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Published in: Acta Mechanica 7/2020

18-04-2020 | Original Paper

Design of a neutral elastic inhomogeneity via thermal expansion

Authors: H. P. Song, K. Song, P. Schiavone, C. F. Gao

Published in: Acta Mechanica | Issue 7/2020

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Abstract

A neutral elastic inhomogeneity does not affect the existing stress field when inserted into an elastic body. It has been shown that no such inhomogeneity can exist under the classical assumption of a perfectly bonded interface between the inhomogeneity and the surrounding material. We show that by introducing a suitable temperature field inside the inhomogeneity it is indeed possible to achieve neutrality regardless of the perfect bonding assumption. Specifically, we show that a nonuniform internal temperature field can induce neutrality in an inhomogeneity in the form of an elastic ring with concentric internal and external boundaries of arbitrary shape. Noting that such a temperature field can be identified also in the case of an unpunched inhomogeneity when the inhomogeneity is line-shaped, we further prove that even a flake-shaped inhomogeneity can be made neutral if the thickness of the flake is much smaller than its length. In the case that the elastic body surrounding the unpunched inhomogeneity is subjected to remote hydrostatic loading, the temperature field within the inhomogeneity will remain uniform and independent of the shape of the inhomogeneity. In fact, in this case, the temperature field inside the inhomogeneity depends only on the elastic parameters of the composite and the direction of the remote loading and can be higher or lower than the operating temperature of the composite.
Literature
1.
go back to reference Milton, G.W., Serkov, S.K.: Neutral coated inclusions in conductivity and anti-plane elasticity. Proc. R. Soc. A 457, 1973–1997 (2001)MathSciNetCrossRef Milton, G.W., Serkov, S.K.: Neutral coated inclusions in conductivity and anti-plane elasticity. Proc. R. Soc. A 457, 1973–1997 (2001)MathSciNetCrossRef
2.
go back to reference He, X., Wu, L.: Thermal transparency with the concept of neutral inclusion. Phys. Rev. E 88, 033201 (2013)CrossRef He, X., Wu, L.: Thermal transparency with the concept of neutral inclusion. Phys. Rev. E 88, 033201 (2013)CrossRef
3.
go back to reference Yang, T., Huang, L., Chen, F., Xu, W.: Heat flux and temperature field cloaks for arbitrarily shaped objects. J. Phys. D Appl. Phys. 46, 305102 (2013)CrossRef Yang, T., Huang, L., Chen, F., Xu, W.: Heat flux and temperature field cloaks for arbitrarily shaped objects. J. Phys. D Appl. Phys. 46, 305102 (2013)CrossRef
4.
go back to reference Chen, H., Chan, C.T.: Acoustic cloaking in three dimensions using acoustic metamaterials. Appl. Phys. Lett. 91, 183518 (2007)CrossRef Chen, H., Chan, C.T.: Acoustic cloaking in three dimensions using acoustic metamaterials. Appl. Phys. Lett. 91, 183518 (2007)CrossRef
5.
go back to reference Wang, X., Schiavone, P.: Neutral coated circular inclusions in finite plane elasticity of harmonic materials. Eur. J. Mech. A Solids 33, 75–81 (2012)MathSciNetCrossRef Wang, X., Schiavone, P.: Neutral coated circular inclusions in finite plane elasticity of harmonic materials. Eur. J. Mech. A Solids 33, 75–81 (2012)MathSciNetCrossRef
6.
go back to reference Song, K., Song, H.P., Schiavone, P., Gao, C.F.: Thermal expansion induced neutrality of a circular and an annular elastic inhomogeneity. J. Appl. Mech. 86, 121010 (2019)CrossRef Song, K., Song, H.P., Schiavone, P., Gao, C.F.: Thermal expansion induced neutrality of a circular and an annular elastic inhomogeneity. J. Appl. Mech. 86, 121010 (2019)CrossRef
7.
go back to reference Mansfield, E.H.: Neutral iioles in plane sheet–reinforced iioles which are elastically equivalent to the uncut sheet. Q. J. Mech. Appl. Math. 6, 370–378 (1953)CrossRef Mansfield, E.H.: Neutral iioles in plane sheet–reinforced iioles which are elastically equivalent to the uncut sheet. Q. J. Mech. Appl. Math. 6, 370–378 (1953)CrossRef
9.
go back to reference Ru, C.Q.: Interface design of neutral elastic inclusions. Int. J. Solids Struct. 35, 559–572 (1998)CrossRef Ru, C.Q.: Interface design of neutral elastic inclusions. Int. J. Solids Struct. 35, 559–572 (1998)CrossRef
10.
go back to reference Tipler, P.A., Mosca, G.: Physics for Scientists and Engineers. Worth Publishers, New York, NY (2008) Tipler, P.A., Mosca, G.: Physics for Scientists and Engineers. Worth Publishers, New York, NY (2008)
11.
go back to reference Zimmerman, R.W., Lutz, M.P.: Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder. J. Therm. Stresses 22, 177–188 (1999)CrossRef Zimmerman, R.W., Lutz, M.P.: Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder. J. Therm. Stresses 22, 177–188 (1999)CrossRef
12.
