Numerical equivalent inclusion method: a new computational method for analyzing stress fields in and around inclusions of various shapes

Nakasone, Yuji; Nishiyama, Hirotada; Nojiri, Tetsuharu

doi:10.1016/s0921-5093(00)00637-7

Cited by 61 publications

(30 citation statements)

References 4 publications

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“…3. The average stress values of all the nodes are shown in Table 2 together with the exact solution (Mura 1987) and relative errors which are expressed as (average value À exact value)/(exact value) Â 100(%) (Nakasone et al 2000). It can be noted that all the relative errors are within 1.3% range from Mura's exact solution.…”

Section: A Spherical Inclusion In An Infinite Mediummentioning

confidence: 96%

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An integral equation approach to the inclusion-crack interactions in three-dimensional infinite elastic domain

Dong

Cheung

2002

Computational Mechanics

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In this paper, an integral equation method to the inclusion-crack interaction problem in three-dimensional elastic medium is presented. The method is implemented following the idea that displacement integral equation is used at the source points situated in the inclusions, whereas stress integral equation is applied to source points along crack surfaces. The displacement and stress integral equations only contain unknowns in displacement (in inclusions) and displacement discontinuity (along cracks). The hypersingular integrals appearing in stress integral equation are analytically transferred to line integrals (for plane cracks) which are at most weakly singular. Finite elements are adopted to discretize the inclusions into isoparametric quadratic 10-node tetrahedral or 20-node hexahedral elements and the crack surfaces are decomposed into discontinuous quadratic quadrilateral elements. Special crack tip elements are used to simulate the ffiffi r p variation of displacements near the crack front. The stress intensity factors along the crack front are calculated. Numerical results are compared with other available methods.

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Section: A Spherical Inclusion In An Infinite Mediummentioning

confidence: 96%

“…Inclusion material may be SiC or Ti-6Al-4V. The related elastic parameters are listed in Table 1 (Nakasone et al 2000).…”

Section: Numerical Examplesmentioning

confidence: 99%

An integral equation approach to the inclusion-crack interactions in three-dimensional infinite elastic domain

Dong

Cheung

2002

Computational Mechanics

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“…It should be mentioned that the eigenstrain solution can represent various physical problems, where the eigenstrains can correspond to the thermal-mismatch strains, the strains due to the phase transformation, the plastic strains, as well as the intrinsic strains in the residual stress problems [17] . Based on the concept of eigenstrains and through the substitution of equivalent inclusions [18] , many practical problems can be modeled and solved efficiently. Typical problems are the substituting or interstitial atoms in crystals, the quantum dot/line structures in semiconductors, the effects of voids, and the indigenous phase or the reinforcement in solids.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional polynomial eigenstrain formulation of boundary integral equation with numerical verification

Guo

Qin

2011

Appl. Math. Mech.-Engl. Ed.

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The low-order polynomial-distributed eigenstrain formulation of the boundary integral equation (BIE) and the corresponding definition of the Eshelby tensors are proposed for the elliptical inhomogeneities in two-dimensional elastic media. Taking the results of the traditional subdomain boundary element method (BEM) as the control, the effectiveness of the present algorithm is verified for the elastic media with a single elliptical inhomogeneity. With the present computational model and algorithm, significant improvements are achieved in terms of the efficiency as compared with the traditional BEM and the accuracy as compared with the constant eigenstrain formulation of the BIE.

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“…In the paper, the original terminology of Eshelby is employed. Following Eshelby's idea of equivalent inclusion and eigenstrain solution, a significantly diverse set of research work has been reported [3][4][5][6][7][8][9][10][11][12] . The eigenstrain solution can…”

Section: Introductionmentioning

confidence: 99%

Computational model for short-fiber composites with eigenstrain formulation of boundary integral equations

Ma¹,

Xia²,

Qin³

2008

Appl. Math. Mech.-Engl. Ed.

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Communicated by GUO Xing-ming)Abstract A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations (BIE) and solved with the newly developed boundary point method (BPM). The model is closely derived from the concept of the equivalent inclusion of Eshelby tensors. Eigenstrains are iteratively determined for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand either through analytical or numerical means. As unknown variables appear only on the boundary of the solution domain, the solution scale of the inhomogeneity problem with the model is greatly reduced. This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM. The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element (RVE), showing the validity and the effectiveness of the proposed computational modal and the solution procedure.

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Numerical equivalent inclusion method: a new computational method for analyzing stress fields in and around inclusions of various shapes

Cited by 61 publications

References 4 publications

An integral equation approach to the inclusion-crack interactions in three-dimensional infinite elastic domain

An integral equation approach to the inclusion-crack interactions in three-dimensional infinite elastic domain

Two-dimensional polynomial eigenstrain formulation of boundary integral equation with numerical verification

Computational model for short-fiber composites with eigenstrain formulation of boundary integral equations

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