Inelastic Constitutive Equation and Damage Evolution Equation of Material with Isotropic Damage

  • Sumio MurakamiEmail author
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 185)


The thermodynamic constitutive theory described in the preceding chapter is applied to inelastic materials with isotropic damage. In Section 4.1, one-dimensional elastic-plastic and elastic-viscoplastic constitutive equations of damaged materials will be described as the basis for the succeeding sections. The application of the constitutive theory of Chapter 3 to the three-dimensional case will be discussed in Section 4.2. The strain energy release rate due to damage development and the stress criterion for elastic-plastic damage growth will be considered in Section 4.3, while Section 4.4 is concerned with the inelastic damage theories based on the hypothesis of mechanical equivalence.


Damage Development Elastic Strain Energy Damage Variable Kinematic Hardening Strain Energy Release Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Besson J, Cailletaud G, Chaboche J-L, Forest S, Blétry M (2010) Non-linear mechanics of materials. Springer, DordrechtGoogle Scholar
  2. Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46:81–98CrossRefGoogle Scholar
  3. Bao Y, Wierzbicki T (2005) On the cut-off value of negative triaxiality for fracture. Eng Fract Mech 72:1049–1069CrossRefGoogle Scholar
  4. Chaboche JL (1988) Continuum damage mechanics, part I general concepts; part II damage growth, crack initiation, and crack growth. J Appl Mech Trans ASME 55:59–72CrossRefGoogle Scholar
  5. Desmorat R, Cantournet S (2008) Modeling microdefects closure effect with isotropic/anisotropic damage. Int J Damage Mech 17:65–96CrossRefGoogle Scholar
  6. Ju JW (1989) On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects. Int J Solids Struct 25:803–833zbMATHCrossRefGoogle Scholar
  7. Lemaitre J (1985) A continuous damage mechanics model for ductile fracture. J Eng Mater Technol Trans ASME 107:83–89CrossRefGoogle Scholar
  8. Lemaitre J (1987) Formulation and identification of damage kinetic constitutive equations. In: Krajcinovic D, Lemaitre J (eds) Continuum damage mechanic: theory and applications, CISM Courses and Lectures No. 295. Springer, Wien, pp 37–89Google Scholar
  9. Lemaitre J (1990) Micro-mechanics of crack initiation. Int J Frac 42:87–99CrossRefGoogle Scholar
  10. Lemaitre J (1992) A course on damage mechanics. Springer, Berlin; 2nd Edition (1996)zbMATHGoogle Scholar
  11. Lemaitre J, Chaboche JL (1985) Mécanique des Matériaux Solides, Dunod, Paris; Mechanics of solid materials, Cambridge University Press, Cambridge (1990)Google Scholar
  12. Lemaitre J, Desmorat R (2005) Engineering damage mechanics. Springer, BelrinGoogle Scholar
  13. Malvern LE (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  14. Perzyna P (1966) Fundamental problems in viscoplasticity. In: Yih CS (ed) Advances in applied mechanics, vol 9. Academic, New York, pp 243–377Google Scholar
  15. Saanouni K, Forster C, Ben Hatira F (1994) On the anelastic flow with damage. Int J Damage Mech 3:140–169CrossRefGoogle Scholar
  16. Ladevèze P, Lemaitre J (1984) Damage effective stress in quasi-unilateral conditions. In: Proceeding of the 16th IUTAM congress, Lyngby, DenmarkGoogle Scholar
  17. Chaboche JL (1997) Thermodynamic formulation of constitutive equations and application to the viscoplasticity and viscoelasticity of metals and polymers. Int J Solids Struct 34:2239–2254Google Scholar
  18. Lemaitare J, Desmorat R, Sauzay M (2000) Anisotropic damage law of evolution. Eur J Mech A/Solids 19:187–208CrossRefGoogle Scholar
  19. Lemaitre J, Chaboche JL (1985) Mécanique des Matériaux Soides. Dunod, Paris; Mechanics of solid materials. Cambridge University Press, Cambridge (1990)Google Scholar
  20. Chaboche JL (1977) Sur l’utilisation des variables d’etat interne pour la description du comportement viscoplastique et de la rupture par endommagement. In: Nowacki WK (ed) Problèmes Non-Linéaires de Mécanique (Proceedings of French-Polish symposium, Cracow 1977). PWN (State Publishing House of Science), Warsaw, pp 137–159Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Nagoya UniversityNagoyaJapan

Personalised recommendations