Elastic-Brittle Damage

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


Besides ductile materials considered hitherto, a variety of brittle materials, like concrete, rocks and ceramics, are widely employed in engineering practice. Their mechanical behavior can not be described by the elastic-plastic damage theory or by the viscoplastic damage theory discussed already. The present chapter is concerned with the damage and the deformation behavior of elastic-brittle materials, and the related continuum damage mechanics theory to describe them. In Section 9.1, to begin with, the microscopic mechanisms of damage and the ensuing mechanical behavior of microcracks in concrete will be discussed. Application of the simplest theory of isotropic damage to the damage process of concrete with unilateral crack effect is descried in Section 9.2.


Uniaxial Compression Uniaxial Tension Brittle Material Damage Development Damage Variable 
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  1. Chaboche JL (1992) Damage induced anisotropy: on the difficulties associated with the active/passive unilateral condition. Int J Damage Mech 1:148–171CrossRefGoogle Scholar
  2. Green ML (1992) Laboratory tests on Salem limestone. Geomechanics Division, Structures Laboratory, Department of the Armey, Vicksburg, MississippiGoogle Scholar
  3. Halm D, Dragon A (1998) An anisotropic model of damage and frictional sliding for brittle materials. Eur J Mech A/Solids 17:439–460MathSciNetzbMATHCrossRefGoogle Scholar
  4. Ju JW (1989) On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects. Int J Solids Struct 25:803–833zbMATHCrossRefGoogle Scholar
  5. Krajcinovic D (1989) Damage mechanics. Mech Mater 8:117–197CrossRefGoogle Scholar
  6. Krajcinovic D (1996) Damage mechanics. North-Holland, AmsterdamGoogle Scholar
  7. Lubarda VA, Krajcinovic D, Mastilovic S (1994) Damage model for brittle elastic solids with unequal tensile and compressive strengths. Eng Fract Mech 49:681–697CrossRefGoogle Scholar
  8. Mazars J (1986) A description of micro- and macro-scale damage of concrete structures. Eng Fract Mech 25:729–737CrossRefGoogle Scholar
  9. Mazars J, Pijaudier-Cabot G (1989) Continuum damage theory – APPLICATION to concrete. J Eng Mech 115:345–365CrossRefGoogle Scholar
  10. Mehta PK (1986) Concrete: structure, properties, and materials. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  11. Murakami S, Kamiya K (1997) Constitutive and damage evolution equations of elastic-brittle materials based on irreversible thermodynamics. Int J Mech Sci 39:473–486zbMATHCrossRefGoogle Scholar
  12. Ortiz M (1985) A constitutive theory for the inelastic behavior of concrete. Mech Mater 4:67–93CrossRefGoogle Scholar
  13. Smith GM, Young LE (1955) Ultimate theory in flexure by exponential function. J Proc ACI 52:349–359Google Scholar
  14. Yazdani S, Schreyer HL (1988) An anisotropic damage model with dilatation for concrete. Mech Mater 7:231–244CrossRefGoogle Scholar
  15. Horii H, Nemat-Nasser S (1985) Compression-induced microcrack growth in brittle solids: axial splitting and shear failure. J Geophys Res B4 90:3105–3125CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Nagoya UniversityNagoyaJapan

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