Abstract
The plane problem of a non-circular rigid inhomogeneity embedded in an infinite thermoelectric matrix under a uniform remote electric current is investigated based on the complex variable method. The inclusion is assumed to be electrically insulated and thermally conductive. Techniques of Faber and Fourier series are used to solve the corresponding boundary value problems. The obtained results show that the shape, bluntness and heat conductivity of the inclusion have a significant effect on the interfacial thermal stress distribution induced by the external electric current. In addition, the Von Mises stress concentration around a non-circular inclusion could be lower than that around a circular inclusion by designing the shape and orientation of the inclusion properly.
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References
DiSalvo, F.J.: Thermoelectric cooling and power generation. Science 285(5428), 703–706 (1999)
Zhang, X., Zhao, L.D.: Thermoelectric materials: energy conversion between heat and electricity. J. Mater. 1(2), 92–105 (2015)
Tritt, T.M., Subramanian, M.A.: Thermoelectric materials, phenomena, and applications: a bird’s eye view. MRS Bull. 31(3), 188–198 (2006)
Bell, L.E.: Cooling, heating, generating power, and recovering waste heat with thermoelectric systems. Science 321, 1457–1461 (2008)
He, W., Zhang, G., Zhang, X., Ji, J., Li, G., Zhao, X.: Recent development and application of thermoelectric generator and cooler. Appl. Energy 143, 1–25 (2015)
He, J., Tritt, T.M.: Advances in thermoelectric materials research: looking back and moving forward. Science 357(6358), eaak9997 (2017)
Kim, G.H., Shao, L., Zhang, K., Pipe, K.P.: Engineered doping of organic semiconductors for enhanced thermoelectric efficiency. Nat. Mater. 12(8), 719 (2013)
Meng, C., Liu, C., Fan, S.: A promising approach to enhanced thermoelectric properties using carbon nanotube networks. Adv. Mater. 22(4), 535–539 (2010)
Li, G., An, Q., Li, W., Goddard III, W.A., Zhai, P., Zhang, Q., Snyder, G.J.: Brittle failure mechanism in thermoelectric skutterudite CoSb3. Chem. Mater. 27(18), 6329–6336 (2015)
Jafari, M., Nazari, M.B., Nasabe, A.T.: Study of the effective parameters on stress distribution around triangular hole in metallic plates subjected to uniform heat flux. J. Therm. Stresses 39(3), 333–344 (2016)
Dai, M., Sun, H.: Thermo-elastic analysis of a finite plate containing multiple elliptical inclusions. Int. J. Mech. Sci. 75, 337–344 (2013)
Wang, X., Shen, Y.P.: A solution of the elliptic piezoelectric inclusion problem under uniform heat flux. Int. J. Solids Struct. 38(15), 2503–2516 (2001)
Yang, Q.Q., Gao, C.F.: Non-axisymmetric thermal stress of a functionally graded coated circular inclusion in an infinite matrix. Mech. Res. Commun. 50, 27–32 (2013)
Wang, P., Wang, B.L., Wang, K.F., Hirakata, H., Zhang, C.: Analysis of three-dimensional ellipsoidal inclusions in thermoelectric solids. Int. J. Eng. Sci. 142, 158–169 (2019)
Dai, M., Gao, C.F.: Perturbation solution of two arbitrarily-shaped holes in a piezoelectric solid. Int. J. Mech. Sci. 88, 37–45 (2014)
Pérez-Aparicio, J.L., Taylor, R.L., Gavela, D.: Finite element analysis of nonlinear fully coupled thermoelectric materials. Comput. Mech. 40(1), 35–45 (2007)
Wang, B.L.: A finite element computational scheme for transient and nonlinear coupling thermoelectric fields and the associated thermal stresses in thermoelectric materials. Appl. Therm. Eng. 110, 136–143 (2017)
Yu, C.B., Zou, D.F., Li, Y.H., Yang, H.B., Gao, C.F.: An arc-shaped crack in nonlinear fully coupled thermoelectric materials. Acta Mech. 229(5), 1989–2008 (2018)
