×

Thermal-elastic field around an elliptical nano-inclusion with interface conduction and interface stress effects. (English) Zbl 1533.74022

Summary: We analyze the thermo-elastic behavior of an elliptical nano-inclusion incorporating interface conduction and interface stress effects when embedded in an infinite matrix under plane deformation. The effect of interface conduction is represented by a highly conductive interface model, while that of interface stress is described via the complete version of the Gurtin-Murdoch model with the residual interface tension. Based on the complex variable method, we obtain, for the case of a constant heat flux applied remotely on the matrix, the uncoupled steady-state temperature field and thermal stress field using conformal mapping and series expansion techniques. We present also a group of numerical examples to illustrate the influence of interface conduction and interface effects on the stress field around the inclusion relative to the aspect ratio and relative stiffness of the inclusion.

MSC:

74F05 Thermal effects in solid mechanics
74B05 Classical linear elasticity
74E05 Inhomogeneity in solid mechanics
74M25 Micromechanics of solids
74S70 Complex-variable methods applied to problems in solid mechanics
Full Text: DOI

References:

[1] Miller, RE; Shenoy, VB, Size-dependent elastic properties of nanosized structural elements, Nanotechnology, 11, 3, 139-147 (2000) · doi:10.1088/0957-4484/11/3/301
[2] Shenoy, VB, Size-dependent rigidities of nanosized torsional elements, Int. J. Solids Struct., 39, 15, 4039-4052 (2002) · Zbl 1040.74007 · doi:10.1016/S0020-7683(02)00261-5
[3] Sharma, P.; Ganti, S.; Bhate, N., Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities, Am. Inst. Phys., 82, 4, 535-537 (2003)
[4] Gurtin, ME; Murdoch, AI, A continuum theory of elastic material surfaces, Arch. Ration. Mech. Anal., 57, 4, 291-323 (1975) · Zbl 0326.73001 · doi:10.1007/BF00261375
[5] Gurtin, ME; Ian, A., Surface stress in solids, Int. J Solids Struct., 14, 6, 431-440 (1978) · Zbl 0377.73001 · doi:10.1016/0020-7683(78)90008-2
[6] Gurtin, ME; Weissmuller, J.; Larche, F., A general theory of curved deformable interface in solids at equilibrium, Philos. Mag. A, 78, 5, 1093-1109 (1998) · doi:10.1080/01418619808239977
[7] Muskhelishvili, NI, Some Basic Problems of the Mathematical Theory of Elasticity (1975), Groningen: Noordhoff, Groningen · Zbl 0297.73008
[8] Tian, L.; Rajapakse, RKND, Analytical solution for size-dependent elastic field of a nanoscale circular inhomogeneity, J. Appl. Mech., 74, 568-574 (2006) · Zbl 1111.74662 · doi:10.1115/1.2424242
[9] Luo, J.; Wang, X., On the anti-plane shear of an elliptic nano inhomogeneity, Eur. J. Mech. A Solids., 28, 5, 926-934 (2009) · Zbl 1176.74045 · doi:10.1016/j.euromechsol.2009.04.001
[10] Sharma, P.; Ganti, S.; Bhate, N., Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities, Appl. Phys. Lett., 82, 4, 535-537 (2003) · doi:10.1063/1.1539929
[11] Wang, S.; Dai, M.; Ru, CQ; Gao, CF, Surface tension-induced interfacial stresses around a nanoscale inclusion of arbitrary shape, Z. Angew. Math. Phys., 68, 127 (2017) · Zbl 1394.74016 · doi:10.1007/s00033-017-0876-7
[12] Wang, GF; Wang, TJ, Deformation around a nanosized elliptical hole with surface effect, Appl. Phys. Lett., 89, 561 (2006)
[13] Hatami, MH; Shodja, HM, Effects of interface conditions on thermo-mechanical fields of multi-phase nano-fibers/particles, J. Therm. Stresses, 32, 1166-1180 (2009) · doi:10.1080/01495730903249243
[14] Gordeliy, E.; Crouch, SL; Mogilevskaya, SG, Transient heat conduction in a medium with multiple spherical cavities, Int. J. Numer. Meth. Eng., 77, 751-775 (2009) · Zbl 1156.80324 · doi:10.1002/nme.2430
[15] Gordeliy, E.; Crouch, SL; Mogilevskaya, SG, Transient heat conduction in a medium with two circular cavities: semi-analytical solution, Int. J. Heat Mass Transf., 51, 3556-3570 (2008) · Zbl 1148.80315 · doi:10.1016/j.ijheatmasstransfer.2007.10.021
[16] Dai, M.; Gao, CF; Schiavone, P., Closed-form solution for a circular nano-inhomogeneity with interface effects in an elastic plane under uniform remote heat flux, J. Appl. Math., 82, 2, 384-395 (2016) · Zbl 1408.74015
[17] Tian, L.; Rajapakse, R., Elastic field of an isotropic matrix with a nanoscale elliptical inhomogeneity, Int. J. Solids Struct., 44, 24, 7988-8005 (2007) · Zbl 1167.74525 · doi:10.1016/j.ijsolstr.2007.05.019
[18] Dai, M.; Gharahi, A.; Schiavone, P., Note on the deformation-induced change in the curvature of a material surface in plane deformations, Mech. Res. Commun., 94, 88-90 (2018) · doi:10.1016/j.mechrescom.2018.10.001
[19] Dai, M.; Wang, YJ; Schiavone, P., Integral-type stress boundary condition in the complete gurtin-murdoch surface model with accompanying complex variable representation, J. Elast., 134, 235-241 (2019) · Zbl 1412.74008 · doi:10.1007/s10659-018-9695-0
[20] Zhang, R., Tang, J.Y., Qiu, J., Dai, M.: Role of interface tension in the thermo-elastic analysis of inclusions: Unified formulation and closed-form results. J. Therm. Stress. (2023)
[21] Dai, M.; Sun, HY, Thermo-elastic analysis of a finite plate containing multiple elliptical inclusions, Int. J. Mech. Sci., 75, 337-344 (2013) · doi:10.1016/j.ijmecsci.2013.07.012
[22] Li, C.; Huang, C.; Wang, S.; Cai, D., A modified Laurent series for hole/inclusion problems in plane elasticity, Z. Angew. Math. Phys., 72, 124 (2021) · Zbl 1468.30010 · doi:10.1007/s00033-021-01552-4
[23] Pei, PY; Yang, HB; Dai, M., Consistency of the boundary value problem of an elastic body involving surface tension in small deformations, Math. Mech. Solids, 28, 6, 1488-1499 (2022) · doi:10.1177/10812865221122151
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.