The crack problem for nonhomogneous materials under antiplane shear loading - A displacement based formulation

Youn Sha Chan; Glaucio H. Paulino; Albert C. Fannjiang

doi:10.1016/s0020-7683(00)00217-1

The crack problem for nonhomogneous materials under antiplane shear loading - A displacement based formulation

Youn Sha Chan, Glaucio H. Paulino, Albert C. Fannjiang

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

73 Scopus citations

Abstract

This paper presents a displacement based integral equation formulation for the mode III crack problem in a non-homogeneous medium with a continuously differentiable shear modulus, which is assumed to be an exponential function, i.e., G(x) = G_o exp(βx). This formulation leads naturally to a hypersingular integral equation. The problem is solved for a finite crack and results are given for crack profiles and stress intensity factors. The results are affected by the parameter β describing the material nonhomogeneity. This study is motivated by crack problems in strain-gradient elasticity theories where higher order singular integral equations naturally arise even in the slope-based formulation.

Original language	English (US)
Pages (from-to)	2989-3005
Number of pages	17
Journal	International Journal of Solids and Structures
Volume	38
Issue number	17
DOIs	https://doi.org/10.1016/s0020-7683(00)00217-1
State	Published - Mar 7 2001
Externally published	Yes

All Science Journal Classification (ASJC) codes

Modeling and Simulation
General Materials Science
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Applied Mathematics

Keywords

Asymptotic analysis
Collocation method
Fredholm integral equation
Functionally graded materials
Hypersingular integrals
Integral equation method
Mode III crack
Stress intensity factors

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10.1016/s0020-7683(00)00217-1

Cite this

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title = "The crack problem for nonhomogneous materials under antiplane shear loading - A displacement based formulation",

abstract = "This paper presents a displacement based integral equation formulation for the mode III crack problem in a non-homogeneous medium with a continuously differentiable shear modulus, which is assumed to be an exponential function, i.e., G(x) = Go exp(βx). This formulation leads naturally to a hypersingular integral equation. The problem is solved for a finite crack and results are given for crack profiles and stress intensity factors. The results are affected by the parameter β describing the material nonhomogeneity. This study is motivated by crack problems in strain-gradient elasticity theories where higher order singular integral equations naturally arise even in the slope-based formulation.",

keywords = "Asymptotic analysis, Collocation method, Fredholm integral equation, Functionally graded materials, Hypersingular integrals, Integral equation method, Mode III crack, Stress intensity factors",

author = "Chan, {Youn Sha} and Paulino, {Glaucio H.} and Fannjiang, {Albert C.}",

note = "Funding Information: We acknowledge the support from the USA National Science Foundation (NSF) through grants CMS-9996378 (previously CMS-9713798) and DMS-9971322. ",

year = "2001",

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doi = "10.1016/s0020-7683(00)00217-1",

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TY - JOUR

T1 - The crack problem for nonhomogneous materials under antiplane shear loading - A displacement based formulation

AU - Chan, Youn Sha

AU - Paulino, Glaucio H.

AU - Fannjiang, Albert C.

N1 - Funding Information: We acknowledge the support from the USA National Science Foundation (NSF) through grants CMS-9996378 (previously CMS-9713798) and DMS-9971322.

PY - 2001/3/7

Y1 - 2001/3/7

N2 - This paper presents a displacement based integral equation formulation for the mode III crack problem in a non-homogeneous medium with a continuously differentiable shear modulus, which is assumed to be an exponential function, i.e., G(x) = Go exp(βx). This formulation leads naturally to a hypersingular integral equation. The problem is solved for a finite crack and results are given for crack profiles and stress intensity factors. The results are affected by the parameter β describing the material nonhomogeneity. This study is motivated by crack problems in strain-gradient elasticity theories where higher order singular integral equations naturally arise even in the slope-based formulation.

AB - This paper presents a displacement based integral equation formulation for the mode III crack problem in a non-homogeneous medium with a continuously differentiable shear modulus, which is assumed to be an exponential function, i.e., G(x) = Go exp(βx). This formulation leads naturally to a hypersingular integral equation. The problem is solved for a finite crack and results are given for crack profiles and stress intensity factors. The results are affected by the parameter β describing the material nonhomogeneity. This study is motivated by crack problems in strain-gradient elasticity theories where higher order singular integral equations naturally arise even in the slope-based formulation.

KW - Asymptotic analysis

KW - Collocation method

KW - Fredholm integral equation

KW - Functionally graded materials

KW - Hypersingular integrals

KW - Integral equation method

KW - Mode III crack

KW - Stress intensity factors

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U2 - 10.1016/s0020-7683(00)00217-1

DO - 10.1016/s0020-7683(00)00217-1

M3 - Article

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SN - 0020-7683

VL - 38

SP - 2989

EP - 3005

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

IS - 17

ER -

The crack problem for nonhomogneous materials under antiplane shear loading - A displacement based formulation

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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