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Mechanical Representation of Damage and Damage Variables

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

Abstract

The procedure of the continuum damage mechanics is to represent first the damage state of a material in terms of properly defined damage variables, and then to describe the mechanical behavior of the damaged material and the further development of the damage by the use of these damage variables. In Section 2.1, methods of the mechanical modeling of material damage are described in the case of uniaxial state of stress. Then Section 2.2 is concerned with extensive discussion of the three-dimensional modeling of material damage and the resulting damage variables, because this is one of the most important problems to secure the reliability of the continuum damage mechanics. The mechanical behavior of a damaged material is usually described by using the notion of the effective stress, together with the hypothesis of mechanical equivalence between the damaged and the undamaged material.

Keywords

Effective Stress Representative Volume Element Damage State Damage Variable Strain Energy Function 
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.

References

  1. Besson J, Cailletaud G, Chaboche J-L, Forest S, Blétry M (2010) Non-linear mechanics of materials. Springer, DordrechtGoogle Scholar
  2. Betten J (1986) Applications of tensor functions to the formulation of constitutive equations involving damage and initial anisotropy. Eng Fract Mech 25:573–584CrossRefGoogle Scholar
  3. Cauvin A, Testa RB (1999) Damage mechanics: basic variables in continuum theories. Int J Solids Struct 36:747–761MathSciNetzbMATHCrossRefGoogle Scholar
  4. Chaboche JL (1982) The concept of effective stress applied to elasticity and to viscoplasticity in the presence of anisotropic damage. In: Boehler JP (ed) Mechanical behavior of anisotropic solids (Proceedings of Euromech Colloquium 115, Grenoble 1979). Martinus Nijhoff, The Hague, pp 737–760Google Scholar
  5. Chaboche JL (1993) Development of continuum damage mechanics for elastic solids sustaining anisotropic and unilateral damage. Int J Damage Mech 2:311–329CrossRefGoogle Scholar
  6. Chaboche JL, Lesne PM, Maire JF (1995) Continuum damage mechanics, anisotropy and damage deactivation for brittle materials like concrete and ceramic composites. Int J Damage Mech 4:5–22CrossRefGoogle Scholar
  7. Chen XF, Chow CL (1995) On damage strain energy release rate. Int J Damage Mech 4:251–263CrossRefGoogle Scholar
  8. Chow CL, Wang J (1987) An anisotropic theory of continuum damage mechanics for ductile fracture. Eng Fract Mech 27:547–558CrossRefGoogle Scholar
  9. Cordebois JP, Sidoroff F (1982a) Damage induced elastic anisotropy. In: Boehler JP (ed) Mechanical behavior of anisotropic solids. Martinuus Nijhoff Publishers, The Hague, pp 761–774CrossRefGoogle Scholar
  10. Goods SH, Brown LM (1979) The nucleation of cavities by plastic deformation. Acta Metall 27:1–15CrossRefGoogle Scholar
  11. Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: part I Yield criteria and flow rules for porous ductile media. J Eng Mater Technol Trans ASME 99:2–15CrossRefGoogle Scholar
  12. Hansen NR, Schreyer HL (1994) A thermodynamically consistent framework for theories of elastoplasticity coupled with damage. Int J Solids Struct 31:359–389zbMATHCrossRefGoogle Scholar
  13. Hayakawa K, Murakami S (1997) Thermodynamical modeling of elastic-plastic damage and experimental validation of damage potential. Int J Damage Mech 6:333–363CrossRefGoogle Scholar
  14. He QC, Curnier A (1995) A more fundamental approach to damaged elastic stress-strain relations. Int J Solids Struct 32:1433–1457MathSciNetzbMATHCrossRefGoogle Scholar
  15. Ju JW (1989) On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects. Int J Solids Struct 25:803–833zbMATHCrossRefGoogle Scholar
  16. Kachanov LM (1974) Foundations of fracture mechanics (in Russian). Izdatielistvo Nauka, MoscowGoogle Scholar
  17. Kachanov M (1980) Continuum model of medium with cracks. J Eng Mech Div Trans ASCE, EM5 106:039–1051Google Scholar
  18. Kachanov LM (1986) Introduction to continuum damage mechanics. Martinus Nijhoff, DordrechtzbMATHGoogle Scholar
  19. Kachanov M (1987) Elastic solids with many cracks: A simple method of analysis. Int J Solids Struct 23:23–43zbMATHCrossRefGoogle Scholar