go back to reference Jafari, M.: Thermal stress analysis of orthotropic plate containing a rectangular hole using complex variable method. Eur. J. Mech. A Solids 73, 212–223 (2019)MathSciNetCrossRef Jafari, M.: Thermal stress analysis of orthotropic plate containing a rectangular hole using complex variable method. Eur. J. Mech. A Solids 73, 212–223 (2019)MathSciNetCrossRef
13.
go back to reference Abtew, M., Selvaduray, G.: Lead-free solders in microelectronics. Mater. Sci. Eng. R 27, 95–141 (2000)CrossRef Abtew, M., Selvaduray, G.: Lead-free solders in microelectronics. Mater. Sci. Eng. R 27, 95–141 (2000)CrossRef
14.
go back to reference Kingery, W.D.: Factors affecting thermal stress resistance of ceramic materials. J. Am. Ceram. Soc. 38, 3–15 (1955)CrossRef Kingery, W.D.: Factors affecting thermal stress resistance of ceramic materials. J. Am. Ceram. Soc. 38, 3–15 (1955)CrossRef
15.
go back to reference Liew, K.M., Kitipornchai, S., Zhang, X.Z., Lim, C.W.: Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders. Int. J. Solids Struct. 40, 2355–2380 (2003)CrossRef Liew, K.M., Kitipornchai, S., Zhang, X.Z., Lim, C.W.: Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders. Int. J. Solids Struct. 40, 2355–2380 (2003)CrossRef
16.
go back to reference Song, K., Song, H.P., Schiavone, P., Gao, C.F.: Thermal stress induced by electric current in the vicinity of an elliptic inclusion in an infinite plate. J. Therm. Stresses 42, 976–992 (2019)CrossRef Song, K., Song, H.P., Schiavone, P., Gao, C.F.: Thermal stress induced by electric current in the vicinity of an elliptic inclusion in an infinite plate. J. Therm. Stresses 42, 976–992 (2019)CrossRef
17.
go back to reference Song, K., Song, H.P., Schiavone, P., Gao, C.F.: Electric current induced thermal stress around a bi-material interface crack. Eng. Fract. Mech. 208, 1–12 (2019)CrossRef Song, K., Song, H.P., Schiavone, P., Gao, C.F.: Electric current induced thermal stress around a bi-material interface crack. Eng. Fract. Mech. 208, 1–12 (2019)CrossRef
18.
go back to reference Song, K., Song, H.P., Li, M., Schiavone, P., Gao, C.F.: Effective properties of a thermoelectric composite containing an elliptic inhomogeneity. Int. J. Heat Mass Transf. 135, 1319–1326 (2019)CrossRef Song, K., Song, H.P., Li, M., Schiavone, P., Gao, C.F.: Effective properties of a thermoelectric composite containing an elliptic inhomogeneity. Int. J. Heat Mass Transf. 135, 1319–1326 (2019)CrossRef
19.
go back to reference Muskhelishvili, N.I.: Some Basic Problems of Mathematical Theory of Elasticity. Noordhoff, Leyden (1975)MATH Muskhelishvili, N.I.: Some Basic Problems of Mathematical Theory of Elasticity. Noordhoff, Leyden (1975)MATH
20.
go back to reference Song, K., Schiavone, P.: Thermally neutral nano-hole and its effect on the elastic field. Eur. J. Mech. A/Solids 81, 103973 (2020)MathSciNetCrossRef Song, K., Schiavone, P.: Thermally neutral nano-hole and its effect on the elastic field. Eur. J. Mech. A/Solids 81, 103973 (2020)MathSciNetCrossRef
21.
go back to reference Zhao, J.H., Du, Y., Morgen, M., Ho, P.S.: Simultaneous measurement of Young’s modulus, Poisson ratio, and coefficient of thermal expansion of thin films on substrates. J. Appl. Phys. 87, 1575–1577 (2000)CrossRef Zhao, J.H., Du, Y., Morgen, M., Ho, P.S.: Simultaneous measurement of Young’s modulus, Poisson ratio, and coefficient of thermal expansion of thin films on substrates. J. Appl. Phys. 87, 1575–1577 (2000)CrossRef
22.
go back to reference Wang, S., Dai, M., Ru, C.Q., Gao, C.F.: Stress field around an arbitrarily shaped nanosized hole with surface tension. Acta Mech. 225, 3453–3462 (2014)MathSciNetCrossRef Wang, S., Dai, M., Ru, C.Q., Gao, C.F.: Stress field around an arbitrarily shaped nanosized hole with surface tension. Acta Mech. 225, 3453–3462 (2014)MathSciNetCrossRef
23.
go back to reference Chen, S.C., Jong, W.R., Chang, J.A.: Dynamic mold surface temperature control using induction heating and its effects on the surface appearance of weld line. J. Appl. Polym. Sci. 101, 1174–1180 (2006)CrossRef Chen, S.C., Jong, W.R., Chang, J.A.: Dynamic mold surface temperature control using induction heating and its effects on the surface appearance of weld line. J. Appl. Polym. Sci. 101, 1174–1180 (2006)CrossRef
24.
25.
go back to reference Dundurs, J.: Effect of elastic constants on stress in a composite under plane deformation. J. Compos. Mater. 1, 310–322 (1967)CrossRef Dundurs, J.: Effect of elastic constants on stress in a composite under plane deformation. J. Compos. Mater. 1, 310–322 (1967)CrossRef
Metadata
Title
Design of a neutral elastic inhomogeneity via thermal expansion
Authors
H. P. Song
K. Song
P. Schiavone
C. F. Gao
Publication date
18-04-2020
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 7/2020
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-020-02677-9

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