Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Continuum Mechanics and Thermodynamics
Published in: Continuum Mechanics and Thermodynamics 1/2023

03-01-2023 | Original Article

A partially debonded circular inhomogeneity in nonlinear thermoelectricity

Authors: Xu Wang, Peter Schiavone

Published in: Continuum Mechanics and Thermodynamics | Issue 1/2023

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We study the two-dimensional thermoelectric problem associated with a circular inhomogeneity partially bonded to an infinite matrix subjected to uniform remote electric current density and energy flux. Both the inhomogeneity and the matrix are composed of nonlinearly coupled thermoelectric materials. The four analytic functions characterizing the thermoelectric fields in the two-phase composite are derived rigorously, in closed-form, by solving two Riemann–Hilbert problems with discontinuous coefficients. We obtain elementary expressions for the normal electric current density and normal energy flux along the bonded portion of the circular interface as well as the thermoelectric potential and temperature jumps across the remaining debonded section.
previous article Plate capacitor problem as a benchmark case for verifying the finite element implementation
next article Microscale investigation of phase transformation and plasticity in multi-crystalline shape memory alloy using discrete dislocation–transformation method

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Appendix
Available only for authorised users
Literature
1.
Song, H.P., Gao, C.F., Li, J.: Two-dimensional problem of a crack in thermoelectric materials. J. Therm. Stresses 38, 325–337 (2015)CrossRef
2.
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)CrossRef
3.
Yu, C., Zou, D., Li, Y.H., Yang, H.B., Gao, C.F.: An arc-shaped crack in nonlinear fully coupled thermoelectric materials. Acta Mech. 229, 1989–2008 (2017)CrossRefMATH
4.
Zhang, A.B., Wang, B.L.: Temperature and electric potential fields of an interface crack in a layered thermoelectric or metal/thermoelectric material. Int. J. Therm. Sci. 104, 396–403 (2016)CrossRef
5.
Yu, C., Yang, H., Li, Y., Song, K., Gao, C.: Closed-form solutions for a circular inhomogeneity in nonlinearly coupled thermoelectric materials. Z. Angew. Math. Mech. 99(8), e201800240-1-e201800240-17 (2019)CrossRef
6.
Song, K., Song, H.P., Schiavone, P., Gao, C.F.: Mechanical performance of a thermoelectric composite in the vicinity of an elliptic inhomogeneity. Q. J. Mech. Appl. Math. 72, 429–447 (2019)CrossRefMATH
7.
Wang, X., Schiavone, P.: A coated circular inhomogeneity in nonlinearly coupled thermoelectric materials. J. Eng. Math. 136, 4-1–4-13 (2022)CrossRefMATH
8.
Suo, Z.: Singularities interacting with interfaces and cracks. Int. J. Solids Struct. 25, 1133–1142 (1989)CrossRef
9.
Ru, C.Q.: Analytic solution for Eshelby’s problem of an inclusion of arbitrary shape in a plane or half-plane. ASME J. Appl. Mech. 66, 315–322 (1999)ADSCrossRef
10.
Perlman, A.B., Sih, G.C.: Elastostatic problems of curvilinear cracks in bonded dissimilar materials. Int. J. Eng. Sci. 5, 845–867 (1967)CrossRefMATH
11.
Toya, M.: A crack along the interface of a circular inclusion embedded in an infinite solid. J. Mech. Phys. Solids 22, 325–348 (1974)ADSCrossRefMATH
12.
Herrmann, J.M.: The displacement field due to an interface crack along an elastic inclusion in a differing elastic matrix. Acta Mech. 105, 207–226 (1994)CrossRefMATH
13.
Nagy, P.B., Nayfeh, A.H.: On the thermoelectric magnetic field of spherical and cylindrical inclusions. J. Appl. Phys. 87(10), 7481–7490 (2000)ADSCrossRef
14.
Marin, M., Öchsner, A.: The effect of a dipolar structure on the hölder stability in Green-Naghdi thermoelasticity. Continuum Mech. Thermodyn. 29(6), 1365–1374 (2017)ADSCrossRefMATH
15.
Abouelregal, A.E., Marin, M.: The size-dependent thermoelastic vibrations of nanobeams subjected to harmonic excitation and rectified sine wave heating. Mathematics 8, 1128 (2020)CrossRef
16.
Marin, M., Vlase, S., Öchsner, A., Craciun, E.M.: Some results on the electroacoustic energy flux for micropolar bodies. Continuum Mech. Thermodyn. 34, 1197–1204 (2022)CrossRef
17.
Craciun, E.M., Soós, E.: Anti-plane states in an anisotropic elastic body containing an elliptical hole. Math. Mech. Solids 11(5), 459–466 (2006)CrossRefMATH
18.
Yang, Y., Ma, F.Y., Lei, C.H., Liu, Y.Y., Li, J.Y.: Nonlinear asymptotic homogenization and the effective behavior of layered thermoelectric composites. J. Mech. Phys. Solids 61(8), 1768–1783 (2013)ADSCrossRef
19.
Yang, H.B., Yu, C.B., Tang, J.Y., Qiu, J., Zhang, X.Q.: Electric-current-induced thermal stress around a non-circular rigid inclusion in a two-dimensional nonlinear thermoelectric material. Acta Mech. 231, 4603–4619 (2020)CrossRefMATH
20.
Ting, T.C.T.: Anisotropic Elasticity: Theory and Applications. Oxford University Press, New York (1996)CrossRefMATH
Metadata
Title
A partially debonded circular inhomogeneity in nonlinear thermoelectricity
Authors
Xu Wang
Peter Schiavone
Publication date
03-01-2023
Publisher
Springer Berlin Heidelberg
Published in
Continuum Mechanics and Thermodynamics / Issue 1/2023
Print ISSN: 0935-1175
Electronic ISSN: 1432-0959
DOI
https://doi.org/10.1007/s00161-022-01181-w

Other articles of this Issue 1/2023

Continuum Mechanics and Thermodynamics 1/2023 Go to the issue

Original Article

Extended tolerance modelling of dynamic problems for thin uniperiodic cylindrical shells

Original Article

Internal resonance and bending analysis of thick visco-hyper-elastic arches

Original Article

Plate capacitor problem as a benchmark case for verifying the finite element implementation

Original Article

Thermomagnetic behavior of a semiconductor material heated by pulsed excitation based on the fourth-order MGT photothermal model

Original Article

Microscale investigation of phase transformation and plasticity in multi-crystalline shape memory alloy using discrete dislocation–transformation method

Original Article

A general stress solution in a plastic region near a traction-free boundary of arbitrary shape under plane-strain conditions

Premium Partners

    Image Credits