On spatial vs referential isotropic fourier’s law in finite deformation thermomechanics

• Autorzy: Wcisło Balbina , Pamin Jerzy , Rose Lars , Menzel Andreas

Identyfikatory

DOI

10.24423/EngTrans.2460.20230214

• Języki publikacji: EN

Abstrakty

EN

This paper deals with the issue of isotropic heat conduction in thermomechanical largestrain problems. The aim of the paper is a comparison of different variants of Fourier’s law used in the literature for a large strain problem. In particular, Fourier’s law is specified either in the reference or in the deformed configuration by using different options of heat flux density vectors which are presented and discussed. The paper includes working examples to illustrate the presented theory. Moreover, different formulations of Fourier’s law are tested by using the finite element method to investigate the influence of the applied variant on simulation results. The analysis reveals that in a strongly deformed area the temperature distribution varies.

Słowa kluczowe

EN

heat conduction; isotropic Fourier’s law; large strains; thermomechanical coupling

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2023
• Tom: Vol. 71, iss. 1
• Strony: 111--140
• Opis fizyczny: Bibliogr. 27 poz., rys., tab., wykr.

Twórcy

autor

Wcisło Balbina

• Chair of Computational Engineering, Cracow University of Technology Cracow, Poland

autor

Pamin Jerzy

• Chair of Computational Engineering, Cracow University of Technology Cracow, Poland

autor

Rose Lars

• Institute of Mechanics, TU Dortmund University Dortmund, Germany

autor

Menzel Andreas

• Division of Solid Mechanics, Lund University Lund, SwedenInstitute of Mechanics, TU Dortmund University Dortmund, Germany
• Division of Solid Mechanics, Lund University Lund, Sweden

Bibliografia

• 1. Abeyaratne R., Continuum Mechanics, Volume II of Lecture Notes on the Mechanics of Solids, Electronic Publication, 2020, http://web.mit.edu/abeyaratne/lecture notes.html.
• 2. Abeyaratne R., Knowles J.K., On the stability of thermoelastic materials, Journal of Elasticity, 53: 199–213, 1999, doi: 10.1023/A:1007513631783.
• 3. Bonet J., Wood R.D., Nonlinear Continuum Mechanics for Finite Element Analysis, 2nd ed., Cambridge University Press, Cambridge 2008.
• 4. Canadija ˆ M., Brnić J., Associative coupled thermoplasticity at finite strain with temperature-dependent material parameters, International Journal of Plasticity, 20(10): 1851–1874, 2004, doi: 10.1016/j.ijplas.2003.11.016.
• 5. de Souza Neto E.A., Perić D., Owen D.R.J., Computational Methods for Plasticity. Theory and Applications, John Wiley & Sons, Ltd, Chichester 2008.
• 6. Haupt P., Continuum Mechanics and Theory of Materials, Springer-Verlag, Berlin 2002.
• 7. Holzapfel G.A., Simo J.C., Entropy elasticity of isotropic rubber-like solids at finite strains, Computer Methods in Applied Mechanics and Engineering, 132(1–2): 17–44, 1996, doi: 10.1016/0045-7825(96)01001-8.
• 8. Hughes T.J.R., The Finite Element Method. Linear Static and Dynamic Analysis, Prentice-Hall, New Jersey 1987.
• 9. Jemioło S., Thermoelasticity and Heat Flux in Anisotropic Materials [in Polish: Termosprężystość i przepływ ciepła w materiałach anizotropowych], Publishing House of the Warsaw University of Technology, Warsaw 2015.
• 10. Korelc J., Automation of the finite element method, [in:] Nonlinear Finite Element Methods, P. Wriggers [Ed.], Springer-Verlag, Berlin Heidelberg, 2008, pp. 483–508.
• 11. Korelc J., Automation of primal and sensitivity analysis of transient coupled problems, Computational Mechanics, 44: 631–649, 2009, doi: 10.1007/s00466-009-0395-2.
• 12. Korelc J., Solinc ˇ U., Wriggers P., An improved EAS brick element for finite deformation, Computational Mechanics, 46: 641–659, 2010, doi: 10.1007/s00466-010-0506-0.
• 13. Korelc J., Wriggers P., Automation of Finite Element Methods, Springer, Switzerland 2016.
• 14. LeMonds J., Needleman A., Finite element analyses of shear localization in rate and temperature dependent solids, Mechanics of Materials, 5(4): 339–361, 1986, doi: 10.1016/0167-6636(86)90039-6.
• 15. Miehe C., Entropic thermoelasticity at finite strains. Aspects of the formulation and numerical implementation, Computer Methods in Applied Mechanics and Engineering, 120(3–4): 243–269, 1995, doi: 10.1016/0045-7825(94)00057-T.
• 16. Mucha M., Wcisło B., Pamin J., Simulation of PLC effect using regularized largestrain elasto-plasticity, Materials, 15(12): Article no. 4327, 21 pages, 2022, doi: 10.3390/ ma15124327.
• 17. Nowacki W., Theory of Elasticity [in Polish: Teoria sprężystości], PWN, Warsaw 1970.
• 18. Oppermann P., Denzer R., Menzel A., A thermo-viscoplasticity model for metals over wide temperature ranges-application to case hardening steel, Computational Mechanics, 69(3): 541–563, 2021, doi: 10.1007/s00466-021-02103-4.
• 19. Reddy J.N., Gartling D.K., The Finite Element Method in Heat Transfer and Fluid Dynamics, CRC Press, Boca Raton 2010.
• 20. Ristinmaa M., Wallin M., Ottosen N.S., Thermodynamic format and heat generation of isotropic hardening plasticity, Acta Mechanica, 194: 103–121, 2007, doi: 10.1007/s00707-007-0448-6.
• 21. Simo J.C., Numerical analysis and simulation of plasticity, [in:] Handbook of Numerical Analysis, P. Ciarlet, J. Lions [Eds], vol. VI, Elsevier Science B.V., Boca Raton, pp. 183– 499, 1998.
• 22. Simo J.C., Miehe C., Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation, Computer Methods in Applied Mechanics and Engineering, 98(1): 41–104, 1992, doi: 10.1016/0045-7825(92)90170-O.
• 23. Vujoˇsević L., Lubarda V.A., Finite-strain thermoelasticity based on multiplicative decomposition of deformation gradient, Theoretical and Applied Mechanics, 28–29: 379–399, 2002, doi: 10.2298/TAM0229379V.
• 24. Wcisło B., Pamin J., Local and non-local thermomechanical modeling of elastic-plastic materials undergoing large strains, International Journal for Numerical Methods in Engineering, 109(1): 102–124, 2017, doi: 10.1002/nme.5280.
• 25. Wriggers P., Nonlinear Finite Element Methods, Springer-Verlag, Berlin 2008.
• 26. Wriggers P., Miehe C., Kleiber M., Simo J.C., On the coupled thermomechnical treatment of necking problems via finite element methods, International Journal for Numerical Methods in Engineering, 33(4): 869–883, 1992, doi: 10.1002/nme.1620330413.
• 27. Zienkiewicz O.C., Taylor R.L., Zhu J.Z., The Finite Element Method: Its Basis and Fundamentals, 6th ed., Elsevier Butterworth-Heinemann, 2005.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).