Song, H.P., Gao, C.F., Li, J.: Two-dimensional problem of a crack in thermoelectric materials. J. Therm. Stresses 38(3), 325–337 (2015)
Zhang, A.B., Wang, B.L.: Explicit solutions of an elliptic hole or a crack problem in thermoelectric materials. Eng. Fract. Mech. 151, 11–21 (2016)
Wang, P., Wang, B.L.: Thermoelectric fields and associated thermal stresses for an inclined elliptic hole in thermoelectric materials. Int. J. Eng. Sci. 119, 93–108 (2017)
Yu, C.B., Yang, H.B., Song, K., Gao, C.F.: Stress concentration around an arbitrarily-shaped hole in nonlinear fully coupled thermoelectric materials. J. Mech. Mater. Struct. 14(2), 259–276 (2019)
Bahk, J., Fang, H., Yazawa, K., Shakouri, A.: Flexible thermoelectric materials and device optimization for wearable energy harvesting. J. Mater. Chem. C 3(40), 10362–10374 (2015)
Zhang, A.B., Wang, B.L., Wang, J., Du, K.: Two-dimensional problem of thermoelectric materials with an elliptic hole or a rigid inclusion. Int. J. Therm. Sci. 117, 184–195 (2017)
Wang, P., Wang, B.L., Wang, K.F., Cui, Y.J.: Analysis of inclusion in thermoelectric materials: the thermal stress field and the effect of inclusion on thermoelectric properties. Compos. B Eng. 166, 130–138 (2019)
Wang, X., Shen, Y.P.: Inclusions of arbitrary shape in magnetoelectroelastic composite materials. Int. J. Eng. Sci. 41(1), 85–102 (2003)
Jafari, M., Nazari, M.B., Taherinasab, A.: Thermal stress analysis in metallic plates with a non-circular hole subjected to uniform heat flux. Eur. J. Mech. A/Solids 59, 356–363 (2016)
Dai, M., Gao, C.F., Ru, C.Q.: Surface tension-induced stress concentration around a nanosized hole of arbitrary shape in an elastic half-plane. Meccanica 49(12), 2847–2859 (2014)
Dai, M., Gao, C.F., Ru, C.Q.: Uniform stress fields inside multiple inclusions in an elastic infinite plane under plane deformation. Proc. R. Soc. A 471(2177), 20140933 (2015)
Dai, M., Gao, C.F.: Non-circular nano-inclusions with interface effects that achieve uniform internal strain fields in an elastic plane under anti-plane shear. Arch. Appl. Mech. 86(7), 1295–1309 (2016)
Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity, 4th edn, pp. 134–147. Noordhoff, Leyden (1975)
Liu, L.P.: A continuum theory of thermoelectric bodies and effective properties of thermoelectric composites. Int. J. Eng. Sci. 55, 35–53 (2012)
Zhang, A.B., Wang, B.L.: Crack tip field in thermoelectric media. Theor. Appl. Fract. Mech. 66, 33–36 (2013)
Hasebe, N., Bucher, C., Heuer, R.: Analyses of thermal conduction and stress induced by electric current in an infinite thin plate with an elliptical hole. J. Therm. Stresses 32(10), 1065–1086 (2009)
Gao, C.F., Noda, N.: Faber series method for two-dimensional problems of an arbitrarily shaped inclusion in piezoelectric materials. Acta Mech. 171, 1–13 (2004)
Yang, W.H.: A generalized Von Mises criterion for yield and fracture. J. Appl. Mech. 47, 297 (1980)
Tang, J.Y., Yang, H.B.: An alternative numerical scheme for calculating the thermal stresses around an inclusion of arbitrary shape in an elastic plane under uniform remote in-plane heat flux. Acta Mech. 230(7), 2399–2412 (2019)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Nos. 11902116 and 11972163) and Natural Science Foundation of Guangdong Province (No. 2017A030313014).
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Yang, HB., Yu, CB., Tang, JY. et al. Electric-current-induced thermal stress around a non-circular rigid inclusion in a two-dimensional nonlinear thermoelectric material. Acta Mech 231, 4603–4619 (2020). https://doi.org/10.1007/s00707-020-02770-z
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DOI: https://doi.org/10.1007/s00707-020-02770-z