A representation theorem for the circular inclusion problem

Ogbonna, Nkem

doi:10.1002/zamm.201300147

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…The expressions for the Airy stress functions for images of all other multipoles can then be obtained similarly as discussed in Section II or by using the compact expression for the image operator I that was derived by Ogbonna in Ref. [54]. While compact analytical expressions for the images of disclination are possible to obtain for traction-free and no-slip boundary conditions, this is not possible for the slip boundary condition.…”

Section: Inclusions In a Semi-infinite Elastic Matrix With Prescribed...mentioning

confidence: 99%

Method of image charges for describing linear deformation of bounded 2D solid structures with circular holes and inclusions

Sarkar,

Cebron,

Brojan

et al. 2020

Preprint

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We present a method for predicting the linear response deformation of finite and semi-infinite 2D solid structures with circular holes and inclusions by employing the analogies with image charges and induction in electrostatics. Charges in electrostatics induce image charges near conductive boundaries and an external electric field induces polarization (dipoles, quadrupoles, and other multipoles) of conductive and dielectric objects. Similarly, charges in elasticity induce image charges near boundaries and external stress induces polarization (quadrupoles and other multipoles) inside holes and inclusions. Stresses generated by these induced elastic multipoles as well as stresses generated by their images near boundaries then lead to interactions between holes and inclusions and with their images, which induce additional polarization and thus additional deformation of holes and inclusions. We present a method that expands induced polarization in a series of elastic multipoles, which systematically takes into account the interactions of inclusions and holes with the external field, between them, and with their images. The results of our method for linear deformation of circular holes and inclusions near straight and curved boundaries show good agreement with both linear finite element simulations and experiments.

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Section: Inclusions In a Semi-infinite Elastic Matrix With Prescribed...mentioning

confidence: 99%

Method of image charges for describing linear deformation of bounded 2D solid structures with circular holes and inclusions

Sarkar,

Cebron,

Brojan

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Composite materials can be viewed as a continuum medium consisting of numerous inhomogeneities, and solutions of such inhomogeneity problems provide a powerful tool in analyzing the effective behavior of composite materials. [10][11][12][13] Coupling among different physical phenomena makes the analysis of the inhomogeneity problem in nonlinear medium considerably more complicated. One such example is thermoelectricity, wherein the electric and thermal transports are nonlinearly coupled.…”

Section: Introductionmentioning

confidence: 99%

Closed‐form solutions for a circular inhomogeneity in nonlinearly coupled thermoelectric materials

Yang²,

et al. 2019

Z Angew Math Mech

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Thermoelectricity is a class of material possessing the ability of interconverting heat and electricity. For the sake of high conversion efficiency, inclusions/fibers are usually introduced into thermoelectric materials. However, the discontinuity of material property and geometry brought by inclusions/fibers might result in severe stress concentration and thus greatly affect the mechanical properties of thermoelectric material in its engineering service. This paper introduces a nonlinear coupled thermal–electrical–mechanical formulation for the plane problem of a circular inhomogeneity embedded in a thermoelectric medium under a combined uniform electric current density and energy flux. A special attention is directed towards the induced thermal stress field which has often neglected in the literature. Using methods based on Cauchy integrals, the complex potentials of the electric field, temperature field and associated stress field are derived explicitly in both the inhomogeneity and the surrounding matrix. The analysis shows that the electrically and thermally induced stress has a linear relationship with the energy flux applied at infinity, but has a nonlinear relationship with the remote electric current density. Numerical simulations are also performed to examine how the inhomogeneity influences the electrically induced thermal stress concentration on the interface. The presented results can be directly used for reliability consideration in design and optimization of thermoelectric composites with circular fibers/inclusions.

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Method of image charges for describing deformation of bounded two-dimensional solids with circular inclusions

et al. 2021

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A representation theorem for the circular inclusion problem

Cited by 3 publications

References 12 publications

Method of image charges for describing linear deformation of bounded 2D solid structures with circular holes and inclusions

Method of image charges for describing linear deformation of bounded 2D solid structures with circular holes and inclusions

Closed‐form solutions for a circular inhomogeneity in nonlinearly coupled thermoelectric materials

Method of image charges for describing deformation of bounded two-dimensional solids with circular inclusions

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