A screw dislocation near a non-elliptical piezoelectric inhomogeneity with internal uniform electroelastic field

Xu Wang; Peter Schiavone

doi:10.1016/j.crme.2019.08.002

A screw dislocation near a non-elliptical piezoelectric inhomogeneity with internal uniform electroelastic field

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. 10, pp. 734-739.

Résumé

Conformal mapping and analytic continuation are employed to prove the existence of an internal uniform electroelastic field inside a non-elliptical piezoelectric inhomogeneity interacting with a screw dislocation. We focus specifically on the case when the piezoelectric matrix surrounding the inhomogeneity is subjected to uniform remote anti-plane mechanical and in-plane electrical loading and a constraint is imposed between the remote loading and the screw dislocation. The constraint can be expressed in a relatively simple decoupled form by utilizing orthogonality relationships between two corresponding eigenvectors. The internal uniform electroelastic field is found to be independent of the presence of the screw dislocation; moreover, it can be expressed in decoupled form.

Reçu le : 2019-07-04
Accepté le : 2019-08-08
Publié le : 2019-08-26

DOI : 10.1016/j.crme.2019.08.002

Mots clés : Uniform electroelastic field, Piezoelectric inhomogeneity, Screw dislocation, Conformal mapping, Analytic continuation

Affiliations des auteurs :

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

@article{CRMECA_2019__347_10_734_0,
     author = {Xu Wang and Peter Schiavone},
     title = {A screw dislocation near a non-elliptical piezoelectric inhomogeneity with internal uniform electroelastic field},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {734--739},
     publisher = {Elsevier},
     volume = {347},
     number = {10},
     year = {2019},
     doi = {10.1016/j.crme.2019.08.002},
     language = {en},
}

TY  - JOUR
AU  - Xu Wang
AU  - Peter Schiavone
TI  - A screw dislocation near a non-elliptical piezoelectric inhomogeneity with internal uniform electroelastic field
JO  - Comptes Rendus. Mécanique
PY  - 2019
SP  - 734
EP  - 739
VL  - 347
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crme.2019.08.002
LA  - en
ID  - CRMECA_2019__347_10_734_0
ER  -

%0 Journal Article
%A Xu Wang
%A Peter Schiavone
%T A screw dislocation near a non-elliptical piezoelectric inhomogeneity with internal uniform electroelastic field
%J Comptes Rendus. Mécanique
%D 2019
%P 734-739
%V 347
%N 10
%I Elsevier
%R 10.1016/j.crme.2019.08.002
%G en
%F CRMECA_2019__347_10_734_0

Xu Wang; Peter Schiavone. A screw dislocation near a non-elliptical piezoelectric inhomogeneity with internal uniform electroelastic field. Comptes Rendus. Mécanique, Volume 347 (2019) no. 10, pp. 734-739. doi : 10.1016/j.crme.2019.08.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.08.002/

Bibliographie
Cité par

[1] N.J. Hardiman Elliptic elastic inclusion in an infinite plate, Q. J. Mech. Appl. Math., Volume 7 (1954), pp. 226-230

[2] J.D. Eshelby The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. R. Soc. Lond. A, Volume 241 (1957), pp. 376-396

[3] J.D. Eshelby The elastic field outside an ellipsoidal inclusion, Proc. R. Soc. Lond. A, Volume 252 (1959), pp. 561-569

[4] J.D. Eshelby Elastic inclusions and inhomogeneities, Prog. Solid Mech., Volume II (1961), pp. 89-140

[5] G.P. Sendeckyj Elastic inclusion problem in plane elastostatics, Int. J. Solids Struct., Volume 6 (1970), pp. 1535-1543

[6] S.X. Gong; S.A. Meguid A general treatment of the elastic field of an elliptic inhomogeneity under anti-plane shear, J. Appl. Mech., Volume 59 (1992), p. S131-S135

[7] C.Q. Ru; P. Schiavone On the elliptical inclusion in anti-plane shear, Math. Mech. Solids, Volume 1 (1996), pp. 327-333

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

[9] V.A. Lubarda; X. Markenscoff On the absence of Eshelby property for nonellipsoidal inclusions, Int. J. Solids Struct., Volume 35 (1998), pp. 3405-3411

[10] L.P. Liu Solution to the Eshelby conjectures, Proc. R. Soc. Lond. A, Volume 464 (2008), pp. 573-594

[11] H. Kang; E. Kim; G.W. Milton Inclusion pairs satisfying Eshelby's uniformity property, SIAM J. Appl. Math., Volume 69 (2008), pp. 577-595

[12] X. Wang Uniform fields inside two non-elliptical inclusions, Math. Mech. Solids, Volume 17 (2012), pp. 736-761

[13] M. Dai; C.F. Gao; C.Q. Ru Uniform stress fields inside multiple inclusions in an elastic infinite plane under plane deformation, Proc. R. Soc. Lond. A, Volume 471 (2015)

[14] M. Dai; C.Q. Ru; C.F. Gao Uniform strain fields inside multiple inclusions in an elastic infinite plane under anti-plane shear, Math. Mech. Solids, Volume 22 (2017), pp. 114-128

[15] 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

[16] 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

[17] 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

[18] Y.E. Pak Force on a piezoelectric screw dislocation, J. Appl. Mech., Volume 57 (1990), pp. 863-869

[19] Y.E. Pak Circular inclusion problem in antiplane piezoelectricity, Int. J. Solids Struct., Volume 29 (1992), pp. 2403-2419

[20] Z. Suo; C.M. Kuo; D.M. Barnett; J.R. Willis Fracture mechanics for piezoelectric ceramics, J. Mech. Phys. Solids, Volume 40 (1992), pp. 739-765

[21] K.Y. Lee; W.G. Lee; Y.E. Pak Interaction between a semi-infinite crack and a screw dislocation in a piezoelectric material, J. Appl. Mech., Volume 67 (2000), pp. 165-170

[22] X. Wang; P. Schiavone Debonded arc shaped interface conducting rigid line inclusions in piezoelectric composites, C. R. Mecanique, Volume 345 (2017), pp. 724-731

[23] X. Wang; H. Fan A piezoelectric screw dislocation in a bimaterial with surface piezoelectricity, Acta Mech., Volume 226 (2015), pp. 3317-3331

Cité par Sources :

Commentaires - Politique