approximation and show superiority of the iterative scheme. Simulations for material combinations utilizing the Dundurs α–β plane reveal its capability. A double-inhomogeneity model illustrates the ability of the new numerical method to predict the stress concentration factor for closely distributed multiple inhomogeneities.

AB - A new numerical method for solving two-dimensional arbitrarily shaped inhomogeneity problems is demonstrated in the present work. Solution is achieved through a discretization consisting of rectangular elements using newly formulated closed-form solutions. An iterative scheme for implementing the numerical equivalent inclusion method, i.e., determining the equivalent eigenstrains, is proposed. Comprehensive benchmarks on numerical convergence with respect to mesh size and iterative number are conducted to demonstrate the performance of the new numerical method. Comparative studies among results are obtained by the proposed iterative scheme, the Gaussian elimination method, and the Hutchinson approximation and show superiority of the iterative scheme. Simulations for material combinations utilizing the Dundurs α–β plane reveal its capability. A double-inhomogeneity model illustrates the ability of the new numerical method to predict the stress concentration factor for closely distributed multiple inhomogeneities.

KW - Inclusion solution

KW - Inhomogeneity

KW - Numerical equivalent inclusion method

KW - Stress concentration factor

UR - http://www.scopus.com/inward/record.url?scp=84908114714&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908114714&partnerID=8YFLogxK

U2 - 10.1007/s10659-014-9477-2

DO - 10.1007/s10659-014-9477-2

M3 - Article

AN - SCOPUS:84908114714

SN - 0374-3535

VL - 118

SP - 39

EP - 61

JO - Journal of Elasticity

JF - Journal of Elasticity

IS - 1

ER -

Numerical Implementation of the Equivalent Inclusion Method for 2D Arbitrarily Shaped Inhomogeneities

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this