Eshelby's problem of inclusion with arbitrary shape in an isotropic elastic half-plane

Lee, Y.-G.; Zou, Wenming; Ren, H.-H.

doi:10.1016/j.ijsolstr.2015.12.024

Cited by 12 publications

(2 citation statements)

References 27 publications

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“…They found that FGM can be suitable material to enclosed the inclusion for SCF reduction. Lee et al (2016) solved the problem of Eshelby's arbitrary shape inclusion. Yang et al (2018) extended their work for tensile load and tested the effect of FGM on SCF around circular, elliptical and rectangular inclusions.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Stress Analysis of Rounded Rectangular Inclusion Enclosed by FGM Layer

Rani

Verma

Ghangas

2023

Int. j. math. eng. manag. sci.

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The aim of the present work is to model and analyze stresses around rounded rectangular inclusion enclosed with functionally graded material (FGM) layer. The inclusion has been considered in an infinite plate which is subjected to far-field tensile stress. The extended finite element method (XFEM) has been used to model the inclusion with non-conformal mesh. The level set functions of circular and rectangular shapes have been used to trace the inclusion boundary with mesh. The FGM has been considered as continuous varying mixture of inclusion and plate materials with power law function along normal direction to the inclusion interface. Young's modulus has been assumed to vary within FGM layer, whereas Poisson's ratio is kept constant. The stress distribution and stress concentration factor (SCF) have been analyzed for different geometrical and FGM parameters. It has been observed that XFEM with level set method efficiently model the difficult shape inclusions such as rounded rectangle. Applying the FGM layer smoothens the stress distribution around rounded rectangular inclusion and significantly reduces SCF. The position of maximum stress shifted from the inclusion interface toward the FGM layer interface. The least SCF has been noted with power law index n = 0.5 and FGM layer thickness t = r.

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Section: Introductionmentioning

confidence: 99%

Modeling and Stress Analysis of Rounded Rectangular Inclusion Enclosed by FGM Layer

Rani

Verma

Ghangas

2023

Int. j. math. eng. manag. sci.

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“…Sass et al [9] first studied the elastic fields of a cuboidal inclusion, for which they offered a Fourier series solution; this problem was later reworked by Faivre [10], who achieved the first explicit solution to the elastic fields of a parallelepipedal inclusion in isotropic elasticity. Further geometries have been studied both in the context of homogeneous eigenstrains and isotropic elasticity and for anisotropic materials [11], with different elastic moduli [12], including solutions for the fields of square plate inclusions [13], cuboids [14], cylinders [15], rod-like inclusions [16], concave inclusions [17], toroids [18], generalized formulations for arbitrary closed geometries [19] and polyhedra [6,20].…”

Section: Introductionmentioning

confidence: 99%

The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions

Gurrutxaga-Lerma

2023

Proc. R. Soc. A.

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The article offers a general formulation for the multipolar field expansion of an inclusion. The multipolar moments of arbitrary order for the ellipsoidal inclusion are derived, showing known features of their elastic fields in both the far and near field. Using integer point enumeration theory, the same formulation is extended to all polytopal inclusions, which serve to model faceted inclusions found in, e.g. igneous and metamorphic rocks, particle reinforced composite materials, or as intermetallic precipitates in alloys. A general algorithm for the calculation of the multipolar moments of polytopes of any number of vertices is derived. A number of examples for tetrahedral, cuboidal and dodecahedral inclusions are given. It is shown that the parity of the axial moment function of a polytopal inclusion mirrors the symmetry of the inclusion. This represents the main properties of their elastic fields, including the long- and near-field decay. If the inclusion is symmetric with respect to a given axes, the fields will decay with 1 / r 2 in the far field and 1 / r 4 in the near field. If symmetry along that direction is lost, as is expected in most real inclusions, the decay rate progresses with 1 / r 2 but the near field with 1 / r 3 .

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Durability Evaluation of Bonded Repairs for the Damaged Metallic Structures Subjected to Mechanical and Thermal Loads

Fedotov

Tsipenko

2020

Advances in Theory and Practice of Computational Mechanics

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Eshelby's problem of inclusion with arbitrary shape in an isotropic elastic half-plane

Cited by 12 publications

References 27 publications

Modeling and Stress Analysis of Rounded Rectangular Inclusion Enclosed by FGM Layer

Modeling and Stress Analysis of Rounded Rectangular Inclusion Enclosed by FGM Layer

The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions

Durability Evaluation of Bonded Repairs for the Damaged Metallic Structures Subjected to Mechanical and Thermal Loads

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