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Some thermodynamical considerations on inelastic deformations including damage processes

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A phenomenological theory of inelastic deformations including damage processes may be based on the fundamental assumption that the body can be considered as a classical continuum and that the principle of uniquely determined local thermodynamical state holds. Within this frame particular balance equations for energy and entropy can be stated describing the interaction between external energy supply and changes of the internal material structure. These balance equations are applied to elastic-plastic deformations including damage processes. The parameters describing the damage state can be considered either as thermodynamical state variables or merely as thermo-mechanical process variables. This distinction leads to different formulations.

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References

  1. Ashby, M. F.: Mechanisms of deformation and fracture. In: Advances in Applied Mechanics23, pp. 117–177 (Hutchinson, J. W., Wu, Th. Y., Eds.) New York: Acad. Press 1983.

    Google Scholar 

  2. Muschik, W.: Thermodynamical constitutive laws-outlines. In [3] pp. 3–25.

    Google Scholar 

  3. Axelrad, D. R., Muschik, W., (Eds.): Constitutive laws and microstructure. Berlin: Springer-Verlag 1988.

    Google Scholar 

  4. Lehmann, Th.: Thermodynamical considerations on plastic and viscoplastic behaviour of solid bodies. In [3] pp. 27–42.

    Google Scholar 

  5. Lehmann, Th.: Internal variables in thermoplasticity. Lecture Notes of the Course “Internal Variables in Thermodynamics and Continuum Mechanics” at CISM Udine (coord. by J. Kestin) 1988.

  6. Lehmann, Th.: On the balance of energy and entropy at inelastic deformations of solid bodies. To be published in Europ. J. Mech. 1 (1989)

  7. Thermann, K.: Foundations of large deformations. In [9] pp. 323–351.

    Google Scholar 

  8. Lehmann, Th.: General frame for the definition of constitutive laws for large nonisothermic elastic-plastic and elastic-viscoplastic deformations. pp. 379–463.

    Google Scholar 

  9. Lehmann, Th., Ed.): The constitutive law in thermoplasticity. Wien-New York: Springer-Verlag 1984.

    Google Scholar 

  10. Lehmann, Th.: Some remarks on the decomposition of deformations and mechanical work. Int. J. Eng. Sci.20, 281–288 (1982).

    Google Scholar 

  11. Bruhns, O. T., Diehl, H.: An internal variable theory of inelastic behaviour at high rates of strain. (to be buplished in Arch. Mech.)

  12. Lehmann, Th.: On a generalized constitutive law for finite deformations in thermoplasticity and thermo-viscoplasticity. In: Constitutive Laws for Engineering Materials pp. 173–184 (Desai, C. S., Krempl, E., Kiousis, P. D., eds.) New York-Amsterdam-London: Elsevier 1987.

    Google Scholar 

  13. Boehler, J. P., (Ed.): Mechanical behaviour of anisotropic solids. Ed. CNRS. The Hague-Boston-London: Martinus Nijhoff Publ. 1982.

    Google Scholar 

  14. Baltov, A., Sawczuk, A.: A rule of anisotropic hardening. Acta Mechanica1, 81–92 (1965).

    Google Scholar 

  15. Lehmann, Th.: Einige Bemerkungen zu einer allgemeinen Klasse von Stoffgesetzen für große plastische Formänderungen. Ing. Arch.41, 297–310 (1972).

    Google Scholar 

  16. Lehmann, Th.: Some considerations concerning information induced anisotropy. (to be published in Proc. IUTAM-Symp. on Yielding, Damage and Failure of Anisotropic Solids, Boehler, J. P., Ed., Grenoble 1987).

  17. Rabotnov, Y. N.: Creep problems in structural members. In: Appl. Math. and Mech.7 (Lauwerier, H. A., Koiter, W. T., eds.). Amsterdam: North-Holland 1969.

    Google Scholar 

  18. Kachanov, L. M.: Introduction to continuum damage mechanics. Dordrecht: Martinus Nijhoff 1986.

    Google Scholar 

  19. Lemaitre, J.: Coupled elasto-plasticity and damage constitutive equations. Comp. Math. Appl. Mech. Eng.51, 31–49 (1985).

