A Volume Integral Equation Technique for Multiple Inclusion and Crack Interaction Problems

Lee, Jungki; Mal, Ajit

doi:10.1115/1.2787282

Cited by 69 publications

(46 citation statements)

References 12 publications

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“…Unlike the classical multizone boundary element method (in which the integral equation for each inclusion and the matrix must be discretized to form a corresponding matrix equation, together with the coupling of each interface bonding condition, the resulting solvable equation can be formed), the present method avoids forming integral equation for each inclusion in which the problem of sharp corners has to be dealt with as explained above. As mentioned by Lee et al (1997), ''as the number of boundary increases, the VIEM (volume integral equation method) becomes more efficient than the BEM; the need to satisfy interface conditions at all the interfaces makes BIEM much more cumbersome to use''…”

Section: Some Remarks About the Methodsmentioning

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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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: Some Remarks About the Methodsmentioning

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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“…The stress field within and outside the inclusions can also be determined in a similar manner. The details of the numerical treatment of (1) for plane elastostatic problems can be found in [5]. Further explanation of the volume integral equation method for isotropic inclusions in an isotropic matrix can also be found in Section 4.3 "Volume Integral Equation Method" by Buryachenko [16].…”

Section: Volume Integral Equation Methodsmentioning

confidence: 99%

“…It can, therefore in principle, be determined through the solution of the equation. An algorithm for the solution of (1) was developed by Lee and Mal [5] by discretizing the inclusions using conventional finite elements. Once u(x) within the inclusions is determined, the displacement field in the matrix can be calculated from (1) by evaluating the integral for x ∉ .…”

Section: Volume Integral Equation Methodsmentioning

confidence: 99%

“…Unfortunately, both methods encounter limitations in dealing with problems involving infinite media or multiple inclusions. However, it has been demonstrated that a recently developed numerical method based on a volume integral formulation can overcome such difficulties in solving a large class of inclusion problems [5][6][7][8][9][10]. One advantage of the volume integral equation method (VIEM) over the boundary integral equation method (BIEM) is that it does not require the use of Green's functions for both the matrix and the inclusions [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Mixed Volume and Boundary Integral Equation Method with Elliptical Inclusions and a Circular/Elliptical Void

Lee

Choi

Han

2013

Advances in Mechanical Engineering

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A mixed volume and boundary integral equation method (mixed VIEM-BIEM) is used to calculate the plane elastostatic field in an unbounded isotropic elastic medium containing multiple isotropic/orthotropic elliptical inclusions of arbitrary orientation and a circular/elliptical void subjected to remote loading. In order to investigate the influence of a circular/elliptical void on the interfacial stress field, a detailed analysis of the stress field at the interface between the matrix and the central isotropic/orthotropic inclusion is carried out for the square packing of eight inclusions and one void, taking into account different values for the orientation angles and concentration of the inclusions. The mixed method is shown to be very accurate and effective for investigating the local stresses in composites containing isotropic/anisotropic fibers and a circular/elliptical void.

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“…In response, we have used the direct integration scheme introduced by Cerrolaza and Alarcon [13], Li et al [14], and Lu and Ye [15] after suitable modifications to address these singularity concerns. A description of the modified method used in the discretization of the volume integral equation is given by Lee and Mal [7,16].…”

Section: Scattering Of Sh Waves In An Unbounded Isotropic Matrix Contmentioning

confidence: 99%

SH Wave Scattering Problems for Multiple Orthotropic Elliptical Inclusions

Lee

Han

Ahn

2013

Advances in Mechanical Engineering

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A volume integral equation method (VIEM) is applied for the effective analysis of elastic wave scattering problems in unbounded solids containing general anisotropic inclusions. It should be noted that this numerical method does not require use of Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is necessary for the analysis. This new method can also be applied to general two-dimensional elastodynamic problems involving arbitrary shapes and numbers of anisotropic inclusions. A detailed analysis of SH wave scattering problems is developed for an unbounded isotropic matrix containing multiple orthotropic elliptical inclusions. Numerical results are presented for the displacement fields at the interfaces of the inclusions in a broad frequency range of practical interest. Through the analysis of plane elastodynamic problems in an unbounded isotropic matrix with multiple orthotropic elliptical inclusions, it is established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing general anisotropic inclusions of arbitrary shapes.

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A Volume Integral Equation Technique for Multiple Inclusion and Crack Interaction Problems

Cited by 69 publications

References 12 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

Mixed Volume and Boundary Integral Equation Method with Elliptical Inclusions and a Circular/Elliptical Void

SH Wave Scattering Problems for Multiple Orthotropic Elliptical Inclusions

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