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Acta Mechanica
Published in: Acta Mechanica 5/2020

05-02-2020 | Original Paper

Design equations of neutral coated inhomogeneities with confocal elliptical interfaces in longitudinal shear

Authors: M. A. Kattis, P. Papanikos, M. E. Tzamali, E. Gkouti

Published in: Acta Mechanica | Issue 5/2020

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Abstract

The design equations of a neutral coated inhomogeneity with confocal elliptic interfaces are derived, when the elastic matrix is subjected to a longitudinal shear. The neutrality of such an inhomogeneity is achieved by inserting an appropriate coating between inhomogeneity and matrix provided that the longitudinal shear applied to the matrix is parallel to one of the elliptical semi-axes. The above general results are verified numerically by designing specific neutral inhomogeneities using finite elements.
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Literature
1.
Mansfield, E.H.: Neutral holes in plane sheet: reinforced holes which are elastically equivalent to the uncut sheet. Q. J. Mech. Appl. Math. 6, 370–378 (1953)MathSciNetCrossRef
2.
3.
Hashin, Z., Shtrikman, S.: A variation approach to the theory of the effective magnetic permeability of multiphase materials. J. Appl. Phys. 33, 3125–3131 (1962)CrossRef
4.
Bjorkman Jr., G.S., Richards Jr., R.: Neutral holes; theory and design. J. Eng. Mech. Div. 108, 945–960 (1982)
5.
Budiansky, B., Hutchinson, J.W., Evans, A.E.: On neutral holes in tailored, layered sheets. J. Appl. Mech. 60, 1056–1058 (1993)CrossRef
6.
Senocak, E., Waas, A.M.: Neutral cutouts in laminated plates. Mech. Compos. Mater. Struct. 2, 71–89 (1995)CrossRef
7.
Benveniste, Y., Miloh, T.: Neutral inhomogeneities in conduction phenomena. J. Mech. Phys. Solids 47, 1873–1892 (1999)MathSciNetCrossRef
8.
Benveniste, Y., Chen, T.: On the Saint-Venant torsion of composite bars with imperfect interfaces. Proc. R. Soc. Lond. A 457, 231–255 (2001)MathSciNetCrossRef
9.
Milton, G.W., Serkov, S.K.: Neutral coated inclusions in conductivity and anti-plane elasticity. Proc. R. Soc. Lond. A 457, 1973–1997 (2001)MathSciNetCrossRef
10.
Chen, T., Benveniste, Y., Chuang, P.C.: Exact solutions in torsion of composite bars: thickly coated neutral inhomogeneities and composite cylinder assemblages. Proc. R. Soc. Lond. A 458, 1719–1759 (2002)CrossRef
11.
Vasudevan, M., Schiavone, P.: Design of neutral inhomogeneities in the case of non-uniform loading. Int. J. Eng. Sci. 43, 1081–1091 (2005)CrossRef
12.
Ru, C.Q.: Interface design of neutral elastic inclusions. Int. J. Solids Struct. 35, 557–572 (1998)CrossRef
13.
Benveniste, Y., Miloh, T.: Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech. Mater. 33, 309–323 (2001)CrossRef
14.
Benveniste, Y.: A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media. J. Mech. Phys. Solids 54, 708–734 (2006)MathSciNetCrossRef
15.
Benveniste, Y.: Corrigendum to: a general interface model for a three-dimensional curved anisotropic interphase between two anisotropic media. J. Mech. Phys. Solids 54, 708–734 (2006)MathSciNetCrossRef
16.
Benveniste, Y.: Corrigendum to: a general interface model for a three-dimensional curved anisotropic interphase between two anisotropic media. J. Mech. Phys. Solids 55, 666–667 (2007)MathSciNetCrossRef
17.
18.
19.
Jarczyk, P., Mityushev, V.: Neutral coated inclusions of finite conductivity. Proc. R. Soc. A 468, 954–970 (2012)CrossRef
20.
Ru, C.Q., Schiavone, P., Mioduchowski, A.: Uniformity of stresses within a three-phase elliptic inclusion in anti-plane shear. J. Elast. 52, 121–128 (1998)MathSciNetCrossRef
21.
Ru, C.Q.: Three-phase elliptical inclusions with internal uniform hydrostatic stresses. J. Mech. Phys. Solids 47, 259–273 (1999)MathSciNetCrossRef
22.
Kattis, M.A., Providas, E.: Two-phase potentials in anisotropic elasticity: antiplane deformation. Int. J. Eng. Sci. 36, 801–811 (1998)MathSciNetCrossRef
23.
Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity (Trans. by Radok, J.R.M.). Noordhoff (1953)
24.
25.
Christensen, R.M., Lo, K.H.: Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27, 315–330 (1979)CrossRef
26.
Cherkaoui, M., Muller, D., Sabar, H., Berveiller, M.: Thermoelastic behavior of composites with coated reinforcements: a micromechanical approach and applications. Comput. Mater. Sci. 5, 45–52 (1996)CrossRef
27.
Cherkaoui, M., Sabar, H., Berveiller, M.: Elastic composites with coated reinforcement: a micromechanical approach for nonhomothetic topology. Int. J. Eng. Sci. 33, 829–843 (1955)MathSciNetCrossRef
28.
Jiang, C.P., Cheung, Y.K.: A fiber/matrix/composite model with a combined confocal elliptical cylinder unit cell for predicting the effective longitudinal shear modulus. Int. J. Solids Struct. 30, 3977–3987 (1998)CrossRef
29.
Hashin, Z.: The interphase/imperfect interface in elasticity with application to coated fiber composites. J. Mech. Phys. Solids 50, 2309–2537 (2002)MathSciNetCrossRef
30.
Duan, H.L., Karihaloo, B.L., Wang, J., Yi, X.: Strain distributions in nano-onions with uniform and non-uniform compositions. Nanotechnology 17, 3380–3387 (2006)CrossRef
31.
Bonfoh, N., Hounkpati, V., Sabar, H.: New micromechanical approach of the coated inclusion problem: exact solution and applications. Comput. Mater. Sci. 62, 175–183 (2012)CrossRef
32.
Markenscoff, X., Dundurs, J.: Annular inhomogeneities with eigenstrain and interphase modeling. J. Mech. Phys. Solids 64, 468–472 (2014)MathSciNetCrossRef
Metadata
Title
Design equations of neutral coated inhomogeneities with confocal elliptical interfaces in longitudinal shear
Authors
M. A. Kattis
P. Papanikos
M. E. Tzamali
E. Gkouti
Publication date
05-02-2020
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 5/2020
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-020-02626-6

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