A screw dislocation near a non-parabolic open inhomogeneity with internal uniform stresses

Xu Wang; Peter Schiavone

doi:10.1016/j.crme.2019.10.006

A screw dislocation near a non-parabolic open inhomogeneity with internal uniform stresses

Xu Wang ¹ ; Peter Schiavone ²

¹ School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China
² Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering, Edmonton, Alberta T6G 1H9, Canada

Comptes Rendus. Mécanique, Volume 347 (2019) no. 12, pp. 967-972.

Abstract

We use conformal mapping techniques and analytic continuation to prove that the stress field inside a non-parabolic open inhomogeneity embedded in a matrix subjected to uniform remote anti-plane stresses can nevertheless remain uniform despite the presence of a screw dislocation in its vicinity. Furthermore, the internal uniform stresses inside the inhomogeneity are found to be independent of both the shape of the inhomogeneity and the presence of the screw dislocation. On the other hand, we find that the existence of the nearby screw dislocation exerts a significant influence on the non-parabolic shape of the inhomogeneity.

Received: 2019-09-21
Accepted: 2019-10-23
Published online: 2019-11-06

DOI: 10.1016/j.crme.2019.10.006

Keywords: Non-parabolic inhomogeneity, Uniform field, Screw dislocation, Anti-plane elasticity, Conformal mapping

Author's affiliations:

Xu Wang ¹; Peter Schiavone ²

¹ School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China
² Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering, Edmonton, Alberta T6G 1H9, Canada

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     author = {Xu Wang and Peter Schiavone},
     title = {A screw dislocation near a non-parabolic open inhomogeneity with internal uniform stresses},
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Xu Wang; Peter Schiavone. A screw dislocation near a non-parabolic open inhomogeneity with internal uniform stresses. Comptes Rendus. Mécanique, Volume 347 (2019) no. 12, pp. 967-972. doi : 10.1016/j.crme.2019.10.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.10.006/

References
Cited by

[1] X. Wang; P. Schiavone Two inhomogeneities of irregular shape with internal uniform stress fields interacting with a screw dislocation, C. R. Mecanique, Volume 344 (2016), pp. 532-538

[2] X. Wang; P. Schiavone A screw dislocation near a non-elliptical piezoelectric inhomogeneity with internal uniform electroelastic field, C. R. Mecanique (2019) (in press) | DOI

[3] X. Wang; L. Chen; P. Schiavone Uniform stress field inside an anisotropic non-elliptical inhomogeneity interacting with a screw dislocation, Eur. J. Mech. A, Solids, Volume 70 (2018), pp. 1-7

[4] M. Dai; P. Schiavone; C.F. Gao Nano-inclusion with uniform internal strain induced by a screw dislocation, Arch. Mech., Volume 68 (2016), pp. 243-257

[5] X. Wang, P. Schiavone, Uniformity of stresses inside a parabolic inhomogeneity, submitted for publication.

[6] J.R. Philip Seepage shedding by parabolic capillary barriers and cavities, Water Resour. Res., Volume 34 (1998), pp. 2827-2835

[7] A.R. Kacimov; Yu.V. Obnosov Steady water flow around parabolic cavities and through parabolic inclusions in unsaturated and saturated soils, J. Hydrol., Volume 238 (2000), pp. 65-77

[8] Z.G. Suo Singularities interacting with interfaces and cracks, Int. J. Solids Struct., Volume 25 (1989), pp. 1133-1142

[9] C.Q. Ru Analytic solution for Eshelby's problem of an inclusion of arbitrary shape in a plane or half-plane, J. Appl. Mech., Volume 66 (1999), pp. 315-322

[10] C.Q. Ru; P. Schiavone; A. Mioduchowski Uniformity of stresses within a three-phase elliptic inclusion in anti-plane shear, J. Elast., Volume 52 (1999), pp. 121-128

[11] T.C.T. Ting Anisotropic Elasticity. Theory and Applications, Oxford University Press, New York, 1996

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