  20. Kanatani K (1984) Distribution of directional data and fabric tensors. Int J Eng Sci 22:149–164MathSciNetzbMATHCrossRefGoogle Scholar
  21. Krajcinovic D (1996) Damage mechanics. North-Holland, AmsterdamGoogle Scholar
  22. Kreuzer E (ed) (1994) Computerized symbolic manipulation in mechanics, CISM Courses and Lectures No. 343. Springer, WienGoogle Scholar
  23. Lemaitre J (1985) A continuous damage mechanics model for ductile fracture. J Eng Mater Technol Trans ASME 107:83–89CrossRefGoogle Scholar
  24. Lemaitre J (1992) A course on damage mechanics. Springer, Berlin; 2nd Edition (1996)zbMATHGoogle Scholar
  25. Lemaitre J, Chaboche JL (1978) Aspect phénoménologique de la rupture par endommagement. Journal de Mécanique Appliquée 2:317–365Google Scholar
  26. Lemaitre J, Dufailly J (1987) Damage measurements. Eng Fract Mech 28:643–661CrossRefGoogle Scholar
  27. Lin J, Liu Y, Dean TA (2005) A review on damage mechanisms, models and calibration methods under various deformation conditions. Int J Damage Mech 14:299–319CrossRefGoogle Scholar
  28. Lubarda VA, Krajcinovic D (1993) Damage tensors and the crack density distribution. Int J Solids Struct 30:2859–2877zbMATHCrossRefGoogle Scholar
  29. Murakami S (1988) Mechanical modeling of material damage. J Appl Mech Trans ASME 55:280–286CrossRefGoogle Scholar
  30. Murakami S, Ohno N (1981) A continuum theory of creep and creep damage. In: Ponter ARS, Hayhurst DR (eds) Creep in structures, proceedings of 3rd IUTAM symposium, Leicester, 1980. Springer, Berlin, pp 422–444Google Scholar
  31. Murakami S, Tominaga M, Rong H (1990) Formulation of elasticity-damage coupling and applicability of effective stress in damage mechanics. Trans Japan Soc Mech Eng Series A Solid Mech Mater Eng 56:2297–2304 (in Japanese)CrossRefGoogle Scholar
  32. Needleman A, Tvergaard V (1984) An analysis of ductile rupture in notched bars. J Mech Phys Solids 32:461–490CrossRefGoogle Scholar
  33. Onat ET, Leckie FA (1988) Representation of mechanical behavior in the presence of changing internal structure. J Appl Mech Trans ASME 55:1–10CrossRefGoogle Scholar
  34. Ortiz M (1985) A constitutive theory for the inelastic behavior of concrete. Mech Mater 4:67–93CrossRefGoogle Scholar
  35. Rabier PJ (1989) Some remarks on damage theory. Int J Eng Sci 27:29–54MathSciNetzbMATHCrossRefGoogle Scholar
  36. Raghavan P, Ghosh S (2005) A continuum damage mechanics model for unidirectional composites undergoing interfacial debonding. Mech Mater 37:955–979Google Scholar
  37. Rousselier G (1987) Ductile fracture models and their potential in local approach of fracture. Nucl Eng Des 105:97–111CrossRefGoogle Scholar
  38. Saanouni K, Forster C, Ben Hatira F (1994) On the anelastic flow with damage. Int J Damage Mech 3:140–169CrossRefGoogle Scholar
  39. Simo JC, Ju JW (1987) Strain- and stress-based continuum damage models, I. Formulation; II. Computational aspects. Int J Solids Struct 23:821–869zbMATHCrossRefGoogle Scholar
  40. Yang Q, Chen X, Zhou WY (2005) On the structure of anisotropic damage yield criteria. Mech Mater 37:1049–1058CrossRefGoogle Scholar
  41. Zheng Q-S, Betten J (1996) On damage effective stress and equivalence hypothesis. Int J Damage Mech 5:219–240CrossRefGoogle Scholar
  42. Cordebois JP, Sidoroff F (1982b) Endommagement anisotrope en élasticité et plasticité. Journal de Mécanique Théorique et Appliquée Numéro Spécial, 45–60Google Scholar
  43. Kachanov LM (1958) On rupture time under condition of creep, Izvestia Akademi Nauk SSSR, Otd. Tekhn. Nauk, No.8, 1958, 26–31 (in Russian)Google Scholar
  44. Vakulenko AA, Kachanov M (1971) Continuum theory of cracked media, Izvestia AN SSSR, Mekhanica Tverdogo Tiela, No. 4, pp 159–166 (in Russian)Google Scholar
  45. Rabotnov Yu N (1968) Creep rupture. In: Hetenyi M, Vincenti M (eds) Proceedings of applied mechanics conference. Stanford University. Springer, Berlin, pp 342–349Google Scholar
  46. Rabotnov Yu N (1969) Creep problems in structural members. North-Holland, AmsterdamGoogle Scholar
  47. Lacy TE, McDowell DL, Willice PA, Talreja R (1997) On representation of damage evolution in continuum damage mechanics. Int J Damage Mech 6:62–95Google Scholar
  48. Chow CL, Lu TJ (1989a) A normative presentation of stress and strain for continuum damage mechanics. Theor Appl Fract Mech 12:161–187MathSciNetCrossRefGoogle Scholar
  49. 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

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