Abstract
The thermodynamics of irreversible processes, using the notion of local state and internal state variables, is used for developing consistent constitutive and damage equations. The Generalized Standard Models are recalled and some of the induced limitations are discussed, both for non linear kinematic hardening in viscoplasticity and for elasto-plastic damage couplings. In order to release some of these constraints, a pseudo-standard approach is formulated and discussed, that allows us to recover most of the classically used constitutive equations and damage models.
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References
Benallal, A. (1989). Thermoviscoplasticité et endommagement des structures. Doctorat d’Etat, Université Pierre et Marie Curie, Paris 6.
Carathéodory, C. (1909). Untersuchungen über die Grundlagen der Thermodynamik. Mathematische Annalen, 67:355–386.
Chaboche, J. L. (1977). Sur l’utilisation des variables d’état interne pour la description de la viscoplasticité cyclique avec endommagement. In Problèmes Non Linéaires de Mécanique, pages 137–159. Symposium Franco-Polonais de Rhéologie et Mécanique, Cracovie.
Chaboche, J. L. (1983). On the constitutive equations of materials under monotonic or cyclic loadings. La Recherche Aérospatiale, (5):31–43.
Chaboche, J. L. (1989). Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int. J. of Plasticity, 5:247–302.
Chaboche, J. L. (1996). Unified cyclic viscoplastic constitutive equations: development, capabilities and thermodynamic framework. In Krauss, A. S. and Krauss, K., editors, Unified Constitutive Laws of Plastic Deformation, pages 1–68. Academic Press Inc.
Chaboche, J. L. (1997). Thermodynamic formulation of constitutive equations and application to the viscoplasticity and viscoelasticity of metals and polymers. Int. J. Solids Structures, 34(18):2239–2254.
Chaboche, J. L. (1999). Thermodynamically founded CDM models for creep and other conditions. In Skrzypek, J. and Altenbach, H., editors, Modeling of Material Damage and Failure of Structures, page in press. Springer.
Chow, C. L. and Wei, Y. (1991). A model of Continuum Damage Mechanics for fatigue failure. Int. J. Fracture, 50:301–316.
Coleman, B. D. and Gurtin, M. E. (1967). Thermodynamics with internal state variables. J. Chem. Phys., 47:597–613.
Germain, P. (1973). Cours de Mécanique des Milieux Continus, volume I. Masson, Paris.
Germain, P. (1974). Thermodynamique des milieux continus. Entropie, 55:7–14. Congrès Français de Mécanique.
Germain, P., Nguyen, Q. S., and Suquet, P. (1983). Continuum thermodynamics. J. of Applied Mechanics, 50:1010–1020.
Halphen, B. and Nguyen, Q. S. (1975). Sur les matériaux standards generalises. J. de Mécanique, 14(l):39–63.
Hansen, N. R. and Schreyer, H. L. (1992). Thermodynamically consistent theories for elastoplasticity coupled with damage. In Damage Mechanics and Localization, volume 142/AMD, pages 53–67. ASME.
Hayhurst, D. R. (1972). Creep rupture under multiaxial state of stress. J. Mech. Phys. Solids, 20(6):381–390.
Ladevèze, P. (1992). On the role of creep continuum damage in structural mechanics. In Ladevèze, P. and Zienkiewiecz, O., editors, New Advances in Computational Structural Mechanics, pages 3–22, Oxford. Elsevier.
Lemaître, J. (1985). A Continuum Damage Mechanics model for ductile fracture. J. of Engng. Mat. Technol., 107:83–89.
Lemaître, J. (1992). A course on Damage Mechanics. Springer.
Lemaître, J. and Chaboche, J. L. (1985). Mécanique des Matériaux Solides. Dunod, Paris.
Mandel, J. (1964). Contribution théorique à l’étude de l’écrouissage et des lois de l’écoulement plastique. Munich. 11th Congress ICTAM.
Murakami, S. and Ohno, N. (1980). A continuum theory of creep and creep damage. In Ponter, A. and Hayhurst, D. R., editors, Creep in Structures, pages 422–443. 3rd IUTAM Symp., Springer-Verlag. Leicester.
Rabotnov, Y. N. (1969). Creep problems in structural members. North-Holland.
Sidoroff, F. (1975). On the formulation of plasticity and viscoplasticity with internal variables. Arch. Mech., Poland, 27(5–7):807–819.
Truesdell, C. and Noll, W. (1965). The non-linear field theories of mechanics. In Flügge, S., editor, Encyclopedia of Physics, volume 3/3, Sec.79, New York. Springer.
Voyiadjis, G. Z. and Kattan, P. I. (1999). Advances in Damage Mechanics: Metals and Metal Matrix Composites. Elsevier.
Zhu, Y. Y. and Cescotto, S. (1995). Fully coupled elastovisco-plastic damage theory for anisotropic materials. Int. J. Solids Structures, 32(11):1607–1641.
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Chaboche, J.L. (2000). The application of the irreversible thermodynamics to the development of constitutive equations. In: Maugin, G.A., Drouot, R., Sidoroff, F. (eds) Continuum Thermomechanics. Solid Mechanics and Its Applications, vol 76. Springer, Dordrecht. https://doi.org/10.1007/0-306-46946-4_6
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DOI: https://doi.org/10.1007/0-306-46946-4_6
Publisher Name: Springer, Dordrecht
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