Comptes Rendus
no. 6
A coated rigid elliptical inclusion loaded by a couple in the presence of uniform interfacial and hoop stresses
Xu Wang1; Peter Schiavone2 
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 346 (2018) no. 6, pp. 477-481.

We consider a confocally coated rigid elliptical inclusion, loaded by a couple and introduced into a remote uniform stress field. We show that uniform interfacial and hoop stresses along the inclusion–coating interface can be achieved when the two remote normal stresses and the remote shear stress each satisfy certain conditions. Our analysis indicates that: (i) the uniform interfacial tangential stress depends only on the area of the inclusion and the moment of the couple; (ii) the rigid-body rotation of the rigid inclusion depends only on the area of the inclusion, the coating thickness, the shear moduli of the composite and the moment of the couple; (iii) for given remote normal stresses and material parameters, the coating thickness and the aspect ratio of the inclusion are required to satisfy a particular relationship; (iv) for prescribed remote shear stress, moment and given material parameters, the coating thickness, the size and aspect ratio of the inclusion are also related. Finally, a harmonic rigid inclusion emerges as a special case if the coating and the matrix have identical elastic properties.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2018.03.005
Keywords: Rigid inclusion, Confocal coating, Uniform interfacial and hoop stresses, Couple, Rigid body rotation, Harmonic inclusion

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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Xu Wang; Peter Schiavone. A coated rigid elliptical inclusion loaded by a couple in the presence of uniform interfacial and hoop stresses. Comptes Rendus. Mécanique, Volume 346 (2018) no. 6, pp. 477-481. doi : 10.1016/j.crme.2018.03.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.03.005/

[1] C.Q. Ru Three-phase elliptical inclusions with internal uniform hydrostatic stresses, J. Mech. Phys. Solids, Volume 47 (1999), pp. 259-273

[2] G.P. Cherepanov Inverse problems of the plane theory of elasticity, Prikl. Mat. Meh., Volume 38 (1974), pp. 963-979

[3] R. Richards; G.S. Bjorkman Harmonic shapes and optimum design, J. Eng. Mech. Div., Proc. ASCE, Volume 106 (1980), pp. 1125-1134

[4] L.T. Wheeler The problem of minimizing stress concentration at a rigid inclusion, J. Appl. Mech., Volume 52 (1985), pp. 83-86

[5] L.T. Wheeler Stress minimum forms for elastic solids, Appl. Mech. Rev., Volume 45 (1992), pp. 1-11

[6] X. Wang; X.L. Gao On the uniform stress state inside an inclusion of arbitrary shape in a three-phase composite, Z. Angew. Math. Phys., Volume 62 (2011), pp. 1101-1116

[7] X. Wang; P. Schiavone Harmonic elastic inclusions in the presence of point moment, C. R. Mecanique, Volume 345 (2017), pp. 922-929

[8] N.I. Muskhelishvili Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff Ltd., Groningen, The Netherlands, 1953

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

[10] G.S. Bjorkman; R. Richards Harmonic holes – an inverse problem in elasticity, J. Appl. Mech., Volume 43 (1976), pp. 414-418

[11] G.S. Bjorkman; R. Richards Harmonic holes for nonconstant fields, J. Appl. Mech., Volume 46 (1979), pp. 573-576

[12] C.Q. Ru A new method for an inhomogeneity with stepwise graded interphase under thermomechanical loadings, J. Elast., Volume 56 (1999), pp. 107-127

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