Anisotropic damage mechanics based on strain energy equivalence and equivalent elliptical microcracks

Usik Lee, George A. Lesieutre, Lei Fang

Research output: Contribution to journalArticlepeer-review

32 Citations (SciVal)


A theory of damage mechanics is introduced based on a principle of strain energy equivalence. This principle is used to develop the effective continuum elastic properties of a damaged solid in terms of the undamaged elastic properties and a scalar damage field. The damage variable is defined as the volume fraction of a damage zone associated with equivalent elliptical microcracks. This definition provides a means by which a damaged isotropic material can exhibit anisotropic (orthotropic) properties, and entails determining effective crack orientation and geometry factors from the local deformation. Strain energy dissipation associated with crack growth (not nucleation) is used to develop a consistent damage evolution equation. This evolution equation is related to the standard power law model of crack growth commonly used in fracture mechanics, and to the equivalent stress measure commonly used in mechanics of plastic deformation. The combination of representing local damage as an effective elliptical crack volume fraction, a consistent damage evolution equation, and the determination of effective elastic properties using a strain energy equivalence principle yields a simple, yet powerful, approach to predicting failure of mechanical components.

Original languageEnglish (US)
Pages (from-to)4377-4397
Number of pages21
JournalInternational Journal of Solids and Structures
Issue number33-34
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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