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Green’s functions for the magneto-electro-elastic anisotropic half-space and their applications to contact and crack problems

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A Correction to this article was published on 08 February 2018

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Abstract

A general solution is obtained for a magneto-electro-elastic half-space \(x_{3}\ge 0\) subjected to arbitrary point forces or arbitrary point dislocations, as well as electric and magnetic influence by using two-dimensional Fourier transform. The final results are presented as single integrals over a unit circle. Using the theory of generalized functions, all basic parameters at the half-space boundary are defined in a finite form, and no computation of any integral is needed. Knowledge of Green’s functions in finite form allows us to derive the governing integral equations for the normal and tangential contact and crack problems, as well as to establish certain relationship between the kernels of the relevant integral equations. We also established some interesting general properties of the determinants, which might be new.

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  • 08 February 2018

    The following text should be changed in the abstract: Using the theory of generalized functions, some basic parameters at the half-space boundary are defined in a finite form, and no computation of any integral is needed. Knowledge of some of the Green’s functions in finite form allows us to derive the governing integral equations for the normal contact and crack problems, as well as to establish certain relationship between the integrands in Fourier transforms of the kernels of the relevant integral equations.

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Acknowledgements

The author expresses his gratitude to his son Isaac for help in various computations and for preparation of this article for publication. The author is also grateful to the reviewers for their valuable comments.

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  1. Archambault Jail, Ste-Anne-des-Plaines, QC, J0N1H0, Canada

    V. I. Fabrikant

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  1. V. I. Fabrikant
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Correspondence to V. I. Fabrikant.

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A correction to this article is available online at https://doi.org/10.1007/s00419-017-1331-0.

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Fabrikant, V.I. Green’s functions for the magneto-electro-elastic anisotropic half-space and their applications to contact and crack problems. Arch Appl Mech 87, 1859–1869 (2017). https://doi.org/10.1007/s00419-017-1293-2

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  • DOI: https://doi.org/10.1007/s00419-017-1293-2

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