    Google Scholar 

  20. Gurson, A. L.: Plastic flow and fracture behavior of ductile materials incorporating void nucleation, growth, and interaction. Ph. D. Thesis, Brown University, Providence, R.I. (1975).

    Google Scholar 

  21. Gurson, A. L.: Porous, rigid-plastic materials containing rigid inclusions-yield function, plastic potential, and void nucleation. Proceedings Int. Conf. Fracture,2A, pp. 357–364 (Taplin, D. M. R., ed.). Oxford-New York: Pergamon Press 1977.

    Google Scholar 

  22. Needleman, A., Tvergaard, V.: An analysis of ductile rupture modes at a crack tip. J. Mech. Phys. Sol.35, 151–183 (1987).

    Google Scholar 

  23. Tvergaard, V.: Effect of yield surface curvature and void nucleation on plastic flow localization. Journ. Mech. Phys. Solids35, 43–60 (1987).

    Google Scholar 

  24. Mear, M. E., Hutchinson, J. W.: Influence of yield curvature on flow localization in dilatant plasticity. Mechanics of Materials4, 395–407 (1985).

    Google Scholar 

  25. Chaboche, J. L.: Continuum damage mechanics: present state and future trends. ONERA, T.P. No. 1986-53.

  26. Perzyna, P., Nowak, Z.: Evolution equation for the void fraction parameter in necking region. Arch. Mech.39, 73–84 (1987).

    Google Scholar 

  27. Murakami, S.: Notion of continuum damage theory and its application to anisotropic creep damage theory. ASME J. Eng. Mat. Techn.105, 99–105 (1983).

    Google Scholar 

  28. Lehmann, Th.: On large elastic-plastic deformations. In: Foundations of Plasticity, pp. 571–585 (Sawczuk, A., ed.) Leyden: Noordhoff Int. Publ. 1973.

    Google Scholar 

  29. Kestin, J., Herrmann, G.: The fundamental elements of an exact thermodynamic theory of damage in elastic solids (to be published).

  30. Murakami, S.: Anisotropic damage theory and its application to creep crack growth analysis. In: Constitutive Laws for Engineering Materials, pp. 187–194 (Desai, C. S., Krempl, E., Kiousis, P. D., eds.) New York-Amsterdam-London: Elsevier 1987.

    Google Scholar 

  31. Murakami, S., Imaizumi, T.: Mechanical description of creep damage state and its experimental verification. J. Mech. Theor. Appl.1, 743–761 (1982).

    Google Scholar 

  32. Tvergaard, V., Needleman, A.: Effect of material rate sensitivity of failure modes in the Charpy V-notch test. J. Mech. Phys. Solids34, 213–241 (1986).

    Google Scholar 

  33. Pam, J., Saje, M., Needleman, A.: Localization of deformation in rate sensitive porous plastic solids. Int. J. Fracture21, 261–278 (1983).

    Google Scholar 

  34. Perzyna, P.: Influence of thermomechanical coupling on dynamic fracture of ductile solids. In: [36] pp. 105–119.

    Google Scholar 

  35. Perzyna, P.: Influence of anisotropic effects on micro-damage process in dissipative solids. (to be published in Arch. Mech.)

  36. Bui, H. D., Nguyen, Q. S., (Eds.): Thermomechanical coupling in solids. Amsterdam-New York-Oxford-Tokyo: North-Holland 1987.

    Google Scholar 

  37. Lehmann, Th., Blix, U.: On the coupled thermo-mechanical process in the necking problem. Int. J. Plasticity1, 175–188 (1985).

    Google Scholar 

  38. Zdebel, U., Lehmann, Th.: Some theoretical considerations and experimental investigations on a constitutive law in thermoplasticity. Int. J. Plasticity3, 369–389 (1987).

    Google Scholar 

  39. Lehmann, Th.: Thermo-mechanical coupling in large deformations particularly in bifurcation problems. In [36] pp. 277–290.

    Google Scholar 

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Slightly extended version of a lecture delivered at the “Symposium on Inelastic Solids and Structures” (Rytro/Poland Sept. 1988) dedicated to the memory of Antoni Sawczuk.

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Lehmann, T. Some thermodynamical considerations on inelastic deformations including damage processes. Acta Mechanica 79, 1–24 (1989). https://doi.org/10.1007/BF01181477

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