Maxwell’s equivalent inhomogeneity and remarkable properties of harmonic problems involving symmetric domains

Published on Jan 1, 2017in Journal of Mechanics of Materials and Structures0.987
· DOI :10.2140/JOMMS.2017.12.179
Sofia G. Mogilevskaya23
Estimated H-index: 23
(UMN: University of Minnesota),
Dmitry Nikolskiy5
Estimated H-index: 5
(UMN: University of Minnesota)
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The paper presents an analysis of elasticity problems involving a single inhomogeneity which possesses certain types of symmetries. As observed earlier, isotropic problems of that kind exhibit some ‘strange’ and remarkable properties. Under the action of uniform far-field stresses, the averages of the fields inside the inhomogeneities preserve the structure of the far-field loads. Here, it is shown that these properties are exhibited for a wider class of problems, which include anisotropic and n...
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Abstract In the present paper, we use Maxwell homogenization scheme to calculate effective transverse conductivity of a fibrous composite with imperfect contact between the matrix and the parallel elliptic fibers. The developed theory extends the Hasselman–Johnson formula to the composites with elliptic fibers. The complete solution of the conductivity problem for single elliptic inclusion with imperfect interface provides the mathematical background of the method. In the Maxwell homogenization ...
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Abstract Maxwell’s concept of an equivalent inhomogeneity is employed for evaluating the effective elastic properties of tetragonal, fiber-reinforced, unidirectional composites with isotropic phases. The microstructure induced anisotropic effective elastic properties of the material are obtained by comparing the far-field solutions for the problem of a finite cluster of isotropic, circular cylindrical fibers embedded in an infinite isotropic matrix with that for the problem of a single, tetragon...
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Maxwell’s concept of equivalent inhomogeneity is employed for evaluating the effective elastic properties of macroscopically anisotropic particulate composites with isotropic phases. The effective anisotropic elastic properties of the material are obtained by comparing the far-field solutions for the problem of a finite cluster of isotropic particles embedded in an infinite isotropic matrix with those for the problem of a single anisotropic equivalent inhomogeneity embedded in the same matrix. T...
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Abstract In this paper, a boundary integral equation formulation for anti-plane shear inhomogeneous medium is presented to study the interaction between the inhomogeneities and cracks. The proposed boundary integral equation formulation only contains out-of-plane interface displacements and out-of-plane discontinuous displacements over cracks. Numerical implementation is simple since the present formulation has considered the shear equilibrium condition over the interfaces between the matrix and...
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Abstract This paper presents a comprehensive review of the far-field-based methodology of estimation of the effective properties of multi-phase composites that was pioneered by Maxwell in 1873 in the context of effective electrical conductivity of a particle-reinforced material. Maxwell suggested that a cluster of particles embedded in an infinite medium subjected to a uniform electrical field has the same far-field asymptotic as an equivalent sphere whose conductivity is equal to the effective ...
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